| 1D & 2D dot arrays (3+ dots) |
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Measurements of a six dot HRL SLEDGE device from the Qubits for Computing Foundry
Adam Mills1, Jonathan Marbey1, Matthew Reed2, Christopher Richardson1, Charles Tahan3, Samuel Carter4 1Laboratory for Physical Sciences, College Park, MD 20740, 2HRL Laboratories, LLC, Malibu, CA 90265, 3University of Maryland, College Park, MD 20742, 4Laboratory for Physical Sciences Abstract: Spin qubits in electrically-controlled Si/SiGe quantum dots have made impressive progress over the past few years in terms of fidelity, number of qubits, and coherence times. One of the advantages of this system is the small size of qubits, making scaling up to very large numbers of qubits more promising. A challenge associated with the small size of quantum dots is the difficulty of consistent fabrication of state-of-the art devices, which have feature sizes of tens of nanometers. To alleviate this barrier to research, the Qubits for Computing Foundry offers semiconductor quantum dot devices as well as superconducting quantum devices to research projects that receive U.S. government funding. We have received six-dot Si/SiGe devices from HRL as part of the Foundry program and performed measurements on exchange-only qubits formed from three dots. The devices are based on the single-layer etch-defined gate electrode (SLEDGE) platform with two quantum dot sensors for measuring charge occupation of dots. We have demonstrated single-qubit control and single-shot readout of an exchange-only qubit. As an example of our capabilities, the figure below represents oscillations in the singlet population of two dots due to a pulse that lowers the tunnel barrier to a third dot. Full qubit control is achieved with the addition of exchange pulses between the first two dots, and fast singlet-triplet readout (down to 1 μs) is achieved through Pauli spin blockade. As next steps we plan to characterize these devices for error rates and leakage, develop new single qubit gate designs, and explore novel SPAM approaches. Access to these state-of-the art devices will advance research in this essential platform for quantum information processing. |
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Tunnel coupling control of FDSOI quantum dots in the few-electron regime
Bruna Cardoso Paz1, Jayshankar Nath1, Jean-Baptiste Filippini2, Jerzy Javier Suarez Berru2, Biel Martinez3, Heimanu Niebojewski3, Benoit Bertrand3, Gregoire Roussely3, Valentin Labracherie3, Maud Vinet1, Matias Urdampilleta2, Tristan Meunier1 1Quobly, 2CNRS, 3CEA Abstract: Scalability is one of the significant advantages of silicon spin qubits over other platforms, making them very promising candidates in the quest for fault-tolerant quantum computing. One of the main challenges from the process integration perspective is the definition of well-defined quantum dots, and the fine control of the position and displacement of the charges within the dots. To achieve this, the chemical potentials and tunnel barriers need to be separately tuned. In this work we approach the regime of interest for large-scale qubit integration, showing that we can deliver high electrostatic coupling control and individual tunability over an array of quantum dots (QDs). To do this we use FDSOI devices fabricated with two metal-gate levels in an industry-compatible CMOS process, operating at 100mK. Transport measurements are performed across a charge detector (SET) that is capacitively coupled to the dots. The device operates in the isolated regime, where the double quantum dot is uncoupled from the reservoirs after 2 electrons are loaded in the system. While the first metal-gate level is used to define the chemical potential of the dots, the second metal-gate level can modulate the tunnel coupling between the QDs over many orders of magnitude within a range of few tenths of mV. The demonstration of high electrostatic control over the coupling between adjacent quantum dots is an important step towards the successful manipulation of spin for quantum computing. Finally, these results support the implementation of different qubit designs using two metal-gate levels. |
| Control and gates (1 to 2 qubits) |
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RF-Reflectometry Measurements of Charge Transitions in a Quantum Dot Array Fabricated on FDX-22 Process
Xutong Wu1, Panagiotis Giounanlis1, Conor Power2, Andrii Sokolov1, Ioanna Kriekouki1, Mike Asker3, Dirk Leipold3, Imran Bashir3, Elena Blokhina2 1Equal1 Labs Ireland, 2University College Dublin, 3Equal1 Labs USA Abstract: In this work, we present experimental results on a commercial FDX-22 nanostructure [1] quantum dot array at 4 Kevin. Our study demonstrates charge-stability diagrams of a double-dot system with asymmetric detuning and asymmetric coupling to the leads. In this case, the fermions are confined in between the gates, utilizing a common-mode voltage as an alternative to back gate control. As opposed to conventional semiconductor quantum dot arrays, our structure does not have any direct plunger electrodes between the gates. We achieve full electrical controlled confinement in between gate electrodes, using a common-mode voltage, acting as a global plunger, applied to reservoir terminals along with gate voltages. Effective plunger action is achieved by adjusting reservoir voltages and gate voltages based on the operating region. The measurement employs RF-reflectometry on one of the reservoirs, which detects capacitive changes on the structure. Unlike direct current measurement, full conductivity of the device isn't necessary. Moreover, the tank circuitry is integrated onto the PCB board, and we've utilized a varactor to fine-tune the matching capacitance and RF-carrier frequency. This enhances the signal-noise ratio of the measurement. In summary, our experimental findings demonstrate the formation of double quantum dots within the commercial FDX-22 nanostructure without the need for plunger gate control. Furthermore, utilizing reflectometry measurement, we achieved single-electron-level detection even at high temperatures, opening up exciting avenues for the development of charge sensor devices. References: 1. FDXTM FD-SOI. https://gf.com/technology-platforms/fdx-fd-soi/ https://gf.com/technology-platforms/fdx-fd-soi/ (2024). |
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Exchange interactions in Germanium hole spin qubits
Mauricio Rodríguez García1, Ahmad Kalo2, Esteban Rodriguez-Mena3, Yann-Michel Niquet2 1CEA/IRIG/MEM/L SIM, 2CEA/IRIG/MEM/L_SIM, 3CEA Grenoble Abstract: We introduce a computational method, derived from configuration interaction, which enables efficient calculations of the spectrum of two-particle problems in very realistic geometries. We apply this method: to a double hole spin qubit in a Germanium heterostructure (see figure). We analyze the nature and physics of the exchange interaction J between such two qubits. We show that the simplest approximation J ~ 4t^2/U is far from accurate near the symmetric operation point (with t the inter-dot tunneling and U the charging energy). We highlight, in particular, the role played by the Coulomb correlations and by the higher-lying singlet and triplet states in the net exchange interaction. We also discuss the mixing of the singlet S and triplet T states by spin-orbit coupling, including the difference of g-factors between the dots and the Rashba interactions while tunneling. The S-T0 mixing is particularly relevant for two-qubit gates and the S-T- mixing for singlet-triplet qubits and for readout. We show that the S-T- mixing is dominated by linear Rashba interactions arising from the inhomogeneous strains that build up upon cool down due to the thermal contraction of metals. This mechanism is much stronger than the usual linear or cubic Rashba interactions at the small vertical electric fields encountered in Germanium heterostructures. The calculated S-T- splittings are consistent with the available experimental data. The S-T0 mixing is, on the other hand, mainly driven by g-factor differences resulting from the structural asymetries between the dots. Both are strongly dependent on the bias point and magnetic field strength and orientation. We finally draw the conclusions for the operation of two-qubit gates and singlet-triplet qubits based on holes. |
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Using the Wiggle Well to generate fast EDSR in Si/SiGe: valley, spin-orbit coupling, and alloy disorder induced effects
Hudaiba Soomro, Mark Eriksson, Benjamin Woods, Mark Friesen University of Wisconsin-Madison Abstract: Silicon-based single-electron spin qubits commonly use micromagnets to create an artificial spin-orbit coupling (SOC) for Electric Dipole Spin Resonance (EDSR); however, this approach faces scalability challenges. Previously, it has been shown that the Wiggle Well may sufficiently enhance the otherwise weak SOC in the conduction band of Si, allowing for implementation of a strong EDSR protocol (see Fig a); preliminary calculations indicate that Rabi frequencies exceeding 500MHz/T may be possible [1]. However, alloy disorder has not been fully accounted for in these calculations. In this work, we show that alloy disorder gives rise to two main effects relevant for EDSR: the generation of a strong valley dipole (providing an additional EDSR mechanism, see Fig b), and a randomized valley phase (providing a position-dependent Rabi frequency). We find that the Rabi frequency depends on the phase difference between the valley coupling and SOC matrix elements. We also show that the alloy-disorder-induced valley dipole effects are more pronounced in the low-valley-splitting regime. These findings deepen our understanding of the Wiggle Well architecture and offer insights into optimizing spin-qubit performance in Si-based quantum devices. References: [1] Woods, B. D., Eriksson, M. A., Joynt, R., & Friesen, M. (2023). Spin-orbit enhancement in Si/SiGe heterostructures with oscillating Ge concentration. Physical Review B, 107(3), 035418. https://doi.org/10.1103/PhysRevB.107.035418 |
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Impact of biased cooling on the operation of undoped Si/SiGe field-effect devices
Laura Diebel1, Lukas Zinkl1, Andreas Hötzinger1, Marco Lisker2, Yuji Yamamoto2, Felix Reichmann2, Dominique Bougeard1 1Institut für Experimentelle und Angewandte Physik, Fakultät für Physik, Universität Regensburg, 2IHP - Leibniz-Institut für Innovative Mikroelektronik Abstract: Most silicon-based quantum circuits capitalize on gate-tunable charge carrier control and the use of the electric field-effect via capacitive coupling. As a consequence, gate dielectrics interfaced with the silicon-based semiconductor play a key role in such devices. The interface between the typically polycrystalline dielectric and the single crystalline semiconductor is receiving more and more attention, since charge traps at this interface may significantly influence the operation of quantum circuits, such as their gate-tunability or charge noise. In this contribution, we systematically study the impact of a non-zero bias applied at room temperature and during cooldown of field-effect stack devices (FED) made from undoped Si/SiGe quantum well (QW) heterostructures. We demonstrate that this procedure - termed biased cooling - allows to intentionally modify the charge state of the interface at cryogenic FED operation temperatures. We studied the influence of biased cooling (BC) on the charge state of the interface as well as the influence of this modified electrostatics on the transport properties of the two-dimensional electron gas (2DEG) in the Si/SiGe QW. We show results from FED in Hall bar geometry from three field-effect stacks which differ in their layout, prominently regarding the presence of a Si cap on top of the semiconductor heterostructure. We particularly discuss the impact of BC on the electron density and the electron mobility under gate-tuning of the 2DEG, as well as on the time stability, saturation behavior and reproducibility of the 2DEG density. We present an empirical model based on charge traps at the dielectric/semiconductor interface, which include all experimental trends observed in our systematic study. Our results show that biased cooling provides a useful tuning parameter for field-effect devices. Furthermore, they contribute to a better understanding of correlations between cryogenic FED operation and the properties of the dielectric/semiconductor interface. |
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Characterization of p-type CMOS Quantum Dot Array Devices with J-gates
Xunyao Luo1, Tsung-Yeh Yang2, Frederico Martins2, Heimanu Niebojewski3, Charles Smith4 1University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom, 2Hitachi Cambridge Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom, 3CEA-Leti, Univ. Grenoble Alpes, F-38000 Grenoble, France, 4Hitachi Cambridge Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom Abstract: Our research introduces progress in the field of silicon quantum computing with the use of p-type silicon quantum dot array devices that incorporate J-gates. Fabricated by CEA-Leti, the devices we are characterizing have gate pitches ranging from 80nm to 100nm and consist of 4-gate and 2-gate configurations with split-gate designs featuring two parallel quantum dot arrays with face-to-face dots, and wrap-around gate designs for single quantum dot array. By utilizing CMOS industry-compatible technology, these fabrication techniques significantly enhance the feasibility of mass production, potentially setting a new standard for scalable quantum device manufacturing. We are using in-situ dispersive readout techniques directly on one of the plunger gates of double quantum dots (DQDs) with the use of a surface-mount resonator. This technique is made possible by the large lever arm provided by the device architecture. We have characterized the devices at cryogenic temperatures (70mK) and demonstrated the formation of DQDs underneath two neighboring plunger gates. Moreover, we have demonstrated the effectiveness of J-gates in controlling the interdot coupling of DQDs. Furthermore, we have identified the Pauli spin blockade (PSB) at the zero detuning and performed T1-time measurements. We are now progressing towards demonstrating single-spin operations with electric dipole spin resonance, enabled by the strong spin-orbit coupling of hole spins. 1. An example 4×2 split-gate device, the readout circuit is connected to the T2-gate and the microwave lines are connected to both T1-gate and T3-gate so that two sets of DQDs can be formed. 2. Interdot charge transition phase measurement as a function of detuning and magnetic field. The phase signal disappears, and the PSB is observed at 2.5T. 3. At 2.5T, a continuous pulse train populates the singlet state and makes the phase signal reappear. 4. T1-time measurement at zero detuning, achieved by varying the duty cycle of the pulse train. |
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Fast, Pulse-Based State Preparation on Silicon Quantum Processors
Christopher Long1, Nicholas Mayhall2, Sophia Economou3, Edwin Barnes3, Crispin Barnes4, Frederico Martins5, David Arvidsson-Shukur5, Normann Mertig5 1University of Cambridge, 2Department of Chemistry, Virginia Tech, Blacksburg, VA 24061, USA, 3Department of Physics, Virginia Tech, Blacksburg, VA 24061, USA, 4Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, CB3 0HE, United Kingdom, 5Hitachi Cambridge Laboratory, J. J. Thomson Ave., Cambridge, CB3 0HE, United Kingdom Abstract: State preparation fidelities on noisy intermediate-scale quantum (NISQ) processors suffer greatly from errors in individual quantum gates, which accumulate over time [1,2]. One potential way to alleviate the issue is fast, pulse-based state preparation. In this talk, I will numerically estimate the minimal evolution times (METs) required for pulse-based state preparation on silicon quantum processors—see Figure (a) for a diagram of the emulated SiMOS device. In particular, I will show that optimized pulses on silicon hardware can prepare the ground states of H2 (see Figure (b) for the optimal pulse shapes), HeH+, and LiH with high accuracy in as little as 2.4ns, 4.4ns, and 27.2ns, respectively—see Figures (c) and (d) for H2. Figure (c) Shows disassociation energies for H2. We optimize the hardware pulses for each fixed evolution time T and bond distance to achieve the best approximation to the ground state energy at that bond distance possible within the allotted time T. Figure (d) depicts the difference between the attained energy by an optimized pulse and the true ground state energy of H2 for a given bond distance and evolution time. The MET beyond which a pulse can achieve the molecular ground state energy with high accuracy is highlighted by a black-and-white line. Remarkably, these pulses are not only two orders of magnitude faster than typical native gates of silicon processors but also considerably faster than the shortest pulses attainable with superconducting transmon qubits [3] displayed as a dashed grey curve. Ultimately, our numerical results show that fast, pulse-based state preparation could play a crucial role in making NISQ algorithms on silicon quantum hardware feasible. [1] K. Dalton et al. Npj Quantum Inf. 10, 18 (2024). [2] C.K. Long et al. Phys. Rev. A 109, 042413 (2024). [3] O.R. Meitei et al. Npj Quantum Inf. 7, 1 (2021). |
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Analysis and 3D TCAD simulations of EDSR in an industrially-compatible FD-SOI device.
