SiQEW 2024: Scientific Program (ordered)

SiQEW 2024: Scientific Program

04.09.2024, Wednesday, 9:00-10:40

Coherent Control of a Triangular Exchange-only Spin Qubit
Joseph Broz¹, Edwin Acuna¹, Jason Petta²
¹HRL Laboratories, ²Department of Physics and Astronomy, University of California - Los Angeles

Abstract:
We investigate a triple quantum dot (TQD) with the dots arranged in a close-packed triangular geometry. This includes measurements of the charge stability in the few-electron regime as well as the dynamical characterization of a three-electron exchange only (EO) qubit encoded into TQD, which serves as a proxy for the coherent performance of the joint electronic spin state of the dots. In all cases, we find that performance is comparable to state-of-the-art demonstrations of EO qubits in linear dot arrays. Thus, our results represent a step towards scaling up quantum dot arrays to larger and more complex structures.

Quantum operations and statistics of a dense 10 spin qubit array
Valentin John¹, Cécile Yu¹, Stefan Oosterhout², Lucas Stehouwer¹, Floor van Riggelen-Doelman¹, Maximilian Rimbach-Russ¹, Stefano Bosco¹, Giordano Scappucci¹, Francesco Borsoi¹, Menno Veldhorst¹
¹QuTech, Delft University of Technology, ²QuTech, TNO

Abstract:
The study of qubits encoded in single spins has so far been limited to small quantum systems, predominantly arranged in 1D lattice configurations and small 2D arrays. While scaling further in two dimensions would be critical for the implementation of error correction schemes, these efforts have been hindered by challenges in material uniformity and noise, in the design and fabrication of a dense gate layout, and in the implementation of efficient tuning strategies.
Here, we investigate an extended 10-qubit system defined on a two-dimensional array of 10 quantum dots in the few-hole regime. Quantum dots are defined on a Ge/SiGe heterostructure grown on a Ge substrate and subjected to an in-plane magnetic field of a few tens of MHz.
We perform an in-depth characterisation of the system obtaining statistics in various properties of each of the 10 qubits in the same condition. Our study first encompasses g-factors and coherence times (T2*), finding distributions with variabilities of 6% and 9%, respectively. We then obtain the EDSR driving strength of each qubit when driven by 22 different gates. To understand our results, we model our system by including capacitive and spin-orbit couplings, and obtain insights on the locality, directionality and potential crosstalk of EDSR in such a dense qubit array. By driving each qubit with the most efficient gate at fixed Rabi frequencies, we benchmark the single-qubit gate performance obtaining fidelities all above 99.4%. In this talk, we will also present to the community some of the challenges encountered in tuning and calibration of our qubit system, and discuss steps forward.

Junction element for two-dimensional connectivity of spin qubits in Ge/SiGe
Inga Seidler, Konstantinos Tsoukalas, Leonardo Massai, Felix Schupp, Matthias Mergenthaler, Gian Salis, Andreas Fuhrer, Patrick Harvey-Collard
IBM Research Europe - Zurich

Abstract:
Current spin qubit devices are mostly based on linear qubit arrays, allowing only for couplings to two neighboring qubits. Holes in Ge/SiGe heterostructures offer the perfect platform for two-dimensional (2D) quantum dot (QD) arrays, thanks to the high confinement quality, high tunability, and larger gate structure dimensions. We implement a junction element in a Y geometry, which couples three double quantum dots via one mediator quantum dot at the intersection (Fig. a). The strong latching effects arising from the absence of reservoirs are mitigated by tuning techniques based on constant charge occupation of the QD array. We show single hole occupation for all seven quantum dots simultaneously and tunnel rate tunability.

Towards the goal of operating this junction as a spin coupling mechanism, we show manipulation of two qubits in one of the arms of the junction (Fig. b). We measure the angular dependence of the qubit frequencies on the applied magnetic field and find that the principal axes of the g-tensor align with the axis of the junction arm at a 150 degree angle, as opposed to one of the main crystal directions (Fig. c). This reinforces the interpretation that the g-tensor properties are determined by electrostatic confinement or strain commensurate with the QD layout.