Pericles Philippopoulos1, Benjamin Bureau2, Philippe Galy3, Salvador Mir Bernado4, Eva Dupont-Ferrier5, Felix Beaudoin1 1Nanoacademic Technologies Inc., 2STMicroelectronics, Université de Sherbrooke, 3STMicroelectronics, 4TIMA, Université Grenoble Alpes, 5Université de Sherbrooke University Abstract: One of the main advantages spin qubits possess over other quantum-computing architectures is the potential to leverage the existing classical semiconductor industrial infrastructure to generate scalable quantum-information-processing systems. The classical semiconductor industry already benefits from a mature set of simulation tools, often referred to as Technology Computer-Aided Design (TCAD) tools, dedicated to characterizing and predicting the features of current and future devices. As we transition toward using semiconductors for quantum applications, it seems likely we will adopt the best practices from classical electronics. This includes the use of TCAD tools. With respect to simulations, there exist two main differences between classical and quantum systems: 1. While classical electronics are operated at room temperature, spin-qubit devices are operated at cryogenic temperatures. 2. There exist operational principles that are only relevant for quantum systems (e.g. quantum superpositions). These differences lead to difficulties in applying TCAD tools optimized for classical systems to quantum devices and suggest a need for specialized software dedicated to understanding quantum systems. We use such a software (QTCAD) to investigate electric-dipole spin-resonance (EDSR) for an electron in the presence of a micromagnet in an industrially-compatible STMicroelectronics Fully Depleted Silicon On Insulator (FD-SOI) device [see (a), electron wavefunctions shown in (b)]. We compute the applied EDSR drive (voltage) amplitude necessary to achieve Rabi oscillations [first row of (c)] on the order of MHz. Moreover, because our simulations give us access to the Hamiltonian describing the device, we can go beyond the rotating-wave approximation to consider leakage out of the qubit subspace [second row of (c)] and bound the single-qubit gate fidelities achievable with the studied EDSR scheme. We also consider how these results are affected by the presence of impurities. This work highlights how specialized TCAD tools can help steer the design of quantum devices. |
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High-fidelity two-qubit gates of hybrid superconducting-semiconducting singlet-triplet qubits
Maria Spethmann1, Stefano Bosco1, Andrea Hofmann2, Jelena Klinovaja1, Daniel Loss1 1University of Basel, 2Univeristy of Basel Abstract: Hybrid systems comprising superconducting and semiconducting materials are promising architectures for quantum computing. Superconductors induce long-range interactions between spin qubits via crossed Andreev processes. These spin-spin interactions are widely anisotropic when the material has strong spin-orbit interactions (SOI). We show that this anisotropy enables fast and high-fidelity two-qubit gates between singlet-triplet (ST) spin qubits. Our design is immune to leakage of the quantum information into noncomputational states. Avoiding leakage is a key open challenge of ST two-qubit gates, because the leakage states have a similar energy as the computational states. Furthermore, the Josephson phase across a Josephson junction removes always-on interactions between the qubits. Our ST qubits do not require additional technologically demanding components nor fine-tuning of parameters, and they operate at low magnetic fields of a few millitesla. Germanium hole gases are promising candidates for our architecture because they have strong and tunable SOI, and are fully compatible with superconductors. The schematics of our coupled hybrid ST qubits are shown in Fig. (a). Two ST qubits, each comprising a double quantum dot, interact via a Josephson junction. This setup is effectively equivalent to two exchange-coupled double quantum dots with fully tunable interactions [Fig. (b)]. Strong SOI induce spin rotations of an angle Φso around an axis nso and yield a large asymmetry of exchange coupling depending on the angle θ between nso and the magnetic field direction nB. Two-qubit interactions J(φ) are controlled by tuning the Josephson phase φ. The interaction can be precisely switched on and off, removing residual interactions and crosstalk that hinder scalability [Fig. (c)]. The large SOI enable high-fidelity gates close to the sweet spot Φso=θ=π/2 without fine-tuning of parameters [Fig. (d)]. By suppressing systematic errors, we estimate infidelities below 10−3, which could pave the way toward large-scale hybrid superconducting-semiconducting quantum processors. |
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Composed SWAP gate in silicon spin qubits
Shaomin Wang, Runze Zhang, Ning Wang, Baochuan Wang, Guoping Guo CAS Key Laboratory of Quantum Information, University of Science and Technology of China Abstract: The SWAP gate is commonly employed in quantum circuits and quantum state transfer. In the standard Ising model which can mostly be used to describe the interaction between qubits, the implementation of the SWAP gate can be easily achieved through switching the exchange coupling with an adiabatic pulse like experiments demonstrated in spin qubits in GaAs/AlGaAs heterostructure. However, the non-negligible Zeeman difference (ΔEz) between qubits adds complexity to this scheme in silicon spin qubits. Two main protocols have been proposed to eliminate effects of large ΔEz for realizing the SWAP gate in silicon qubits. The ac-SWAP utilizes microwave to mitigate the influence of ΔEz, but this introduces additional challenges such as heating effects and a more intricate control system. Alternatively, composed SWAP gate (C-SWAP) where composite pulse sequence is used to correct the error caused by ΔEz in exchange oscillation. Here we demonstrate experimentally a C-SWAP gate based on two spin qubits in double quantum dots in natural Si/SiGe heterostructure, which involves carefully designing the form of the pulse sequence to preserve exchange oscillation while correcting for angle deviations caused by ΔEz. By enabling rapid turn on/off of exchange coupling electrically, we were able to achieve two-axis control in the two-qubit ST Bloch sphere, theoretically allowing for generation of arbitrary states. We have designed a series of pulse sequence protocols and compared them in experiments. We observed oscillations between up-down and down-up states across all schemes albeit with varying gate times and fidelities. Furthermore, we successfully generated Bell states using the C-SWAP gate and conducted analysis on gate error and noise. Moving forward, our focus will be on improving fidelity and applying this technique to state transfer applications. |
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Shuttling-based holonomic quantum gates for semiconductor spin qubits
Baksa Kolok and András Pályi Budapest University of Technology and Economics Abstract: A quantum system constrained to a degenerate energy eigenspace can undergo a nontrivial time evolution upon adiabatic driving, described by a non-Abelian Berry phase. This type of dynamics may provide logical gates in quantum computing that are robust against timing errors. A strong candidate to realize such holonomic quantum gates is an electron or hole spin qubit trapped in a spin-orbit-coupled semiconductor, whose twofold Kramers degeneracy is protected by time-reversal symmetry. In this work, we propose and quantitatively analyze a protocol to experimentally characterize the holonomic single-qubit gates induced by the non-Abelian Berry phase when a spin qubit is shuttled around a loop of quantum dots. The device, shown in the figure, includes an on-chip wire and a reservoir besides the loop. These ingredients are used for initialization and read out. In semiconductor spin-qubit devices with strong spin-orbit interaction, e.g. planar SiGe/Ge quantum dot arrays, every loop induces a unitary transformation upon shuttling a spin qubit through it. This technique is suitable for realizing a universal single qubit holonomic gate set on a device with multiple quantum dot loops. We also present extensions of the original protocol: a) a version characterizing the local internal Zeeman field directions in the dots, b) a simplified protocol offering the near-term measurement of the non-Abelian Berry phase. We expect the protocols to be realized in the near future, as all key elements have been already demonstrated in spin-qubit experiments. The strong spin-orbit interaction and weak hyperfine interaction of holes in Si or Ge quantum wells make these materials strong candidates to observe these effects; the recently realized 3-4-3 Ge quantum dot array is especially promising due to its high material quality and the two-dimensional layout that enables shuttling a qubit through a loop. |
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Measurement-Based Methods of State Manipulation in Encoded Spin Qubits
Matthew Brooks1 and Charles Tahan2 1Laboratory of Physical Sciences, 2Univeristy of Maryland Abstract: Spin qubits in semiconductor quantum dots (QDs) offer long coherence times, fast control by spin-spin exchange interaction and scalability from advanced manufacturing methods of industrial semiconductor foundries. Recent advances in spin qubit devices have allowed for the application of algorithmic state initialisation with rounds of measurements followed by conditional gates and/or additional measurements. Such methods are also applicable to measurement-based methods of control. With considered application of exchange pulses and Pauli spin blockade measurements both within and outside the sub-space of encoded multi-QD spin qubits, resource efficient protocols for state manipulation may be devised without a necessity for magnetic field gradients or QD g-factor variations. |
| Cryo-electronics |
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RF Diode Thermometry
Thomas Swift1, Grayson Noah2, Ross Leon2, Fernando Gonzalez-Zalba2, Alberto Gomez-Saiz2, John Morton3 1UCL & Quantum Motion, 2Quantum Motion, 3UCL and Quantum Motion Abstract: Fault-tolerant quantum computing will require the integration of classical circuitry close to or on the same chip as qubits operating at cryogenic temperatures. These classical circuits will dissipate power and affect qubit operation. An experimental technique to probe these static and dynamic effects are therefore of interest to the field and will help improve our understanding of the recent temperature-dependence observed in semiconductor spin-qubit systems [1]. In this work, we further increase the sensitivity of diode thermometry by using radiofrequency reflectometry (RF) techniques, demonstrating state-of-the-art cryogenic temperature sensing capabilities and maintaining sensitivity down to 20mK. We conduct pulsed heating experiments with a resolution of <1µs commensurate with that achieved in semiconductor qubit architectures. The ability to probe at high frequency provides insight into the dynamic temperature behaviour of the chip as a result of both localized (on-chip) and global (PCB) level heating. This technique will allow future experimental studies of quantum thermodynamics in nanoelectronic systems as well as increase our understanding of dynamic power dissipation in cryoelectronic and quantum circuits. [1] Undseth et al 2023 - Hotter is Easier: Unexpected Temperature Dependence of Spin Qubit Frequencies. Physical review. X, 13(4). doi:https://doi.org/10.1103/physrevx.13.041015. |
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Semiconducting qubits with embedded control and readout cryo-CMOS circuits
Mathieu Darnas1, Mathilde Ouvrier-Buffet2, Candice Thomas3, Jean-Philippe Michel3, Jean Charbonnier3, Matias Urdampilleta4, Yvain Thonnart5, Franck Badets5, Tristan Meunier2, Baptiste Jadot3 1CNRS Néel Institute, Univ, Grenoble Alpes, 2CNRS Néel Institute, Univ, Grenoble Alpes, 3Univ. Grenoble Alpes, CEA, Leti, F-38000 Grenoble, France, 4Cnrs, 5CEA-Leti Abstract: The compatibility between state-of-the-art Si-MOS spin qubits and cryoelectronic circuits enables their co-integration at low temperatures in a compact manner. Studying the compatibility between these two fields is thus necessary to increase the number of qubits and thus pave the way for scale-up. In fact, the increase of controlled connections, due to the desire to control and characterize many devices simultaneously, leads to a reduction in the cooling power of the cryostat due to the thermal conduction of these lines. Moreover, it is unreasonable to directly connect many thousand lines in a large-scale perspective. It is also interesting to develop low-temperature measurement circuits to improve some of their performances. For example, in the case of the readout circuits, placing current amplifiers near qubits may decrease the parasitic capacitance and increase the readout bandwidth, as well as reduce the thermal noise of the amplification chain. However, a new problem is emerging : the power consumption of the cryoCMOS circuit. Conventional cryostats are not suitable for high power dissipation. That's why we present a CMOS demultiplexer and a transimpedance amplifier operating at 4K with adjustable power consumption. Firstly, with the demultiplexer, we prove that it is able to control 64 potentials with a refresh rate that go up to 320MHz with a low power consumption depending on its frequency, 3.54µW/MHz (fig.1). Secondly, the 10MΩ gain transimpedance amplifier presents a variable power consumption and, consequently, an adjustable bandwidth over several orders of magnitude (fig.2), while maintaining circuit stability. Finally, this work highlights the first results of a CMOS demultiplexer and a transimpedance amplifier circuit connected to a double silicon quantum dot in a 4K setup, as well as in a conventional cryostat reaching temperatures of a few mK. This last experiment made us deal with thermal issues, underlining the need for good thermalization. |
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A compact superconducting solenoid for spin qubit experiments
Jeremy Morgan1, Giovanni Oakes2, Jonathan Warren2, Miguel Gonzalez Zalba2, Ross Leon2, John Morton1 1UCL & Quantum Motion, 2Quantum Motion Abstract: Silicon spin-qubits provide a promising route towards developing a fault-tolerant quantum computer due to their high-qubit density and potential for integration with classical electronics. However, in order to perform experiments on potential quantum processors, a static magnetic field operating at cryogenic temperatures is required to lift the degeneracy of spin states. Conventional three-axis superconducting solenoid magnets are large and expensive, and furthermore, due to the increased mass, extend the time required to reach the base temperature of a dilution refrigerator. Here we demonstrate a variable field single-axis NbTi optimised split pair coil magnet capable of magnetic field strengths up to 1 T with a bore size of 28 mm, shown in Figure (a). This mini-magnet offers the advantages of permanent magnet solutions, reducing cost and footprint, while enabling variable magnetic field intensities which are instrumental in finding qubit resonance frequencies. We show Elzerman spin readout on a single electron confined in a gate-defined quantum dot with this magnet at approximately 750 mT, shown in Figure (b,c). The compact nature of the mini-magnet with low stray field enables any dilution refrigerator to perform multiple spin experiments at significantly lower cost. |
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Interfacing Qubits and Control/Readout Electronics using Cryo-CMOS FD-SOI Technology
Stavroula Kapoulea, Hossein Eslahi, Zeeshan Ali, Mohammed Waqas Mughal, Meraj Ahmad, Farman Ullah, Martin Weides, Hadi Heidari University of Glasgow Abstract: Interfacing qubits with control and readout electronics is critical in enabling efficient and scalable quantum computing systems. Considering the millions of qubits required to achieve quantum advantage, interconnecting a multi-qubit platform with room-temperature electronics, and acquiring a scalable quantum system seems impractical. The control/readout interface is shifted from the room-temperature environment to the dilution refrigerator to enhance the interconnection efficiency within the quantum computing stack. However, state-of-the-art dilution refrigerators provide only tens of μW of cooling power at mK temperatures, making integration of qubits and control/readout electronics at this stage infeasible. Therefore, the control/readout interface is provisionally positioned at the 4 K stage of the cryostat. Cryogenic complementary metal-oxide-semiconductor (CMOS) nanoscale technology emerges as a promising candidate for implementing well-established circuitry, ultimately ensuring optimal system-level performance. Figure 1(left) illustrates the quantum computing stack alongside the cryogenic stages within the ProteoxMX dilution refrigerator, highlighting the control and readout signal paths within the analog front-end. Currently, the analog/mixed-signal circuits for implementing the control/readout signal processing, including mixers, filters, amplifiers, and data converters, are designed, and simulated under room-temperature conditions, due to the lack of a cryogenic Process Design Kit (cryo-PDK). However, reliable cryogenic models for electronic components characterized at less than 4 K, will soon be indispensable in evaluating circuits' performance under cryogenic conditions before fabrication, providing a cost-effective route to optimal performance. For now, leveraging Global Foundries 22nm Fully-Depleted-Silicon-On-Insulator (FD-SOI) technology facilitates the development of cryogenic circuits, due to the enhanced control capabilities through the transistors' back-gate node, which allows for restoring the transistor's threshold voltage and mobility affected by the cryogenic environment. Furthermore, the low-voltage operation, i.e., 0.8 V power supply, enables energy-efficient systems, thus rendering this technology very advantageous for enabling practical quantum solid-state hardware. Post-layout simulations regarding the digital-to-analog converter reconstruction filter are indicatively presented in Figure 1(right). |
| Dopants & nuclear spin qubits |
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Towards Gallium acceptor spin qubits
Dennis van der Bovenkamp University of Twente Abstract: Hole spin qubits have gained more interest in the last few years. Their anisotropy and tunability of the g-factor give rise to interesting physics. Together with the full electric control of the hole spin states and strong spin orbit coupling, they provide a promising candidate for scalable quantum computers. The downside of this strong spin-orbit coupling is the increase in decoherence form electrical noise [1]. Group-III acceptor spin qubits in silicon showcase the advantage of long-range entanglement when operating at so-called ‘sweet spots', where the interface-induced spin–orbit terms provide insensitivity to fluctuations in the electric field. These sweet spots occur at values where there is also a maximum in EDSR driving strength, making acceptor spin qubits an attractive candidate for enhancing T2* times [2]. A crucial element in achieving acceptor-based spin qubits is inducing Heavy Hole (HH) – Light Hole (LH) splitting. Previously it has been shown that sufficient HH-LH splitting can be achieved using electrode-induced strain [3]. Here, we provide the first experimental results towards achieving a Gallium acceptor-based qubit. We go in detail regarding fabrication of single hole transistors using aluminium gates, which are important to induce strain and achieve HH-LH splitting. We implant gallium atoms nearby a single hole transistor that will be used to read out the hole spin states of a weakly bounded hole to a gallium acceptor. [1] J. Salfi et al (2016), ‘Charge-Insensitive Single-Atom Spin-Orbit Qubit in Silicon' [2] J. Salfi et al (2016), ‘Quantum computing with acceptor spins in Silicon' [3] S. D. Liles et al (2021), ‘Electrical control of the g-tensor of the first hole in a silicon MOS quantum dot' |
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Characterization of single 209-Bi donors in Si nanoelectronic devices
Amber Heskes, Mario Cignoni, Dennis van der Bovenkamp, Quim Torrent Nicolau, Joost Ridderbos, Floris Zwanenburg University of Twente Abstract: Semiconductor devices have emerged as promising candidates for spin qubits, leveraging well-established CMOS processes. Among the semiconductor qubit hardware platforms, single group-V donors in silicon showcase outstanding properties, including extended coherence times – a crucial requirement for achieving high-fidelity quantum computation, as demonstrated for 31-P implanted devices [1]. The unique characteristics of group-V donors with nuclear spin – which stem from the rich physics of the nuclear-electron spin interactions – pave the way to new applications. Among group-V donors, the atypical properties – such as strong hyperfine constant and large nuclear spin number [1, 2] – of silicon-bismuth defect systems constitute a strong rationale for studying the encoding of quantum information on single bismuth donors. Indeed, the spin of the electron and nucleus of a single 209-Bi donor can be driven at magnetic field sweet spots – known as Clock Transitions (CTs) – where the qubit is first-order insensitive to magnetic field noise [3]. The presence of ESR CTs has been experimentally reported for Bi clusters [4]. In contrast, CTs for single-atom donors are thus far unexplored. Moving to a lower concentration of Bi atoms, coherence times are expected to be further extended due to the reduction of the Bi spin bath, making single atom 209-Bi an excellent platform for realizing highly coherent spin qubits. In this study, the fabrication and characterization of single 209-Bi-implanted electrostatically-gated Si nanodevices are discussed. The experimental results include charge sensing and manipulation of donor charge states. Additionally, clear spin signatures at finite magnetic fields and single-shot spin readout are reported, marking a significant step forward towards encoding quantum information in electrons loosely bound to single bismuth donors. [1] A. Morello et al. (2020). [2] A. L. Saraiva et al. (2015). [3] M. H. Mohammady, et. al (2010). [4] G. Wolfowicz et al. (2013). |
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Detecting quantumness in the uniform precession of a single nuclear qudit
Arjen Vaartjes1, Martin Nurizzo2, Lin Zaw3, Xi Yu2, Benjamin Wilhelm2, Danielle Holmes2, Daniel Schwienbacher2, Anders Kringhøj2, Mark van Blankenstein2, Alexander Jakob4, Fay E. Hudson2, Kohei Itoh5, Andrew S. Dzurak2, David N. Jamieson4, Valerio Scarani6, Andrea Morello2 1School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW 2052, Australia, 2UNSW, 3National University of Singapore, 4University of Melbourne, 5Keio University, 6University of Singapore Abstract: The quest for real-world tests of quantumness has started decades ago, with the most famous example the Bell test probing nonlocality. Yet, quantumness remains a broad term, encompassing multiple facets such as entanglement, contextuality or non-locality. While the spin-1/2 illustrates several of these properties its statistics can be cast within local hidden-variable models and its dynamics map directly to the precession of a classical gyroscope. Once d > 3 quantumness emerges, enabling states that violate local hidden-variable theories, and encode error-correctable logical qubits within a single quantum object. Here we address the challenge of detecting quantumness in the time evolution of an 8-dimensional nuclear qudit using a uniform precession protocol developed by Zaw et al. based on an original work of Tsirelson. In this experiment quantumness is certified simply by asking how often the x coordinate of a uniformly precessing object in the (xy)-plane is positive. A violation of the classical bound in this protocol falsifies the existence of a classical probability distribution that explains the observed statistics. We present our experimental demonstration of this protocol focusing on a family of non-classical states in a spin-7/2 123Sb nucleus, implemented within a silicon nano-electronic device. Specifically, we demonstrate the creation of Schrödinger cat states within the large spin with a fidelity of 94 %. Subsequently, using a generalized rotating frame we apply the uniform precession protocol. Our results reveal a significant violation of the classical bound, surpassing it by 10 standard deviations for the spin-cat state. Notably, the spin cat state also maximizes the quantum fisher information, highlighting the usefulness of quantum states that violat e the classical bound in the uniform precession protocol. These results show a first demonstration of the uniform precession protocol and prove our ability to create high-fidelity nonclassical states in a single nuclear qudit. |
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Sensing at the Heisenberg Limit with a high-spin Donor in Silicon
Benjamin Wilhelm1, Xi Yu1, Danielle Holmes1, Arjen Vaartjes1, Daniel Schwienbacher1, Martin Nurizzo1, Anders Kringhoj1, Mark van Blankenstein1, Alexander Jakob2, Pragati Gupta3, Fay Hudson1, Kohei Itoh4, Andrew Dzurak1, Barry Sanders3, David Jamieson2, Andrea Morello1 1UNSW Sydney, 2University of Melbourne, 3University of Calgary, 4Keio University Abstract: Quantum metrology has enabled unprecedented measurements precision and sensitivity. Conventional quantum sensors commonly use entangled spin-1/2 particles to achieve a metrological advantage over the Standard Quantum Limit. However, these systems often require numbers of at least 10-100 atoms to achieve a sizeable metrological gain. High-spin systems such as the 123Sb donor in silicon (fig. 1a,b) have recently gained interest as an efficient resource for quantum technologies as they offer larger Hilbert space (fig. 1c) with less physical resources compared to qubit architectures. In fact, a single 123Sb donor with spin I=7/2 can offer the same metrological properties as seven entangled spin-1/2 particles. Yet, quantum metrology with high-spin systems still remains relatively unexplored. Here, we present strategies to use a single 123Sb donor for quantum sensing. One key ingredient of these protocols is the non-linear quadrupole interaction (fig. 1c) between a donor and electric field gradients in its vicinity. This interaction makes each nuclear magnetic resonance transition individually addressable, allowing us to implement spin-squeezing protocols such as One-Axis-Twisting. With this method we are able to create the highly non-classical Schrödinger cat state (fig. 1e) that enables quantum sensing at the Heisenberg limit. Additionally, by modulating the nuclear quadrupole interaction we are able to implement Two-Axis Countertwisting – another protocol to create valuable states for quantum metrology (fig. 1f). We demonstrate how we can use the two methods to create states for sensing magnetic and electric fields. We show that our scheme beats the standard quantum limit and enables quantum sensing near the Heisenberg limit. |
| Fabrication |
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Infuence of device fabrication methods on transport properties of Ge/SiGe heterostructures
Nikunj Sangwan, Eric Jutzi, Christian Olsen, Andrea Hofmann University of Basel Abstract: Holes in germanium (Ge) have been established as a platform for spin qubits. Their advantages include a strong spin-orbit interaction, large excited state splitting energies, low effective mass, and clean Ge/SiGe interfaces that effectively confine states with a long mean free-mean path. Importantly, device fabrication plays a crucial role in the advancements of Ge/SiGe research, and, currently, the research community faces problems with irreproducibility and device variation. Taking a deeper look into different fabrication steps might highlight reasons for the these problems. We present optical and electrical characterization of Ge/SiGe devices prepared with different fabrication recipes. In particular, we vary pre-fabrication surface treatments, oxide deposition parameters, and etching methods. Our preliminary results indicate that the surface treatment and the temperature of the oxide deposition influence the accumulation behavior and the effective field-effect gating of charge carriers in the active Ge quantum well. These results provide important insights necessary for reliable and reproducible fabrication of spin qubit devices. |
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Gate-defined quantum point contacts in a germanium quantum well
Jiyin Wang Beijing Academy of Quantum Information Sciences Abstract: We report an experimental study of quantum point contacts defined in a high-quality strained germanium quantum well with layered electric gates. At zero magnetic field, we observe quantized conductance plateaus in units of 2e2/h. Bias-spectroscopy measurements reveal that the energy spacing between successive one-dimensional subbands ranges from 1.5 to 5 meV as a consequence of the small effective mass of the holes and the narrow gate constrictions. At finite magnetic fields perpendicular to the device plane, the edges of the conductance plateaus get splitted due to the Zeeman effect and Lande g factors are estimated to be 6.6 for the holes in the germanium quantum well. We demonstrate that all quantum point contacts in the same device have comparable performances, indicating a reliable and reproducible device fabrication process. Thus, our work lays a foundation for investigating multiple forefronts of physics in germanium-based quantum devices that require quantum point contacts as a building block. |
| Large-scale characterization |
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Quantum Dot level characterization of industrial Si MOS spin qubit devices
Amina Sadik1, Sam Fiette1, Emmanuel Chanrion1, Louis Hutin1, Heimanu Niebojewski1, Nils Rambal1, Maud Vinet2, Benoit Bertrand1, Pierre-André Mortemousque1 1CEA Leti, 2CEA Leti (Now at Quobly) Abstract: Recently, significant progress has been achieved in the automation of silicon quantum dot (QD) device calibration. Automated methods have been used to tackle various stages of the calibration process, from tuning the device parameters [1, 2], to understanding the fabrication process [3-5]. Here, we introduce a methodical approach to characterize single electron regime of QDs within FD-SOI split gate devices at 1K, employing a non-simplified configuration of the constant interaction (CI) model. Emphasizing the necessary measurements for addressing the model, the numerical resolution enables the exploration of mutual coupling between the detector and the QD, along with other quantum dot properties (gate capacitance, cross capacitance, lever arms, and charging energies). We demonstrate, as well, the robustness of the resolution and discuss ongoing efforts towards automation in analysis. We, thereby, provide initial statistical insights into device behavior and present comparative analyses of technological splits, including variations in gate length and channel width. Additionally, we introduce a study about the back-gate effect and we discuss correlations between physical quantities at both zero and positive back-gate voltages, shedding light on the limitations of the constant interaction model. References: [1] J. Ziegler et al. Toward Robust Autotuning of Noisy Quantum Dot Devices (Phys. Rev. Applied 2022). [2] A; R; Mills, et al. Computer-automated tuning procedures for semiconductor quantum dot arrays (2019). [3] R. Pillarisetty et al. High Volume Electrical Characterization of Semiconductor Qubits (IEDM 2019). [4] L. Contamin, et al. Methodology for an efficient characterization flow of industrial grade Si-based qubit devices (IEDM 2022). [5] S. Neyens, et al. Probing single electrons across 300 mm spin qubit wafers (2023). |
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Parallel Silicon-charge-pump architecture, with operation temperature of above and below liquid-helium temperature
Ajit Dash1, Steve Yianni2, MengKe Feng3, Fay Hudson2, Andre Saraiva2, Andrew Dzurak2, Tuomo Tanttu4 1UNSW, 2UNSW, Diraq, 3University of New South Wales / Diraq, 4UNSW & Diraq Abstract: Semiconductor tunable-barrier single-electron pumps can produce output current of hundreds of picoamperes at sub-parts-per-million precision, approaching the metrological requirement for the direct implementation of the current standard. Here we operate a silicon metal-oxide-semiconductor electron pump up to a temperature of 14 K to qualitatively understand the effect of temperature on charge-pumping accuracy. The uncertainty of the charge pump is tunnel limited below liquid-helium temperature, implying lowering the temperature further does not greatly suppress errors [1]. Hence, highly accurate charge pumps could be achieved in a 4He cryogenic system, further promoting use of the revised quantum current standard across national measurement institutes and industries worldwide. Further we propose a physical architecture of a cryogenic dc-source-module that incorporates several charge pumps in parallel on a single-chip to potentially fulfill the metrological requirement. The total current produced by the dc-source module is given by the summation of the quantized current collected from individual charge-pumps while transferring single-electrons per voltage cycle. [1] A. Dash et al. Phys. Rev. Appl. 21, 1 (2024). |
| New directions |
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A study of symmetry-protected topology of surfaces of maximum entanglement in Si, Ge and GaAs for spin-qubit architectures