With the goal of implementing three-way and 2D qubit connectivity, we will show the progress towards linking qubits in different arms of the junction.

Four-Spin Qubit Chain in SiMOS with Independent Parity Readout
Cameron Jones¹, Santiago Serrano Ramirez², Jonathan Yue Huang³, MengKe Feng⁴, Nard Dumoulin Stuyck², Tuomo Tanttu², Wee Han Lim², Andre Saraiva², Arne Laucht³, Andrew Dzurak², Chih-Hwan Yang³
¹University of New South Wales, ²UNSW & Diraq, ³UNSW Sydney, ⁴University of New South Wales / Diraq

Abstract:
To date, high fidelity single and two qubit gates have been routinely achieved in Silicon-MOS (SiMOS) devices. Demonstration of qubit entanglement with more than two qubits in such devices has however remained elusive. In this work we present a four-qubit device formed by a linear array of SiMOS quantum dots, each populated by an electron spin qubit, as seen in figure 1.a. An on-chip antenna allows for electron spin resonance for single qubit operations, and electrode gates between dots provide tuneable exchange coupling required for two-qubit operations. With this device, we demonstrate coherent single qubit operation of all four qubits, as well as pairwise exchange coupling between each nearest neighbour qubit pair. This allows for universal qubit control of the four-qubit processor. Additionally, we are able to achieve high fidelity initialisation of all qubits, and independent parity readout of the Q1-Q2 and Q3-Q4 pairs in a single measurement shot. Finally, we demonstrate the generation of a 3-qubit Greenberger–Horne–Zeilinger (GHZ) state. By performing quantum state tomography on the entangled state, we reconstruct the density matrix shown in figure 1.b. From these measurements, we calculate a Mermin witness value for the state that is greater than the classical limit of 2. This shows successful 3 qubit entanglement in a SiMOS device, using two pairs of parity readout.

Grover's algorithm in a four-qubit silicon processor above the fault-tolerant threshold
Ian Thorvaldson¹, Dean Poulos², Christian Moehle², Saiful Misha², Hermann Edlbauer², Jonathan Reiner², Helen Geng², Benoit Voisin², Michael Jones², Matthew Donnelly¹, Luis Pena², Charles Hill¹, Casey Myers¹, Joris Keizer¹, Yousun Chung², Samuel Gorman¹, Ludwik Kranz¹, Michelle Simmons¹
¹Silicon Quantum Computing, CQC2T, ²Silicon Quantum Computing

Abstract:
Spin qubits in silicon are strong contenders for realizing a practical quantum computer. This technology has made remarkable progress with the demonstration of single and two-qubit gates above the fault-tolerant threshold and entanglement of up to three qubits. However, maintaining high fidelity operations while executing multi-qubit algorithms has remained challenging due to challenges of crosstalk. In this talk, we present results of a four-qubit silicon processor with every operation above the fault tolerant limit and a demonstration of Grover's algorithm with a ~95% probability of finding the marked state (see Fig. a), one of the most successful implementations to date [1]. Our four-qubit processor is made of three phosphorus atoms and one electron spin precision-patterned into 1.5 nm² isotopically pure silicon (see Fig. b). The strong resulting confinement potential, without the need for confinement gates reduces crosstalk and leverages the benefits of all-to-all connectivity of the nuclear spins provided by the hyperfine interaction. This not only allows for efficient multi-qubit operations, but also provides individual qubit addressability. Together with the long coherence times of the nuclear and electron spins, this results in all four single qubit fidelities above 99.9% and controlled-Z gates between all pairs of nuclear spins above 99% fidelity. The high control fidelities, combined with >99% fidelity readout of all nuclear spins, allows for the creation of a three-qubit Greenberger-Horne-Zeilinger (GHZ) state with 96.2% fidelity (see Fig. c), the highest reported for semiconductor spin qubits so far. Such nuclear spin registers can initialised with high fidelity [2] and coupled via electron exchange [3], establishing a path for larger scale fault-tolerant quantum processors.