Mira Ramakant Sharma1 and David DiVincenzo2 1RWTH Aachen University, 2Peter Gruenberg Institute, Theoretical Nanoelectronics, Forschungszentrum Juelich Abstract: We evaluate tight-binding analytical expressions to calculate the g-tensor of electron and hole spins for group IV and III-V semiconductors with focus on crystalline Si, Ge and GaAs -- the leading hosts for gate-controlled spin qubits. Recalling that the electron g-factor for bulk Si is +2 but -0.44 for bulk GaAs indicates the need to diagnose the occurrence of large variations in g. Mathematically, these values are the singular values of the asymmetric g tensor. Using the determinant of g, det(g), as a diagnostic, we see large regions of k-space, for many bands in these semiconductors, where det(g) has an inverted sign. The topology of the surfaces where det(g) = 0 is particularly intricate in the case of the first conduction bands of Si and the second conduction band of Ge. We observe that these surfaces can be as complex as Fermi surfaces and share similar characteristics. We show that, considering just the spin contribution 𝑔S to the g tensor, surfaces where 𝑑𝑒𝑡(𝑔𝑆)=0, which also commonly occur, indicate the occurrence of maximal spin-orbital entanglement in the Bloch states |
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Neural networks for quantum environment characterization and shadow tomography of silicon spin qubits
Bill Coish1, Victor Wei2, Alev Orfi3, Felix Fehse4, Pooya Ronagh5, Christine Muschik6 1Department of Physics, McGill University, 2McGill University, University of Waterloo, 3McGill University, University of Waterloo, NYU, 4McGill University, 5Unviersity of Waterloo, 6University of Waterloo Abstract: I will discuss two cases where we have found neural networks to be an important practical tool. The first is in studying decoherence/dynamics for quantum systems that are well described by the "Gaudin magnet" (central-spin) model [1]. This model precisely describes the decoherence dynamics of an electron-spin qubit in silicon interacting with a nuclear spin environment. Although the model has many symmetries (it is integrable), finding closed-form solutions for the dynamics is nevertheless highly challenging. We speculate that neural networks may soon be able to exploit these symmetries to find more efficient numerical solutions to this and other problems of integrable quantum systems. Working from this intuition, we have developed theoretical tools that could be used to efficiently characterize the nuclear-spin environment of an electron-spin qubit by measuring the response of this qubit to a drive at the "NMR" frequency, coupled with an efficient neural-network representation of the dynamics problem [1]. I will also discuss recent work on improving classical shadow tomography of quantum states with a neural-network ansatz [2]. See figure for a graphical representation of the differences between conventional neural-network quantum state tomography (NNQST, Fig. a) and our new protocol that incorporates classical shadows: neural--shadow quantum state tomography (NSQST, Fig. b). By constraining results found via classical shadows to a physical (neural-network) representation of the underlying pure quantum state, certain features of the quantum state can be extracted more effectively than would be possible using the standard formulation of classical shadow tomography, in a realistic setting (including noisy gates and measurements). In particular, we have shown that it is possible to find an accurate neural-network representation of the quantum state being studied, even in the presence of generic noise sources, with no noise calibration or mitigation. |
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Thermal engineering of silicon quantum-dot array structures
Takeru Utsugi1, Nobuhiro Kusuno2, Takuma Kuno1, Noriyuki Lee1, Itaru Yanagi1, Toshiyuki Mine1, Shinichi Saito1, Digh Hisamoto1, Ryuta Tsuchiya1, Hiroyuki Mizuno1 1Hitachi, Ltd., 2Hitachi, Ltd Abstract: Heating is a critical issue in large-scale quantum computers based on quantum-dot (QD) arrays. The rise in electron temperature due to heating leads to shorter coherence times, readout errors, and an increase in charge noise. Heating due to radiation inside dilution refridgerators, inflow of heat through wires, loss of applied microwave signals, and local current are expected to escalate with the large-scale integration of qubits. To address this issue, we investigate the optimal design of the heat inflow paths in QD array structures, a crucial step toward mitigating the heating effects. Here, we propose a simple thermal circuit model to describe the heating effect of the silicon QD array, as shown in Fig. 1 (a). In our model, each element of the QD array is described by an effective thermal circuit by considering the thermal properties using the Wiedeman-Franz law, see Fig. 1(b). This results in a thermal transmission line. To validate our model, we measure the electron temperature (Te) in a QD array device using Coulomb blockade thermometry (CBT) with a single electron transistor (SET), see Fig. 1 (c). A local heater is realized by flowing current through the barrier gates (BG) of the QD array. We then measure the distance dependence between the local heater and SET, see fig. 1 (d). We found that our model reproduces the experimental result. We further confirm the validity of both our model and experimental result by COMSOL Multiphysics® simulation, which can capture the detailed structure and thermal distribution of small devices but is unsuitable for large-scale structures. Our model is not only simple and intuitive but also scalable, paving the way for optimizing the thermal structure of large-scale quantum computers in silicon. This work is supported by JST Mooshot R&D Grant No. JPMJMS2065. |
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Magnetospectroscopy of Elongated Jellybean Dots in Silicon
MengKe Feng1, Dylan Liang2, Jesús Cifuentes1, Philip Mai1, Christopher Escott1, Andrew Dzurak1, Arne Laucht1 1University of New South Wales / Diraq, 2University of New South Wales Abstract: As we move towards building a fully fault tolerant quantum computer, one of the challenges that we should address is scalability. One of the many ways of overcoming complexities in scalability is to implement long-range coupling in a sparse array of quantum dots, such that it becomes possible to integrate electronics and wiring into the architecture [1]. Of the many methods of long-range coupling, the one we will discuss here is the use of a multi-electron quantum dot as a mediator of exchange interaction between neighbouring dots, also known as a jellybean dot, owing to its physical shape [2,3]. To investigate the electronic structure and properties of the jellybean dot, we utilise a simulation tool primarily based on the Hartree-Fock formalism. Using this simulation tool, we are able to calculate the energies and wavefunctions of multi-electron quantum dot systems. In this study we examine the charge and spin properties of the jellybean dot through magneto-spectroscopy, where we are able to extract the charging energies for each electron, as a function of a varying external magnetic field. We can then correlate this result with the charge and spin densities obtained from the same simulation, which will allow us to understand better the spin filling of such a multi-electron quantum dot. Figure below shows the typical confinement potential used in the simulations in (a) as well as the surface roughness profile in (b). (c) shows both the total and last electron charge densities. (d) highlights some of the results of a magneto-spectroscopy simulation. |
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Proposal of 3D stacked spin qubit system
Tetsufumi Tanamoto Teikyo University Abstract: Spin qubit systems are one of the promising candidates for Si based quantum computing. As semiconductor technologies continue to advance daily and the era of 3D circuits is on the rise[1], active usage of the state-of-the-art technologies to spin qubit system is necessary. Here, the implementation of the 3D qubit system has been proposed as a near-future structure of spin qubit system. The proposed spin qubit system is quantum dot (QD) arrays based on the nanosheet transistor structure (Fig.1). Here, the measurement process of QD arrays is theoretically investigated using resonant tunneling, controlled by a conventional transistor which are assumed to be embedded into the stacked structure of Fig.1. Because the energy-difference between the up-spin and down-spin states is very small, the detection of the qubit state is of prime importance in this field. Moreover, many wires are required to control qubit systems. Therefore, the integration of qubits and wires is also an important issue. It is shown that the number of possible measurements during coherence time can exceed a hundred under the backaction of the measurements owing to the nonlinear characteristics of resonant tunneling[2,3] [1] Y. -Y. Chung, et al.,2022 IEDM, 34.5 (2022). [2] T. Tanamoto and K. Ono, J. Appl. Phys. 134, 214402 (2023). [3] T. Tanamoto and K. Ono, AIP Advances 11, 045004 (2021). This work was supported by MEXT Q-Leap Program , Grant Number JPMXS0118069228, Japan, and JSPS KAKENHI JP22K03497 Fig.1: Cross-section of the stacked qubits which realize two-dimensional qubit array aiming at the surface code. The orange part indicates a common gate, which controls the potential of the QDs. (b) (c) Bird's eye view of the 3D stacked qubit system. Qubits are surrounded by channel-QDs. Sources and drains of different channel-QDs are independently accessed by attaching different bias lines to the sources and drains. |
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Ge/Si Nanowires: A Platform for Superconducting Qubits
Han Zheng1, Luk Yi Cheung1, Nikunj Sangwan1, Carlo Ciaccia1, Artem Kononov1, Roy Haller1, Joost Ridderbos2, Andreas Baumgartner3, Erik Bakkers4, Christian Schönenberger1 1Department of Physics, University of Basel, 2Institute of Nanotechnology, University of Twente, 3Swiss Nanoscience Institute, University of Basel, 4Dep. of Appl. Phys., Eindhoven University of Technology Abstract: Transmon qubits based on superconducting circuits are currently the most popular platform for small and intermediate scale quantum technology applications. However, there are several challenges, such as the large size and hence the difficulty in scaling to many qubits, the sensitivity to flux noise and the associated power load for driving qubits through flux lines. A possible solution are semiconductor-superconductor hybrid systems called gatemon qubits where the Josephson junction is realized by a gate-tunable weak link (gatemon). Such gatemons have intensively been studied in III-V semiconductor 2D and 1D platforms and, recently, work has been started also on using type-IV semiconductors, such as Si and/or Ge. Here, we present a gatemon qubit based on a Ge/Si core-shell nanowire Josephson junction. On this new platform we demonstrate the electrical tunability and coherent manipulation, with coherence times on par with other gatemon platforms. We also study the current-phase relation of Ge/Si Josephson junctions and demonstrate, that the narrow core of Ge allows for junctions with one or two channels only. In short junctions the electric current carrying channels are ballistic and highly transmissive opening a way to realize parity protected 4e gatemon devices. In this talk, we will also address recent attempts to realize an Andreev level and Andreev spin qubit using the same platform. Figure caption Al-GeSi-Al gatemon: (a) SEM image of a GeSi core-shell nanowire with Al source and drain contacts alloyed into the Ge core. (b) Transmon circuit with a T-gate capacitor (red) capacitively coupled to a read-out transmission line λ/4 resonator. (c) Rabi oscillations, (d) relaxation time, (e) Ramsey sequence to extract an estimate of the dephasing time shown in (f). |
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Agnostic Phase Estimation
David Arvidsson-Shukur1, Xingrui Song2, Flavio Salvati3, Chandrashekhar Gaikwad2, Nicole Yunger Halpern4, Kater Murch2 1Hitachi Cambridge Laboratory, 2Washington University in St. Louis, 3University of Cambridge, 4NIST and University of Maryland Abstract: Phase estimation is crucial to quantum-information processing. Several quantum algorithms use phase estimation as a subroutine for finding unitary operators' eigenvalues. Furthermore, phase estimation is used in quantum metrology, the field of improving measurements' sensitivities by harnessing quantum resources. Theoretically, phase estimation concerns the determination of the phase α of a unitary Uα=eiαH, where H is the generator of the unitary. In conventional phase estimation, one must know H precisely to prepare input states and readout settings such that α can be estimated optimally. If H is unknown, one can first learn about it through quantum-process tomography. However, process tomography requires many applications of Uα, plus many measurements. The number of applications of a unitary quantifies resource usage in quantum computing and metrology. Hence tomography is costly. Furthermore, one often cannot leverage process tomography. For example, consider a magnetic field whose direction changes in time. To facilitate targeted error correction, we might need to measure the field strength α at specific instances in time. Then, the probes must be prepared optimally beforehand. We show that entanglement manipulation can enable optimal estimation of α, even without information about H. Further, we perform experiments using a two-qubit superconducting quantum processor (Fig. 1). Our α estimation achieves a quantum advantage, outperforming every entanglement-free strategy. Moreover, our agnostic phase-estimation protocol is of particular importance to Silicon spin qubits. Our protocol can optimally characterise the strength of magnetically induced coherent errors in Silicon qubits, without knowledge of the magnetic field's direction. Consider the unwanted qubit rotation Uα=eiαnσ/2, where n is the unknown direction of a (real or effective) magnetic field and α is the unknown strength of the coherent error. By implementing natural singlet-triplet initialisations and measurements our agnostic-phase-estimation protocol allows the optimal quantification of α with no knowledge of the magnetic-field direction. |
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Low-Distance Surface Code Emulation for Silicon-based Spin Qubits
Oscar Gravier1, Valentin Savin1, Tristan Meunier2, Thomas Ayral3 1CEA-LETI, Grenoble Alpes University, 2Institut Néel, CNRS Grenoble, France, 3Eviden Quantum Lab Abstract: The last few years have seen significant progress in the field of silicon-based quantum technology, consolidating the development of single-qubit and two-qubit gates with increasing controllability and fidelity. A key component for the realization of a large-scale fault-tolerant quantum computer is quantum error correction, which shields quantum information from decoherence effects, providing exponentially scalable resilience to noise. We report the logical qubit performance of the 17-qubit rotated surface code (see left figure), based on the emulation of a realistic noise model on the Qaptiva quantum computing emulator, developed by Eviden. We rely on physical level simulations to derive noise models for one and two-qubit gates, considering two sources of noise acting on the Larmor frequency and the exchange energy. Strategies have been initiated on improving their fidelity, leading to the introduction of gates more resilient to noise. We then perform an optimization of the syndrome extraction circuit using Si-qubit technology native gates, yielding a circuit of 68 gates and depth 10. Further, we introduce a new performance metric of the logical qubit, referred to as logical qubit coherence time, obtained by performing a Ramsey-like experiment on the logical qubit, and providing a performance metric directly comparable against the coherent time of the physical qubit. In the absence of exchange energy (J) noise, our numerical results reveal a significant enhancement in the logical qubit coherence time compared to the physical one (see right figure). However, upon introduction of noise in the exchange energy, the error contribution from two-qubit gates becomes predominant, resulting in a saturation of logical qubit performance, thus rendering physical qubit coherence time improvements ineffective. Additional simulations have also been conducted, providing a fine characterization of the error correction performance for different regions of the noise parameters space. |
| Noise, quality metrics & material growth |
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Impact of disorder on the charge and spin properties of hole spin qubits in Ge
Biel Martinez i Diaz1 and Yann-Michel Niquet2 1Université Grenoble Alpes, CEA-LETI, Grenoble, France, 2Université Grenoble Alpes, CEA-IRIG, Grenoble, France Abstract: With the remarkable progress achieved in the last years, spin qubits hosted in SiGe epitaxial heterostructures have proven one of the most promising spin-based platforms for quantum computation. Both electrons in Si/SiGe and holes in Ge/SiGe have shown an important growth of the number of qubits and the demonstration of two-dimensional arrays, key milestones for scalability. The reason behind the recent success of epitaxial heterostructures is likely to be found on their expected low level of disorder. Indeed, embedding the active layer in crystalline SiGe should provide a lower variability on the electrical environment of the qubits with respect to Si Metal-Oxide-Semiconductor (MOS) platforms. Unlike their electron counterparts, hole spin qubits in Ge/SiGe heterostructures experience a variety of Spin-Orbit-Coupling (SOC) mechanisms that in presence of disorder can lead to important qubit-to-qubit fluctuations. The bounds of this variability, even if observed in the most recent experiments, are to-date unknown. In this work, we quantify the impact of disorder on the charge and spin properties of Ge spin qubits. We mainly focus on the variations of the gyromagnetic g factors, the magnetic axes and the Rabi frequencies; and compare the obtained results with recent experiments. We explore the implications of the expected qubit-to-qubit fluctuations into the feasibility of large-scale architectures, and hint possible strategies to mitigate the impact of disorder. |
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Materials for spin qubits, on an off the beaten track
Giordano Scappucci TU Delft, QuTech Abstract: In the Scappucci Lab at TU Delft, QuTech we design, make and validate SiGe heterostructures for quantum technologies with the underlying belief that breakthroughs in materials shall empower the next leap in quantum computing. Our approach to spin-qubit materials relies on continuous feedback loops based on SiGe heterostructure design and epitaxial growth, high throughput quantum transport and measurements of qubits as sensors of the quantum material. In this poster I will overview the group's latest advancement that comprise: 1) Achieving record mobility (above 4 millions cm2/Vs) in group IV heterostructures. This is obtained in a strained Ge quantum well buried deeper than usual, but still at a distance feasible to support quantum dots. 2) Developing conventional Si quantum wells where the delicate engineering of the quantum well thickness and surrounding interfaces allows for achieving together low disorder and high average valley splitting. These results are now published in npj Quantum Information 10, Article number: 32 (2024) 3) Developing unconventional Si quantum wells where the Ge concentration profile is designed to increase the electron wavefunction overlap with Ge atoms. In these experiments we see clear signatures of valley splitting increase, at least at the 2DEG level. 4) Progress towards integrating novel superconductors with the Ge platform to improve the toolbox for hybrid Ge quantum technologies. 5) Advancement we made in characterising Qarpet, our architecture for high-volume qubit characterisation. These include statistical measurements of charge noise over micron scale distance on the heterostructures. |
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Singlet-Triplet Qubit in a Low Charge Noise FdSOI Unit Cell
Pierre Hamonic1, Martin Nurizzo2, Jay Nath3, Matthieu Dartiailh3, Benoit Bertrand4, Heimanu Niebojewski4, Pierre-louis Julliard3, Bruna Cardoso-Paz3, Maud Vinet3, Tristan Meunier5, Matias Urdampilleta6 1Neel Institute CNRS Grenoble, France, 2Néel Institute CNRS Grenoble, France, 3Quobly Grenoble, France, 4CEA-LETI Grenoble, France, 5Néel Institute, CNRS Grenoble, France and Quobly Grenoble, France, 6Cnrs Abstract: Silicon-based spin qubit platforms is a promising approach to quantum computing as demonstrated by the recent implementations of quantum algorithms. Scalability has however been a recurring issue, with the charge sensors used for readout having a significant footprint. Here, we present the operation of a silicon unit cell with embedded readout and coherent manipulation. This unit cell is fabricated in a 300mm FDSOI foundry (Fig(a)). It comprises an isolated double quantum dot (DQD) which requires no tunnel-coupled reservoir nor charge sensor to perform single shot spin readout and coherent manipulation. For this purpose, we combine two methods: first, we load a controlled number of electrons in the DQD, which is subsequently isolated from reservoirs and operated out of equilibrium, Fig(b). Second, we use gate-based reflectometry technique to probe singlet triplet states in a single-shot manner. Based on these approaches, we characterize both the S-T- and S-T0 qubits, from which we extract the different energies at play (Fig(c)). The isolation regime allows to tune the exchange interaction between the two dots by playing with the confinement potential. Moreover, the decoupling from reservoirs leads to a charge noise below 1μeV/√Hz, extracted from free induction decay measurements. This is more than one order of magnitude improvement compared to qubits in similar devices. We believe that the combination of dispersive readout and the operation of the qubits decoupled from the reservoirs greatly facilitate an easy tuning and manipulation of the system, and make our system suitable as a scalable silicon quantum unit cell. |
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Highly enriched 28Si by localised focused ion beam irradiation for silicon spin quantum technologies
Ravi Acharya1, Shao Qi Lim2, Maddison Coke1, Mason Adshead1, Nicholas Gillespie3, Kexue Li1, Barat Achinuq1, Rongsheng Cai1, A.Baset Gholizadeh1, Janet Jacobs1, Jessica Boland1, Sarah Haigh1, Katie Moore1, David Jamieson3, Richard Curry1 1The University of Manchester, 2CQC2T, The University of Melbourne, 3The University of Melbourne Abstract: Donor electron spins in silicon are some of the most coherent systems in the solid-state and are compatible with standard semiconductor device processing techniques, especially ion implantation. In natural silicon (NatSi) spin coherence times are limited by the presence of the spin bath of the nuclear spin I=1/2 29Si isotope at an abundance of 4.7%. We present here a novel technique to produce highly enriched 28Si (I=0) in which the problematic 29Si isotope is depleted to an unprecedented 2.3 ppm (see figure). We employ ion beam irradiation with a 45 keV 28Si focused ion beam with fluences exceeding 1019 ions cm-2 over 22 µm by 22 µm areas in high purity NatSi substrates. Nanoscale secondary ion mass spectrometry (NanoSIMS) analysis has verified 29Si depletion over depths of ~200 nm with impurities (C, O) below the detectable limit, comparable with the original high purity substrate. Following implantation, the ~200 nm surface amorphous layer is regrown by solid phase epitaxy and transmission electron microscopy (TEM) diffraction patterns show crystallinity comparable to the substrate (see figure). Theoretical calculations shown in Witzel et al., Physical Review Letters, 105(18), 187602, 2010, predict Hahn-echo electron spin coherence times extending up to seconds at this enrichment level, signifying that this highly depleted material represents a new frontier of coherent silicon-based spin qubits. To explore the coherence of ensembles of donor spins implanted into this new material we employ low-field (<100 G) electrically detected magnetic resonance on devices that incorporate a 22 µm by 22 µm by 200 nm volume of our highly enriched silicon implanted with 31P ions. In this low field regime, the prominent electron-nuclear spin mixing means the same device architecture, implanted with 123Sb (I=7/2), allows us to investigate the three unique low-field ESR-type Zeeman clock transitions of this high spin nuclei. |
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A silicon semiconductor vacuum: donor spin coherence in isotopically engineered 28Si
Shao Qi Lim1, Ravi Acharya2, Nicholas Gillespie3, Brett Johnson4, Alexander Jakob1, Daniel Creedon5, Sergey Rubanov6, Richard Curry2, Jeffrey McCallum1, David Jamieson1 1CQC2T, The University of Melbourne, 2The University of Manchester, 3The University of Melbourne, 4RMIT University, 5CSIRO Clayton, 6Bio21 Institute, The University of Melbourne Abstract: One of the many advantages of using silicon as a qubit environment is that its most abundant isotope, 28Si, has zero nuclear spin and thus provides a "semiconductor (spin) vacuum". Natural silicon (natSi), however, contains 4.67% of 29Si which has a non-zero nuclear spin, resulting in local magnetic perturbations and degraded qubit spin coherence. Previously, we have shown that we can greatly suppress this source of decoherence through the isotopic enrichment of silicon by high fluence (≥1x1018 cm-2) ion implantation of 28Si ions into natSi substrates, resulting in ~100 nm of 28Si on the surface with sub-250 ppm 29Si over 8x8 mm2 areas. Larger areas and lower levels of 29Si can be achieved by increasing the irradiated area and ion fluence, respectively. This method can also be applied to silicon-on-insulator substrates, as shown in the figure (top panel). Following ion implantation, a solid phase epitaxy anneal restores the crystallinity of the lattice as confirmed by electron diffraction. These enriched 28Si samples will be employed to examine donor spin coherence phenomena of ensembles of implanted donors of the order of 106 donor spins. This donor density is comparable to quantum computer architectures such as the flip-flop qubit scheme and thus allows us to assess the compatibility of our enriched silicon for large-scale devices. To date, we have performed low-field (<100 G) continuous wave electrically detected magnetic resonance (EDMR) measurements on 31P and 31PF2 molecular ion implanted natSi and 28Si epi-layers (ISONICS) enriched to ~700 ppm 29Si (see figure, bottom panel). The molecular ions allow for high fidelity deterministic ion implantation for near-surface donors. In the near term these measurements will be repeated in our implantation enriched 28Si along with the use of pulsed-EDMR to measure the 31P donor electron spin coherence times (T2*). |
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Proposed real-time charge noise measurement via valley state reflectometry
David Kanaar1, Hasim Ercan2, Mark Gyure2, Jason Kestner1 1UMBC, 2UCLA Abstract: We theoretically propose a method to perform in situ measurements of charge noise during logical operations in silicon quantum dot spin qubits. Our method does not require ancillary spectator qubits but uses the valley states of the electron in silicon as an ancillary degree of freedom located exactly at the electron. By coupling the valley transition dipole element to the field of an on-chip microwave resonator, rapid reflectometry allows us to measure valley splitting fluctuations caused by charge noise. This dipole moment is caused by sharp interface steps or alloy disorder in the well. Using tight binding simulations we show that with realistic interface disorder a pure silicon quantum well results in a small dipole but adding 5% germanium to the quantum well does result in a large dipole. Further, we derive analytic expressions for the signal-to-noise ratio when including the dominant source of noise, photon shot noise in the resonator. From the tight-binding simulations, we extract the key parameters (valley splitting and valley dipole elements) under realistic disorder. Using these parameters we find that unity signal-to-noise ratio can often be obtained with measurement below 1ms opening the potential for closed-loop control, real-time recalibration, and feedforward circuits. The uploaded figure schematically shows the device and amplification chain used for the proposed measurements. The valley states with charge densities, |ψ|, and the dipole moment between them, x₀₁, which couples to the resonator are shown in the figure which couples to the resonator. |
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Gate Materials and Process Variations: Exploring Their Influence on Transport Properties in Silicon MOS Devices
Md. Mamunur Rahman1, Jonathan Yue Huang1, Alexandra Dickie1, Steve Yianni1, Kok Wai Chan1, Fay Hudson1, Chris Escott2, Andrea Morello1, Arne Laucht1, Andre Saraiva2, Andrew Dzurak1, Wee Han Lim2 1School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, NSW 2052, Australia, 2Diraq, Sydney, NSW, Australia Abstract: Hall bar carrier mobility and percolation density are two commonly-used metrics to assess the quality of metal-oxide-semiconductor (MOS) interface. By investigating the quantum transport properties of Hall bars, valuable insights can be obtained for fabrication process optimisation and gate materials selection for SiMOS qubit device. In this work, we fabricated a variety of six-terminal Hall bar transistors on high-quality 8-nm SiO2 gate oxide thermally grown on a high-resistivity natural silicon substrate as shown in Fig 1(a). We varied fabrication parameters such as top gate material, metal deposition process, and lithography type. The measurements were performed using a standard four-wire lockin technique in a variable temperature insert (VTI) system at ∼1.7 K. Figure 1(b) compares the peak mobility of Al-gated Hall bar device deposited via thermal evaporation or e-beam evaporation while Figure 1(c) shows a comparison between UV photolithography and electron beam lithography at two different acceleration voltages. We observed that device exposure to an electron beam during either gate metal deposition or gate patterning stages leads to the creation of additional negative charge centers in the oxide, resulting in the degradation of electron mobility of the device. In Figure 1(d), we compare the peak mobility of devices made by different gate materials: Al, Pd and TiPd. Aluminium-gated device shows the highest mobility. A possible explanation is that "Alneal" reduces the Si/SiO2 interface trap density by atomic hydrogen, which is formed during an oxidation of Al with residual water molecules in the oxide. Pd and TiPd-gated devices show relatively low mobility which could be explained by strain-induced modulation on the conduction band of silicon by Pd and oxygen scavenging of Ti from the underlying SiO2. In summary, the analysis on transport properties of Hall bar provides valuable information for quantum dot fabrication, paving the way for a large-scale silicon quantum processor. |
| Quantum simulation |
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Calibration of the Cryogenic Semiconductor Model for the Simulation of the Quantum Dots Fabricated on FDX-22 Process
Andrii Sokolov1, Conor Power2, Xutong Wu2, Ioanna Kriekouki3, Mike Asker4, Panagiotis Giounanlis3, Dirk Leipold4, Imran Bashir4, Elena Blokhina3 1Equal1 Labs Ireland, 2University College Dublin, 3Equal1 Laboratories Ireland, 4Equal1 Laboratories USA Abstract: In this work, we present our results on a calibrated model of a commercial FDX-22 nanostructure using the simulation tool Quantum TCAD, along with our experimental verification of all model predictions. Unlike previous studies and operations performed on similar commercial devices using high back-gate voltages, we demonstrate here that quantum dots can be formed in the device by applying a much lower common-mode voltage to the source and drain, while the back gate remains grounded. The calibration of the model was based on a Coulomb blockade effect observed on a single-gate transistor (Fig.1 a-c) fabricated on the same technology as the multi-gate array. The quantum well formed in a fully depleted channel of the transistor was very shallow (Fig.1 d-f) and therefore could be observed at the particular set of simulation parameters. The fitting of the lever arm and overall position of the Coulomb diamond (Fig.1 g) allows us to extract these parameters. As a result, the calibrated QTCAD model allows us to predict the biasing conditions of quantum wells forming. In addition, the model predicted the flip of the conduction band when the quantum wells can form under the gates and between the gates under different biasing conditions. An overall offset between the prediction and the experimental results was approximately 200 mV. |
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Tailoring quantum error correction to spin qubits
Bence Hetenyi and James Wootton IBM Research - Zurich Abstract: Spin qubits in semiconductor structures bring the promise of large-scale 2D integration, with the possibility to incorporate the control electronics on the same chip. In order to perform error correction on this platform, the characteristic features of spin qubits need to be accounted for. E.g., qubit readout involves an additional qubit which necessitates careful reconsideration of the qubit layout. The noise affecting spin qubits has further peculiarities such as the strong bias towards dephasing. In this work we consider state-of-the-art error correction codes that require only nearest-neighbour connectivity and are amenable to fast decoding via minimum-weight perfect matching. Compared to the surface code, the XZZX code, the reduced-connectivity surface code, the XYZ2 matching code, and the Floquet code all bring different advantages in terms of error threshold, connectivity, or logical qubit encoding. We present the spin-qubit layout required for each of these error correction codes, accounting for reference qubits required for spin readout. The performance of these codes is studied under circuit-level noise accounting for distinct error rates for gates, readout and qubit decoherence during idling stages. |