[1] I. Thorvaldson et. al., arXiv:2404.08741 (2024)
[2] J. Reiner et. al., Nat. Nanotechnol. (2024)
[3] L. Kranz et. al., Phys. Rev. Appl. 19, 024068 (2023)

04.09.2024, Wednesday, 11:10-12:50

Light-induced offset charge in Si/SiGe quantum dots as a proxy for radiation impacts
Brighton Coe¹, Michael Wolfe², Jared Benson², Tyler Kovach², Alysa Rogers², Deanna Campbell³, Spencer Weeden², Robert Mcdermott², Gabriel Bernhardt², Donald Savage⁴, Max Lagally⁴, Shimon Kolkowitz⁵, Mark Eriksson²
¹University of Wisconsin Madison, ²University of Wisconsin Madison Department of Physics, ³Sandia National Laboratories, ⁴University of Wisconsin Madison Department of Material Science and Engineering, ⁵University of California Berkeley Department of Physics

Abstract:
State-of-the-art quantum error correction codes cannot correct for correlated errors. Recently, it has been shown that radiation impacts induce correlated errors in superconducting qubits. An important open question for semiconductor qubits is whether electron-hole pairs induced by radiation impacts in the bulk of the chip can propagate through the Si-to-SiGe interface and induce offset charge shifts in gate defined Si/SiGe quantum dot qubits.

Here, we imitate such radiation impacts in Si/SiGe quantum dot devices using a fiber optic connection in a 3K cryogenic refrigerator to deposit energy from multiple 1.6 eV photon-impacts on the back side of the host silicon substrate. We show that such photon impacts shift the Coulomb blockade behavior of gate-defined quantum dots at the surface of the chip. We track multiple offset charge shifts from a series of photon bursts by using active feedback to sit on the side of a Coulomb blockade peak. Using this technique, we uncover a strong correlation between photon bursts and observed offset charge shifts.

Using G4CMP we simulate the propagation of large numbers of electron-hole pairs through the substrate. Surprisingly, but consistent with the experimental data, we find that electron-hole pairs induced by illuminating on the backside of the wafer can propagate long distances and impact operation of quantum dot qubits on the front side of the wafer. This finding is important because radiation impacts would likely occur in the bulk of the wafer, and electron-hole pairs will affect the qubits if they propagate upwards to surface or near-surface regions of the Si/SiGe heterostructure.

We observe such offset charge shifts in experiments on devices from different growth systems and with different substrate thicknesses: one grown at UW-Madison with fabrication done in part at Sandia National Laboratories, and the other an Intel Tunnel Falls device.

Noise Correlations in a Silicon Five-Qubit Array
Leon Camenzind¹, Yi-Hsien Wu¹, Juan Rojas-Arias¹, Akito Noiri¹, Kenta Takeda¹, Takashi Nakajima¹, Takashi Kobayashi², Ik Kyeong Jin¹, Amir Sammak³, Peter Stano¹, Giordano Scappucci⁴, Daniel Loss⁵, Seigo Tarucha⁶
¹RIKEN Center for Emergent Matter Science (CEMS), Wako, Japan, ²RIKEN Center for Quantum Computing (RQC), Wako, Japan, ³QuTech, Delft University of Technology, Delft, The Netherlands & Netherlands Organization for Applied Scientific Research (TNO), Delft, The Netherlands, ⁴QuTech, Delft University of Technology, Delft, The Netherlands & Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands, ⁵RIKEN Center for Emergent Matter Science (CEMS), Wako, Japan & RIKEN Center for Quantum Computing (RQC), Wako, Japan & Department of Physics, University of Basel, Basel, Switzerland, ⁶RIKEN Center for Emergent Matter Science (CEMS), Wako, Japan & RIKEN Center for Quantum Computing (RQC), Wako, Japan

Abstract:
Understanding the noise environment of semiconductor qubits is crucial for advancing spin-based quantum computing. While quantum error correction techniques can effectively address spontaneous, uncorrelated errors, the presence of correlated noise poses significant challenges to these protocols.

In our Silicon-28/Silicon-Germanium spin qubits, the surrounding environment of semiconductors and oxides introduces sources of two-level systems (TLS), which, through the micromagnets used for spin manipulation, convert electrical noise from local TLSs into qubit energy noise (Fig. a). Importantly, these TLS can be shared among qubits, resulting in correlated noise and, thus, correlated quantum gate errors. Here, we report on qubit-qubit correlated noise in a five-qubit array.