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A Digital Twin for Quantum Dot Arrays
Tara Murphy1, Giovanni Oakes2, Katarina Brlec2, James Williams2, Andrew Fisher3, Henry Moss4, Fernando Gonzalez Zalba2, David Wise2 1University of Cambridge, Quantum Motion Technologies, 2Quantum Motion Technologies, 3Quantum Motion Technologies, UCL, 4University of Cambridge Abstract: Spins in semiconductor quantum dots represent a very large-scale integration route for quantum computing hardware. To better understand the complexity of these systems as they scale up and design algorithms to automatically navigate their multidimensional voltage spaces, many efforts have been devoted to creating quantum dot array simulators. These simulators are typically based on the well-established Constant Interaction (CI) model. Although a good first approximation, this model fails to capture key experimental features of these systems. Besides, such simulators focus on charge occupancy or direct current signals, and hence cannot be directly matched to the output of rapid measurement techniques such as radio-frequency (RF) reflectometry. Here, we present a physics-based quantum dot array simulator capable of realistically replicating the outputs of RF-reflectometry measurements by calculating tunnel rates for different charge transitions. Furthermore, we utilise Poisson-Schrödinger simulations of prototypical MOS quantum dot devices to inform voltage dependencies for tunnel couplings and capacitance matrices, linking device geometry to RF-reflectometry outputs. Implemented in JAX, an accelerated linear algebra library, our simulator also facilitates rapid computation and generation of large, realistic datasets. Auto-differentiation enables integration into machine learning and auto-tuning frameworks for future applications. The simulator provides the users with the flexibility to tailor the measurement setup to their specific quantum dot arrangements and sensor placements. Our work contributes to bridging the gap between experimental, modelling, and computational approaches, providing researchers with a valuable tool for exploring quantum dot devices, training quantum engineers, and advancing the field of machine learning algorithms and autotuning for quantum devices. |
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Quantum simulation of a 2D Fermi-Hubbard model with silicon quantum dots in Si/SiGe
Ning Wang, Jia-Min Kang, Wen-Long Lu, Bao-Chuan Wang, Guo-Ping Guo University of Science and Technology of China Abstract: Semiconductor quantum dots are promising candidates for realizing both practical quantum computation and quantum simulation by harnessing the potential scalability using advanced semiconductor manufacturing techniques. For quantum simulation, quantum dots have served as small-scale simulators for exploring many-body physics, such as Mott transition, Nagaoka ferromagnetism, and topological states. Despite these simulators primarily being employed in semiconductor materials such as gallium arsenide, planar germanium, and donors, there has been a noticeable lack of application in planar silicon. Moreover, parameter tunable 2D quantum dot arrays are manifestly more widely applicable in both digital and analog quantum simulations, yet there is also currently a lack of relevant experimental explorations. As a demonstration of quantum simulation using 2D silicon quantum dot array, we present here a small-scale quantum simulator utilizing a gate-defined 2×2 quantum dot array fabricated on Si/SiGe heterostructure to simulate an extended 2D Fermi–Hubbard model. The dot array exhibits excellent tunability, enabling us to achieve independent control over Hamiltonian parameters, including electron filling and tunnel coupling. We measure the quantum transport behavior at low-temperature through both charge sensing and DC transport. By tuning the nearest-neighbor tunnel couplings from weak to strong regime, we observed the emergence and collapse of the collective Coulomb oscillations, indicative of a transition process from localization to delocalization. This behavior is analogue to the interaction-driven Mott metal-to-insulator transition, albeit in a finite-size system. Furthermore, our device architecture allows for controlled introduction of diagonal coupling, offering promising avenues for investigating Mott physics in the presence of frustration, which is pivotal for understanding various emergent phenomena such as high-Tc superconductivity and quantum spin liquids. |
| Qubit array (3+ qubits) |
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Micro- and nanomagnet stray field investigation for manipulation of spin qubits
Michele Aldeghi1, Rolf Allenspach1, Andriani Vervelaki2, Daniel Jetter2, Floris Braakman2, Martino Poggio2, Gian Salis1 1IBM Research Zurich, 2University of Basel Abstract: The stray field of micromagnets is often exploited to manipulate the spin state of electrons confined in semiconductor quantum dots. Recent devices use micromagnet shapes that have been engineered on the assumption of a uniform magnetization (macrospin) in the entire volume of the magnet. At the fields typically used for spin qubits experiments magnetization is however not uniform, implying significant deviations of the stray field from the designed values and thus compromising manipulation speed and single qubit addressability (Panel a). We quantify these deviations from a uniform magnetization pattern, highlighting the influence of magnet shape, material and crystallinity on different magnet designs by comparing micromagnetic simulations, SQUID microscopy and spin qubit experiments. We find that magnetocrystalline anisotropy and fabrication related imperfections are the biggest sources of stray field variability, leading to modulations of up to 0.5 GHz in Larmor frequency. We map the out-of-plane stray field of iron micromagnets, finding large driving gradients (> 1 mT/nm) but also non-negligible variations (> 5 mT) along the surface of the magnets due to magnetocrystalline anisotropy, surface roughness and incomplete magnet saturation (Panel b). To minimize these variations we propose a paradigm shift towards iron nanomagnets, as a viable alternative to currently used micromagnet designs. We present nanomagnet designs that provide large driving gradients (3 mT/nm), low dephasing and Larmor frequency differences > 2 GHz between neighboring qubits arranged on two dimensional arrays. |
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Universal control and benchmarking of four singlet-triplet qubits
Xin Zhang1, Elizaveta Morozova2, Maximilian Rimbach-Russ1, Daniel Jirovec3, Tzu-Kan Hsiao4, Pablo Cova Fariña1, Chien-An Wang1, Stefan Oosterhout5, Amir Sammak5, Giordano Scappucci6, Menno Veldhorst1, Lieven Vandersypen1 1QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2QuTech, TU Delft, 3TU Delft/ QuTech, 4National Tsing Hua University, 5QuTech and Netherlands Organisation for Applied Scientific Research (TNO), 6TU Delft, QuTech Abstract: With high-fidelity readout and control, single-spin qubits in semiconductor quantum dots present a highly promising platform suitable for fault-tolerant quantum computing. However, significant challenges persist for scaling such systems. Two of these challenges include the utilization of Pauli spin blockade (PSB) readout, which only gives 1 qubit information out of 2 qubits in a single shot, and the presence of microwave crosstalk, which is aggravated in larger quantum dot arrays. In this context, spin qubit encodings which are controlled by baseband control signals, are worthwhile to explore [1,2]. Here, we revisit the singlet-triplet qubit in germanium quantum dots and demonstrate universal control of 4 interacting singlet-triplet (S-T-) qubits with baseband-controlled pulses only [1]. All four qubits can be simultaneously initialized, individually controlled, and sequentially measured using PSB at magnetic fields as low as 5 mT. The average singlet-qubit gate fidelities are all well above 99%, measured with randomized benchmarking, as shown below. Furthermore, we investigate swap-like two-qubit gate operations to entangle neighboring qubits, yielding Bell state fidelities ranging from 74% to 89.7%. These results are on par with previous results for singlet-triplet (S-T0) qubits in GaAs, but with a twice larger qubit count. Future work will be focused on studying crosstalk, which will be important to assess the scaling potential of this approach. |
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Low-frequency stability of semiconducting spin qubits in silicon
Kenji Capannelli1, Brennan Undseth2, Eline Raymenants3, Irene Fernandez de Fuentes1, Florian Unseld1, Sergei Amitonov4, Larysa Tryputen1, Amir Sammak4, Giordano Scappucci1, Lieven Vandersypen1 1TU Delft, QuTech, 2Delft University of Technology, 3QuTech, 4Equal1 Abstract: Recent achievements for semiconductor spin qubits in silicon include high-fidelity two-qubit gates and universal control of 6 qubits in a linear array. However, the ability to perform high-fidelity algorithms for an extended period of time is impacted by the presence of low-frequency noise and requires constant recalibration of qubit control parameters. In this work, we focus our attention onto the impact of low-frequency noise on the qubit frequencies in the context of performing single-qubit gates via EDSR driving with a micromagnet gradient field. We probe the stability of the qubit frequencies in two devices, a linear 6-dot array (6D2S) and a 2x2 array, utilising Ramsey-like experiments to track the drift in qubit frequencies over several hours and collecting drift data over a period of several months. We find that the qubit frequency deviations are consistent over time and remain below the drift threshold for implementing an efficient Xπ/2 rotation with 99.99% fidelity, showcasing a remarkable long-term stability of qubit frequencies. We also observe a subset of qubits with a strong coupling to a local two-level fluctuator and instances of large discrete jumps in qubit frequency, which would reduce the Xπ/2 rotation fidelity to 99.948% and 99.917% respectively. Plotted in the figure is the average 1-hour frequency deviation observed for qubits in both the 6D2S (left) and 2x2 (right) devices. Error bars correspond to the minimum and maximum deviation observed within a 1-hour time interval, with total data collection time varying between 14-42 hours. We can notice the difference in frequency deviations from dot-to-dot and a systematically higher qubit frequency drift in the 2x2 device when compared to the 6D2S device. We further perform spectral analysis of the obtained time traces and find 1/f-like noise spectra and characterise this behaviour across different dots, devices and days. |
| Readout |
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Gate-Dispersive Readout of a Ge/Si Core/Shell Nanowire Quantum Dot at Perfect Impedance Matching
Simon Svab1, Rafael Eggli1, Taras Patlatiuk1, Erwin Franco Diaz1, Dominique Trüssel1, Miguel Carballido1, Pierre Chevalier Kwon1, Ang Li2, Erik Bakkers2, Andreas Kuhlmann1, J. Carlos Egues3, Stefano Bosco4, Daniel Loss5, Dominik Zumbühl1 1University of Basel, 2TU Eindhoven, 3University of Basel, Universidade de Sao Paulo, 4TU Delft, University of Basel, 5University of Basel, CEMS RIKEN Abstract: Radio frequency reflectometry enables high bandwidth readout of semiconductor quantum dots. Impedance matching is crucial for sensitivity but challenging at cryogenic temperatures. Gallium arsenide varactor diodes are typically used but fail below 10K and in magnetic fields. We explore a compact, scalable varactor based on strontium titanate with similar capacitance tunability. It achieves robust, temperature and field-independent matching down to 11mK and up to 2T in-plane field. We demonstrate gate-dispersive charge sensing with a Germanium/Silicon core/shell nanowire quantum dot and furthermore characterize a dispersive signature of Pauli spin blockade, paving the way towards gate-dispersive single-shot spin readout. *Supported by NCCR SPIN, FET-open TOPSQUAD, SNSF, SNI, EMP. |
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Analysis of a Simultaneous Gate-Based Reflectometry Readout of Multiple Spin Qubits Using a Multi-Tone Frequency Generator
Mathilde Ouvrier-Buffet1, Alexandre Siligaris2, José Luis Gonzalez Jimenez3, Mathieu Darnas4, Baptiste Jadot5, Tristan Meunier6 1CNRS, Institut Neel, Univ. Grenoble Alpes, Grenoble, France, 2CEA-LETI, Univ. Grenoble Alpes, Minatec Campus, Grenoble, France, 3CEA-LETI,Univ. Grenoble Alpes, Minatec Campus, Grenoble, France, 4CNRS Néel Institute, Univ, Grenoble Alpes, 5Univ. Grenoble Alpes, CEA, Leti, F-38000 Grenoble, France, 6Quobly, CNRS, Institut Néel, Univ. Grenoble Alpes,Grenoble, France Abstract: Silicon based quantum technologies are attractive for large-scale integration. In this context it is interesting to study fast and compact readout techniques. One main challenge is to scale-up the experimental setup, by reducing the wiring density used to down drive signals to individual qubits, to increase the volume of qubits for simultaneous access. In this perspective, exploring the specific RF requirements for Si-based qubits readout is necessary. This work provides a thin understanding of dispersive readout based on conventional measurement setups through an analytical definition of the detected quantum state. The phase-shift separating the states estimation is based on the study of a tank resonator directly connected to the gate defining the quantum dot and capacitively coupled to a 50 Ω feedline. This model takes account of physical characteristics of coldplaced resonator. Therefore, it allows full resonator design according to the phase-shift as well as reflected and absorbed power. This work also provides an in-depth analysis, based on an industrial standard modelling, of multi-qubit reflectometry measurements, integrating low-temperature frequency demultiplexing and innovative multi-frequency synthesis to drive the injection signals. The measurement chain analysis, in addition to highlighting the well-known impact of LNA noise, is focus on the incidence, of demultiplexer sizing and powers involved in the setup, on readout performances as SNR shown in Figure 1.(a). Finally, we present the multi-tone synthesis enabling simultaneous generation of 2 to 10 frequencies with the same spectral spacing. This circuit, designed in 45nm CMOS SOI technology, is based on harmonic oscillators recombination (Figure 1.(b)) operating in the sub-10GHz range and injected by the same low frequency reference signal adjustable from 250 MHz to 1 GHz. It reaches a power difference over channels of the order of 0.2 to 2 dB, while benefiting from good noise performances for a 0.27 mm2 area. |
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Floquet theory of longitudinal readout with cavity photons
Alessandro Chessari1, Esteban Rodriguez-Mena1, J. C. Abadillo-Uriel2, Victor Champain1, Simon Zihlmann1, Romain Maurand1, Yann-Michel Niquet3, Michele Filippone1 1CEA Grenoble, 2Instituto de Ciencia de Materiales de Madrid, 3CEA/IRIG/MEM/L Sim Abstract: In the context of circuit quantum electrodynamics (cQED), fast qubit measurements rely on the mechanism of dispersive readout: a transverse interaction between the two lowest levels of a superconducting artificial atom and a resonator shifts the frequency of the resonator, enabling quantum non-demolition (QND) measurements. Recently, a longitudinal interaction had been proposed as a way to perform faster-than-dispersive measurements in superconducting qubits. However, mechanisms to achieve such interaction are nowadays hard to connect, as they stem from distinct theoretical frames, adopting different approximations. Such situation calls for a unified description, embracing different devices and regimes. We devise a Floquet theory to establish a universal connection between AC Stark shift, longitudinal coupling and dispersive readout in cQED. We find that when a qubit transversally coupled to a resonator is driven at the resonator frequency, the resonator probes the Floquet spectrum of the qubit at the drive amplitude. An effective longitudinal interaction then arises from the slope of the Floquet spectrum while a dispersive shift arises from the curvature. We derive semi-analytical results supported by exact numerical calculations, which we apply to superconducting and spin cQED settings, providing a unifying, seamless and simple description of longitudinal and dispersive readout in generic cQED systems. Our approach unifies the adiabatic limit, where the cavity dynamics is so slow that the longitudinal coupling results from the static spectrum curvature, with the diabatic one, where the static spectrum plays no role. We find that resonances between different replicas in the Floquet spectrum lead to a degradation of the readout in the adiabatic regime and to the ionization of the qubit. On the other hand, diabatic readout is equally effective, with the advantage to avoid multi-photon processes. |
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Challenges and solutions for RF reflectometry techniques in accumulation mode silicon MOS devices.
Scott Liles1, Isaac Vorreiter2, Joe Hillier2, Krittika Kumar2, Santiago Serrano3, Steve Yianni3, Kok Chan3, Wee Han Lim3, Fay Hudson3, Andrew Dzurak3, Alex Hamilton2 1University of New South Wales, 2UNSW, 3Diraq, Sydney, NSW, Australia Abstract: Radio frequency (RF) reflectometry techniques allow extremely fast and sensitive electrical measurements of quantum devices [1]. However, not all quantum device structures are equally suited for RF techniques. In particular, accumulation-mode devices in MOS silicon have traditionally presented a challenge for implementing RF reflectometry [2-4]. A primarily issue when performing RF measurements of accumulation-mode devices stems from the large parasitic capacitance between the electron (or hole) gas and the overall accumulation gate (or top gate TG). This capacitance between the electron gas and the accumulation gate provides a low-impedance path to ground, which causes unwanted reflections of the RF signal. Furthermore, the high resistivity of MOS silicon causes further unwanted reflections of the RF signal within the leads (and ohmic contacts) of the device. As a consequence, RF measurements of accumulation devices tend to be primarily sensitive to the parasitic capacitance of the electron (or hole) gas, and not necessarily the region under study, such as the quantum dot. In this work we study RF reflectometry measurements of a single electron transistor formed in an accumulation-mode silicon MOS device. We investigate two methods for overcoming the existing challenges. Firstly, we modify the circuit design to decouple the accumulation gate from the RF ground, which suppresses unwanted reflections of RF signal [2,3]. Secondly, we implement a ‘split-gate' design [4] for the accumulation gate (Figure 1a,b), allowing the RF response to be sensitive primarily to the impedance of the RF-SET (Figure 1c). By combining these two techniques we show a significant enhancement in RF reflectometry measurements of accumulation-mode MOS silicon devices. [1] Vigneau, F.,et al. (2023). Applied Physics Reviews. [2] Taskinen, L. J., et al. (2008). Review of Scientific Instruments. [3] MacLeod, S. J., et al. (2014). Applied Physics Letters. [4] Liu, Y. Y., et al. (2021). Physical Review Applied. |
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Split-gate Radio-Frequency Reflectometry in Si-MOS gate-defined Quantum Dots
Sheng-Kai Zhu, Ning Chu, Hai-Ou Li University of Science and Technology of China Abstract: Radio frequency (RF) detection circuits are widely used for rapid and high-fidelity detection of charge and spin states in semiconductor quantum dots. However, the commonly used method of applying RF signal from ohmic contacts has several problems: leakage of RF signals due to the capacitances between the accumulation gates and the two-dimensional electron gas beneath it, along with the dissipation of RF signals caused by the resistance of the two-dimensional electron gas. For the first time, we have adopted the split gate method in the Si-MOS quantum dot system, splitting the accumulation gate into two parts and applying the RF signal from the split accumulation gate. This method not only utilizes the original leakage channel as a coupling channel but also avoids the problem of dissipation resistance. Thereby, we achieve RF reflectometry when the ion implantation area is more than 80μm away from the SET, and achieve a charge detection with a fidelity above 99% in an integration time of 140ns. |
| Shuttling |
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Hole Flying Qubits in Quantum Dot Arrays
David Fernández1, Yue Ban2, Gloria Platero1 1ICMM-CSIC, 2UC3M Abstract: Recent advancements in semiconductor Quantum Dot Arrays (QDAs) have propelled the field towards greater scalability, unlocking applications in quantum computation, information processing, and simulation. Notably, hole spin qubits have garnered attention for their minimal hyperfine interaction and intrinsic Spin-Orbit Interaction (SOI). This study investigates QDAs as quantum links, facilitating information transfer between distant dots. Despite the increasing popularity of long-range transfer protocols [1], the advantages of SOI in QDAs are largely untapped. We propose a novel method employing Shortcuts to Adiabaticity (STA) protocols to implement hole-flying qubits in QDAs. Our investigation demonstrates the tunability of hole spin rotation during transfer by adjusting the number of dots and SOI via external electric fields (Fig. (a)). This tunability controls the rotated angle and modulates the rotation vector. We employ a sequence of up to three long-range transfers to simultaneously implement a general one-qubit gate (Fig. (c)). The generation of entangled pairs between distant sites can be sped up using quantum gates in parallel to the transfer (Fig. (d)). The low population of intermediate sites protects the qubit against possible electric fluctuations acting over the QDA. Furthermore, we propose strategies to mitigate dephasing effects, integrating dynamical decoupling protocols during the transfer process (Fig. (b)). These findings extend to systems with multiple interacting particles, enabling long-range quantum entanglement distribution. Additionally, we demonstrate long-range spin transfer in half-filled QDAs, leveraging SOI in combination with high magnetic fields to establish dark states that prevent the population of intermediate states. Our study advances the understanding of long-range transfer in QDAs, addressing critical aspects for practical quantum computation. We propose QDAs to overcome scalability issues, employing them as quantum links to interconnect computing nodes in a sparse architecture of a quantum chip. [1] Y. Ban, et al., Nanotech. 29, 505201 (2018). |
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2D Spin-Qubit Architecture for Surface Code Error Correction using Multi-Electron Couplers
Rubén Otxoa, Frederico Martins, Normann Mertig, Charles Smith Hitachi-Cambridge Abstract: Spin-qubits are an appealing quantum computation platform, due to their long and stable coherence times. A central point of a quantum computer, is not only its computational advantage for certain problems, but also its propensity to have errors. Therefore error correction techniques have become a pivotal point in developing large-scale fault-tolerant quantum computers. Here, we propose a two-dimensional spin-qubit architecture implementing surface code error correction. At the centre of the proposal are multi-electron quantum dots which are used as couplers to mediate interactions among spin-qubits in two dimensions. The couplers induce a Heisenberg exchange, preserving speed and coherence of the resulting spin–qubit interaction. The quantum dots hosting spin qubits are addressed by the experimentally demonstrated ability to precisely control voltage signals [1]. In the proposed architecture, the connection of qubits and couplers is incorporated to allow for 2D connectivity between cells (see Figure 1A). The repeating unit cell pattern creates connection islands where electrical contacts are made for the classical control electronics as depicted in Figure 1B. A major benefit of this approach is that the interconnect wiring density is drastically reduced. We then show how the proposed architecture is used to operate a surface code. In summary, this makes our proposal a promising contender for implementing large-scale quantum simulations. |
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Charge shuttling in a FDSOI quantum dot array
Guillermo Haas1, Mathieu Toubeix2, Pierre Hamonic1, Eric Eyraud1, Matthieu Dartiailh3, Bruna Cardoso Paz3, Benoit Bertrand4, Heimanu Niebojewski4, Maud Vinet3, Tristan Meunier5, Matias Urdampilleta6 1Neel Institute CNRS Grenoble, France, 2CEA-LIST, 3Quobly, Grenoble, France, 4CEA-LETI Grenoble, France, 5Neel Institute CNRS, Quobly, Grenoble, France, 6Cnrs Abstract: Connecting solid state quantum nodes requires the development of coherent link to transfer quantum information. In this context, few strategies have been explored going from optical and microwave photon interfaces to physical displacement of the qubits. In this poster, we demonstrate preliminary results of single electron transfer in quantum dot array fabricated in 300mm foundry. For this purpose, we have used isolated double quantum dots as quantum nodes read by gate-based reflectometry combined with fast charge shuttling between the nodes using a bucket brigade method. We demonstrate single and multiple charge transport between consecutive nodes. We believe that the combination of charge shuttling between isolated double quantum dots and our previous demonstration of coherent control in a single node opens the way for a scalable quantum architecture in silicon. |
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Conveyor-mode shuttle tomography for potential disorder mapping of a quantum bus in Si/SiGe
Ran Xue1, Max Beer2, Inga Seidler3, Simon Humpohl4, Jhih-Sian Tu5, Stefan Trellenkamp5, Tom Struck4, Hendrik Bluhm4, Lars Schreiber3 1RWTH Aachen University, Aachen, Germany, 2JARA Institute for Quantum Information - RWTH Aachen University, 3JARA Institute for Quantum Information, 4RWTH Aachen University; ARQUE Systems GmbH, 5Helmholtz Nano Facility (HNF), FZJ Abstract: Coupling qubits within a monolithic qubit-array is one of the most promising approaches for building scalable quantum computers on a Si/SiGe heterostructure. However, the homogeneity of the electrostatic potential poses obstacles to scalability and to robust long-range coupling of qubits and induces characterization overhead. The quantum bus (QuBus) based SpinBus architecture [1] promises the feasibility of coupling qubits by shuttle electrons in conveyer-mode i.e. the electron is adiabatically transported while confined to a propagating sinusoidal potential in a gate-defined quantum channel, despite of the presence of local charged defects [2, 3]. Using a 10 μm long QuBus, we experimentally demonstrate an all-electrical tomography technique namely the shuttle tomography. It opens up new possibilities for probing local potential variations in the Si/SiGe heterostructure by varying the shuttle confinement as a function of the electron position [4]. In addition, it enables the detection of potential imperfections in an electrostatic setting, which is very similar to typical qubit potentials. We present a second method for characterizing electrostatic disorder being sensitive to correlation lengths longer than the QD distance. |
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Numerical simulation of coherent spin-shuttling in silicon devices across dilute charge defects
Arnau Sala1, Nils Ciroth1, Lasse Ermoneit2, Thomas Koprucki2, Markus Kantner3, Hendrik Bluhm1, Lars Schreiber1 1JARA Institute for Quantum Information, 2WIAS Berlin, 3Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Abstract: Recent advances in coherent conveyor-mode spin qubit shuttling are paving the way for large scale quantum computing platforms with long- and mid-range connectivity, which can only be achieved with high quality spin qubit shuttles that preserve quantum coherence [1]. Owing to this limitation, we investigate numerically the impact of electrostatic disorder on the coherence of a spin qubit in Si-based devices. To this end, we model different Si/SiGe and Si-MOS heterostructures and electrostatic gate layouts and simulate the conveyor-mode shuttling of an electron under the influence of dilute charge defects placed randomly in close proximity to the shuttle lane (see Fig. 1). In our analysis we consider different locations of a single charge defect with respect to the center of the shuttle lane, multiple orbital states of the electron in the shuttle with g-factor differences between the orbital levels, orbital relaxation induced by electron-phonon interaction, and different shuttling velocities. We solve the time-dependent dynamics of the shuttled electron using a density matrix formalism and investigate under which conditions the qubit accumulates a larger nondeterministic phase. Our study will serve to better identify the critical charge defect density of the heterostructure for conveyor-mode spin qubit shuttle devices and quantify their impact on the coherence of a qubit. [1] V. Langrock, J. A. Krzywda, N. Focke, I. Seidler, L. R. Schreiber, and Łukasz Cywiński, Blueprint of a Scalable Spin Qubit Shuttle Device for Coherent Mid-Range Qubit Transfer in Disordered Si/SiGe/SiO2, PRX Quantum 4, 020305 (2023). |
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Coherent electron-spin shuttling for mapping valley splitting in Si/SiGe quantum devices
Mats Volmer1, Malte Neul1, Tom Struck1, Isabelle Sprave1, Arnau Sala1, Laura Diebel2, Lukas Zinkl2, Lino Visser1, Lukasz Cywinski3, Dominique Bougeard2, Hendrik Bluhm1, Lars Schreiber1 1JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, Germany, 2Fakultät für Physik, Universität Regensburg, 93040 Regensburg, Germany, 3IF PAN Abstract: Electron shuttling is a promising method for establishing long-ranged connectivity in spin qubit chips. Recently, a new utility of spin shuttling [1] for material characterization has been discovered. We can use coherent electron shuttling to map out different local material parameters such as the variation of the electron g-factor [1] and the valley splitting [2]. Low valley splitting is one of the most significant challenge to the operability and scalability of electron spin qubits as it limits coherence via spin-valley hotspots or uncontrolled valley excitations [3]. Traditional techniques for characterizing valley splitting, such as magnetospectroscopy [4], are thorough yet time-intensive and lack the necessary spatial and energy resolution for effective local assessment. We demonstrate a novel method [2] leveraging conveyor-mode spin-coherent electron shuttling [1] for two-dimensional mapping of local valley splitting. Our approach utilizes an Einstein-Podolsky-Rosen (EPR) spin-pair to detect magnetic field-dependent anticrossings between ground and excited valley states. It achieves sub-µeV energy accuracy and nanometer-scale lateral resolution, offering a faster alternative with comparable precision to established methods. One area of device improvement potential is the fabrication of ion implanted Ohmic contacts, which currently relies on a high temperature annealing step for dopant activation. This step leads to Germanium diffusion into the quantum well which reduces the effectiveness of new heterostructure designs. To reduce the thermal load in the active qubit region, we developed a local annealing process using a laser as an alternative to global furnace annealing to preserve the interface sharpness in the heterostructure as grown [5]. [1] T. Struck ea., Nat. Commun. 15, 1325 (2024). [2] M. Volmer, T. Struck ea., arXiv: 2312.17694 (2023). [3] V. Langrock, J. A. Krzywda ea., PRX Quantum 4, 020305 (2023). [4] J.P. Dodson ea., Phys. Rev. Lett. 128, 146802 (2022). [5] M. Neul et al., Phys. Rev. Mater. 8, 043801 (2024). |
| Spin-photon coupling |
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Flopping-mode spin qubit in driven germanium and silicon planar double quantum dot
Yaser Hajati and Guido Burkard University of Konstanz Abstract: Semiconductor quantum dots, with confined electron or hole spins, hold promise for quantum information processing due to their efficient electric field-driven qubit manipulation. However, susceptibility to noise poses a challenge that may hinder qubit effectiveness. Here, we explore the impact of charge noise on a planar double quantum dot spin qubit under AC gate influence, focusing on the flopping-mode spin qubit with spin-orbit interaction. Employing a rotating wave approximation within a time-dependent Schrieffer-Wolf effective Hamiltonian, we derive analytic expressions for the Rabi frequency of single electron or hole double quantum dot spin qubit oscillations. Our findings reveal that strategically driving the qubit off-resonance effectively mitigates charge noise influence, leading to dynamic sweet spot manifestation. This modulation significantly improves quantum gate fidelity, particularly within specific drive parameter ranges and detuning during qubit manipulation. Furthermore, our study unveils the potential of inducing a second-order dynamic sweet spot in the proposed qubit, tunable by drive and double quantum dot parameters. Understanding the importance of driving qubits off-resonance is crucial for developing high-coherence planar double quantum dot spin qubits, both for electrons in silicon and holes in germanium. |
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Pulsed electron spin resonance protocols for quantum memory applications
Patricia Oehrl1, Florian Fesquet1, Nadezhda Kukharchyk2, Kirill Fedorov2, Rudolf Gross2, Hans Huebl2 1Walther-Meissner-Institut, Technical University Munich, 2Walther-Meissner-Institut, Technical University Munich, Munich Center for Quantum Science and Technologies Abstract: The storage of quantum states is one of the key elements for future multimode quantum networks, which enable various applications, such as secure communication and distributed quantum computing [1]. In order to avoid frequency conversion between multiple quantum nodes, several requirements have to be met, including frequency compatibility and connectability between the chosen quantum systems. Solid-state spin ensembles, such as phosphorus donors in silicon demonstrate exceptional coherence times and resonant transitions in the GHz range, and thus are promising candidates for the realization of quantum memories compatible with superconducting circuits [2]. Here, we present an experiment exploring quantum memories in a hybrid system consisting of a superconducting lumped-element microwave resonator coupled to a phosphorus donor electron spin ensemble hosted in silicon at millikelvin temperatures. We analyze this system with respect to the characteristic coupling strength, loss rates, as well as coherence times. In detail, we investigate the storage efficiency of coherent microwave signals based using pulsed electron spin resonance protocols with different shapes of the input pulse, as shown in the figure. We evaluate our measurement results using an input-output model. To this end, we quantify the overall performance of our hybrid system, consisting of the microwave resonator and spin ensemble. Finally, we present an experimental setup and first results towards storing quantum states in our hybrid system. Here, we use Josephson parametric amplifiers to generate squeezed microwave states, which are later coupled to our spin ensemble and extracted using the spin echo sequence. [1] M. Pompili et al., Science 372, 6539 (2021) [2] M. Steger et al., Science 336, 1280 (2012) We acknowledge support by the German Research Foundation via Germany's Excellence Strategy (EXC-2111-390814868), the German Federal Ministry of Education and Research via the project QuaMToMe (Grant No. 16KISQ036). This research is part of the Munich Quantum Valley. |
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Spin circuit QED in the time-domain
Tobias Bonsen, Xiao Xue, Jurgen Dijkema, Guoji Zheng, Sander de Snoo, Amir Sammak, Giordano Scappucci, Lieven Vandersypen QuTech, TU Delft Abstract: Semiconductor spin qubits hold promise for quantum computation due to their long coherence times and potential for scaling. So far, interactions between spin qubits are limited to spins a few hundreds of nanometers apart. A distributed architecture with local registers and long-range couplers will be needed to scale up to millions of qubits. Circuit quantum electrodynamics can provide a pathway to realize interactions between distant spins. In this poster, we present our realization of long-range spin-spin interactions using an on-chip superconducting resonator in two regimes. First with two spins detuned from the resonator frequency, allowing the demonstration of two-qubit iSWAP logic via virtual photons. Next, we tune the two spin frequencies to match the resonator frequency and demonstrate spin state-transfer using real resonator photons. We first show universal single-qubit control over two distant spin qubits separated by 250 µm and characterize their coherence times. Next, we couple the two spins via virtual photons in a superconducting resonator, and show two-qubit logic between the distant qubits with the interaction strength characterized by the iSWAP oscillation frequency. This frequency is consistent with spectroscopic measurements. Furthermore, we demonstrate that the coupling strength as well as the coherence times of the qubits can be tuned by the inter-dot tunnel coupling and the spin-cavity detuning. Finally, we operate the system in a regime where the two spins are resonant with the resonator. Here, we show coherent spin-photon oscillations (vacuum Rabi oscillations) and utilize this to demonstrate spin-state transfer in this resonant spin-photon regime. In future work we intend to implement single-shot readout and improve the spin lifetimes while coupled to the resonator. These results pave the way for scalable networks of spin qubits on a chip. |
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Triple quantum dot coupled to tunable Josephson junction array resonator in 28Si/SiGe
Young uk Song1, Seungbum Woo1, Wonjin Jang2, Jaemin Park1, Franco Palma2, Fabian Oppliger2, Elena Acinapura2, Radha Krishnan2, Lucas Stehouwer3, Davide Esposti3, Giordano Scappucci3, Pasquale Scarlino2, Dohun Kim1 1Seoul National University, 2EPFL, 3TU Delft, QuTech Abstract: Coupling distant spin qubits via a superconducting resonator is a promising method to enhance the scalability and connectivity of semiconductor quantum processors. While early studies indeed demonstrated strong coupling of charge and spin degree of freedom to microwave photons, the development of a novel device structure is motivated by the need to enhance the resonator's impedance which can lead to improved coupling strength. In this presentation, we present semiconductor/superconductor hybrid devices of gate-defined triple quantum dots galvanically coupled to a tunable and high-impedance Josephson junction array resonator (Fig. 1). We discuss considerations for high-yield fabrication of the following key components: quantum dot array with overlapped gate design on an isotopically purified 28Si/SiGe heterostructure and built-in low-stray-capacitance quantum dot charge sensor compatible with rf-reflectometry, the tunable Josephson junction array resonators with optimized Josephson inductance, and various filter designs in the gate electrodes for minimizing photon loss. We also present preliminary measurement results of quantum dot formation, tunability of the resonator with an in-plane magnetic field, and coupling between charge or encoded spin qubit states and microwave photons of the resonator. |
| Valleys or hole physics |
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Optimized field-effect control of 2D hole gases in shallow Ge/GeSi quantum wells
Jakob Walsh1, Pauline Drexler1, Rudolf Richter1, Eleonora Buchholz1, Dominique Bougeard2 1Institut für Experimentelle und Angewandte Physik, Fakultät für Physik, Universität Regensburg, 2Institut für Experimentelle und Angewandte Physik, Fakultät für Physik, Universität Regensburg Abstract: Field-effect-controlled, undoped Ge/GeSi quantum well (QW) heterostructures have recently emerged as a promising platform for quantum technology applications, such as the implementation of spin qubits or gate-tunable Josephson junctions. In current devices, the gate dielectric is typically deposited onto the semiconductor heterostructure post-epitaxy, hence involving contact of the latter with air. At the same time, studies correlating the field-effect control for example with the nature of the dielectric or with surface treatments of the Ge/GeSi heterostructure before the deposition of the dielectric are scarce. Here, we present a systematic study of the field-effect control of two-dimensional hole gases (2dhg) in Ge/GeSi QWs. From our results, we postulate that the presence of a large amount of dangling bonds at the surface of the semiconductor heterostructure under oxidizing conditions induces interface defects which impede the field-effect control of the 2dhg. This experimentally manifests in tunneling from the QW towards the interface starting already at low hole densities, immediately after 2dhg accumulation, causing reduced capacitive coupling of the gate to the 2dhg. Additionally, accumulation current instabilities with time constants of the order of minutes are observed. We show that the design of the heterostructure cap, in combination with a suitable surface treatment before the deposition of the gate dielectric, optimize the capacitive coupling and suppress tunneling from the 2dhg towards the interface to the dielectric, even for QWs buried less than 50 nm below the interface. We also find the variability in the accumulation thresholds and accumulation current instabilities to be reduced. |
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In situ-grown superconducting thin films on surface-near GeSi/Ge quantum wells for gate-tunable superconducting quantum circuits
Pauline Drexler1, Vera Weibel2, Luigi Ruggiero2, Christian Olsen2, Marcus Wyss3, Alexander Vogel3, Andrea Hofmann2, Dominique Bougeard4 1Institut für Experimentelle und Angewandte Physik, Fakultät für Physik, Universität Regensburg, 2Departement Physik, Universität Basel, 3Nano Imaging Lab, Swiss Nanoscience Institute, University of Basel, 4Institut für Experimentelle und Angewandte Physik, Fakultät für Physik, Universität Regensburg Abstract: Two-dimensional hole gases (2DHG) in germanium have recently been identified as a promising platform for the realization of field-effect controlled Josephson junctions, which could be used to realize innovative superconducting qubit concepts and novel cryoelectronic elements in quantum circuits. A key ingredient of this functionality relies on superconducting reservoirs, which shall induce superconductivity into a segment of the gate-controlled 2DHG via proximity. Different strategies to interface superconducting thin films with 2DHG in germanium have recently been realized. Here, we present hybrid heterostructures with in situ-grown aluminium thin films on surface-near GexSi1-x/Ge/Ge0.8Si0.2 quantum wells (QWs). We use solid source molecular beam epitaxy (MBE), growing the semiconductor heterostructure and the superconducting thin film in dedicated MBE chambers, respectively. An ultrahigh vacuum connection between both chambers allows us to deposit the aluminium film onto the pristine, as-grown semiconductor surface. We have systematically varied the Ge concentration 0.8 <x |
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Valley physics and its influence on shuttling of spin qubits in Si/SiGe heterostructures
Guido Burkard and Jonas Lima University of Konstanz Abstract: Predicting and controlling the valley splitting and phase in silicon-based quantum dots is of critical importance for spin qubit control, shuttling, and scalability, and numerous experimental and theoretical studies have investigated the rich valley physics near the Si/SiGe heterointerface. We present a three-dimensional extended effective-mass theory which we apply to obtain the electron envelope function and to predict the spatially varying valley splitting EVS=2|Δ| and valley phase arg(Δ) of realistic disordered interfaces [1], see Figure (a). It turns out that the probability distributions p(Δ ) and p(EVS) of the complex inter-valley coupling and thus the valley splitting depend on the quantum dot size x0 and location [2], as shown in Figure (b). In the charge shuttling scenario, the spatially varying inter-valley coupling Δ shown in Figure (c) leads to an interesting modified Landau-Zener problem where the shuttling speed is not always limited by the valley splitting alone but by a combination of valley splitting and phase difference [3]. |
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Coulomb Blockade Spectroscopy of Holes in Ge/SiGe with a Charge Sensor
Lisa Sommer1, Inga Seidler1, Felix Schupp1, Stephan Paredes1, Stephen Bedell2, Patrick Harvey-Collard1, Gian von Salis1, Matthias Mergenthaler1, Thomas Ihn3, Andreas Fuhrer1 1IBM Research Europe - Zurich, 2IBM Quantum, T.J. Watson Research Center, 3Solid State Physics Laboratory, ETH Zürich Abstract: For the utilization of valence band holes in spin qubits, it is interesting to investigate the low lying energy states of the first few holes confined in a quantum dot. Here, the shape of the confinement potential is expected to strongly impact the related quantum properties. We use charge sensing of a double quantum dot in a strained Ge/SiGe quantum well (see Fig. a) to study the addition energy spectrum of one of the two dots as a function of magnetic field and hole number. By comparing with a Fock-Darwin model, we gain insight into the shell filling and asymmetry of the confinement potential. Using additional gate electrodes, we electrostatically shape the quantum dot to have a more or less symmetric two-dimensional confinement potential. Furthermore, sweeping the magnetic field orientation both in- and out-of-plane (see Fig. b) allows us to map the anisotropy of the g-tensor which, for B~1 T, is consistent with the previously published observations. A fit of the thermal broadening of the charge transition lines as a function of temperature facilitates the determination of the relevant virtual gate lever arms at B=0 T for each hole number when measuring the addition spectrum. Due to the large out-of-plane g-factor (g~11 in our case) for Ge/SiGe quantum wells, the Zeeman energy dominates over the orbital energy for magnetic fields B>1 T. At higher magnetic fields and spin states, the magnetic field dependence is up to 5 times larger than expected. We discuss these findings in light of possible multi-hole interaction effects and confinement potential shapes. |
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Leveraging the tunability of hole spin qubits
Stefano Bosco QuTech, TU Delft Abstract: Hole nanostructures are leading candidates for large-scale quantum computers due to their pronounced spin-orbit interactions (SOIs) and remarkable tunability. I will show various strategies for harnessing this tunability to enhance the performance of current hole spin qubits, with a focus on both silicon and germanium qubits. One avenue of exploration involves exploiting the tunable nature of hole spin qubits to mitigate the impact of charge and hyperfine noise, which directly influences the qubit decoherence time. By identifying optimal operating conditions, referred to as sweet spots, where such noise is effectively eliminated, the performance of the qubits can be significantly improved. Moreover, charge noise presents a significant obstacle for shuttling spins, a critical requirement to establish long-range connectivity between distant qubits. I will discuss how SOIs can induce intricate spin dynamics that effectively filter out low-frequency noise, thereby improving the efficiency of spin shuttling processes. Furthermore, the influence of SOIs extends to two-qubit gates, where exchange anisotropies, induced by these interactions, offer avenues for accelerating the execution of two-qubit gates without compromising fidelity. This implies that by leveraging the unique properties of SOIs, novel methods can be devised to expedite gate operations, paving the way towards large-scale spin based quantum information processing. |
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Single-Spin Polarimetry with Holes in Silicon
Lorenzo Peri1, Felix-Ekkehard von Horstig1, Monica Benito2, Christopher Ford3, M. Fernando Gonzalez-Zalba4 1Quantum Motion; University of Cambridge, 2University of Augsburg, 3University of Cambridge, 4Quantum Motion Abstract: Spins confined in semiconductor quantum dots (QDs) are promising candidates for quantum information processing. These systems are subject to spin-orbit coupling (SOC), which causes increased qubit variability but offers the enticing opportunity for all-electrical control, generating growing interest in hole-based architectures. However, the presence of SOC inevitably poses challenges. Particularly, for spin readout, it may lift Pauli spin-blockade (PSB) many readout schemes rely upon. We shed light, experimentally and theoretically, on the problem of spin-projective measurements in double QDs subject to SOC. We recast the dynamics of this system in terms of the simpler behaviour of a single spin travelling through an active medium, a process akin to photon polarimetry. By reframing the problem, we provide new insight on well-known concepts such as g-tensors misalignment, spin-conserving, and spin-flip tunnel couplings, offering a geometrical interpretation for SOC-induced avoided crossings and emphasising the conditions to avoid PSB lifting. We explore these concepts experimentally using a spin-orbit-coupled double QD, realised as a gate-defined QD tunnel-coupled to a Boron acceptor in a p-type silicon nanowire FET (a-b). We perform the single-spin equivalent of optical polarimetry by adiabatically connecting the (1,1) spin ground-state and the (0,2) spin-singlet of the Boron while monitoring the radio-frequency reflectometry signal for changing magnetic field direction (c-d). From the geometry behind PSB and its lifting arises a simple picture of how the blockade is modified by the presence of SOC, naturally leading to a figure of merit: the maximum achievable readout fidelity, quantifiable in terms of experimentally measurable device parameters such as g-tensor misalignment, and direction and magnitude of spin-flip tunnelling. This work poses a fundamental upper bound on PSB readout in the (inevitable) presence of SOC, acting as a cautionary tale for future QD quantum-computing architectures, particularly hole-based, and highlighting which parameters to focus on to mitigate its effect. |
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Exchange-driven two-hole spin qubit in Germanium
Jaime Saez-Mollejo1, Daniel Jirovec2, Stefano Bosco2, Maximilian Rimbach-Russ2, Yona Schell1, Josip Kukucka1, Andrea Ballabio3, Daniel Chrastina3, Giovanni Isella3, Georgios Katsaros1 1Institute of Science and Technology Austria, 2QuTech, TU Delft, 3L-NESS, Politecnico di Milano, Como Abstract: Germanium spin qubits have moved from the demonstration of coherent qubits [1-3] to the operation of a four-qubit processor [4], the implementation of the first steps towards error correction [5] and the exploration of larger-scale systems [6]. Spin manipulation can be achieved via Electron Spin Resonance [7], Electron Dipole Spin Resonance (EDSR) [8], g-Tensor Magnetic Resonance (g-TMR) [9], or exchange interaction [10]. In systems with strong spin-orbit interaction, such as Ge, the driving mechanism involved is typically either EDSR, g-TMR, or a combination of both. Here, we show a double quantum dot spin qubit hosted in a Ge/SiGe heterostructure operated in a regime where the exchange interaction dominates or is comparable to the Zeeman energy difference. We demonstrate microwave-driven transitions of two-hole spin states, including a double-flip transition from T- to T+. We study the Rabi frequency dependence as a function of detuning, ε, and in-plane and out-of-plane magnetic field, B, concluding the qubits are driven by exchange modulation. Surprisingly, we do not observe signatures of EDSR or g-TMR driving and discuss the possible reasons. As we observe the spin transitions in-plane and out-of-plane, we try to quantify the impact of hyperfine interaction in the inhomogeneous dephasing time T2* to answer the question: are hole spin qubits less coherent out-of-plane? [11] [1] Watzinger et al. Nat. Comm 9, 3902 (2018) [2] Jirovec et al. Nat. Mat. 20, 1106 (2021) [3] Hendrickx et al. Nature 577,487 (2020) [4] Hendrickx et al. Nature 591, 580 (2021) [5] van Riggelen et al. npj Quantum Inf 8, 124 (2022) [6] Wang et al. arXiv:2402.18382 (2024) [7] Koppens et al. Nature 442, 766 (2006) [8] Nadj-Perge et al. Nature 468, 1084 (2010) [9] Crippa et al. PRL 120,1337702 (2018) [10] Takeda et al. PRL 124, 117701 (2020) [11] Fischer et al. PRB 78, 155329 (2008) |