We measure individual qubit energy fluctuations through Bayesian estimations on Ramsey sequences and additionally measure energy fluctuations of two flanking charge sensors. Our methodology facilitates a comprehensive exploration of the noise environment by enabling the characterization of individual qubit noise power spectral densities and cross-correlation power spectral densities. This reveals distinct noise profiles and correlation spectra influenced by local TLS environments in the array.

For an integration time of 2.7h, our five qubits show T₂^* around 4-5 μs matching expectations from the measured noise spectral densities. We observe relatively strong correlations between neighboring qubits, with a notable reduction for next-neighbors and only minimal correlations to third-neighbor qubits (Fig. b). This trend is confirmed in the qubit-sensor correlations. Further, we can alter the position of our qubits by gate voltages and demonstrate a polynomial decay of noise correlations with qubit-qubit spatial separation.

Our findings indicate an associated correlation length between 100 and 200nm, thus underscoring the feasibility of building large arrays of spin qubits for Silicon-based quantum computing architectures. The observed short correlation distance and the potential to mitigate correlations through local gating hold significant promise for scalable implementation of quantum error correction codes.

Extracting noise cross-spectra from single-shot measurements
Juan Rojas-Arias¹, Peter Stano¹, Daniel Loss²
¹RIKEN, ²University of Basel, RIKEN

Abstract:
As qubit arrays continue to scale in size, there is a growing need to include the analysis of cross-correlations in the toolbox for studying noise in quantum processors. In this work, we introduce a novel approach for extracting the noise cross power spectral density (cross-PSD) of a qubit pair experiencing dephasing. Our method leverages single-shot readouts from a Ramsey-type experiment (Fig. 1a), offering resilience against errors in state preparation and measurement. Notably, this approach allows to perform spectroscopy across a wide frequency range, extending the spectral range when compared to current methods. In Fig. 1b we present the successful implementation of the method to simulated data, where both the magnitude (upper panel) and phase (lower panel) of a pre-defined non-monotonic cross-PSD are properly extracted.

Using valley relaxation hotspots to boost spin-shuttling fidelity in Si quantum wells
Merritt Losert¹, Rajib Rahman², Lars Schreiber³, Susan Coppersmith², Mark Friesen¹
¹University of Wisconsin-Madison, ²University of New South Wales, ³JARA Institute for Quantum Information

Abstract:
Highly variable valley splittings in Si/SiGe heterostructures pose a challenge for high-fidelity shuttling of Si spin qubits. Regions of low valley splitting lead to valley excitations, which in turn cause dephasing of the spin qubit. In this work, we propose a scheme to strongly enhance the spin-shuttling fidelity by making use of valley-relaxation hotspots. In contrast with conventional devices, where valley relaxation rates are typically in the range of 0.1 – 10 kHz, we show here that much higher relaxation rates of 50 MHz or more can be achieved in structures where the electron overlaps significantly with Ge, such as narrow quantum wells or wells containing Ge. Such hotspots are prevalent in regions with large valley splittings and large inter-valley dipolar matrix elements, arising from SiGe random-alloy disorder. Here, we derive analytical models for the statistical distributions of valley splittings, dipolar matrix elements, and relaxation rates due to alloy disorder, and we verify these models with tight-binding simulations. Then, by performing simulations of spin shuttling in the presence of alloy disorder, we show how these hot spots can reduce the shuttling infidelities, with average shuttling infidelities near 0.1 – 0.01%, for shuttling velocities between 1 – 10 m/s and shuttling trajectories of 5 microns. This is in contrast with shuttling infidelities near unity for conventional heterostructures, over the same parameter regime. Our work therefore provides an effective and simple solution to the a key obstacle for spin shuttling in Si.

Impact of growth front segregation and post-growth annealing on the valley energy splitting of spin qubits in silicon heterostructures
Jan Klos¹, Jan Tröger², Jens Keutgen³, Merritt Losert⁴, Helge Riemann⁵, Nikolay Abrosimov⁵, Joachim Knoch⁶, Hartmut Bracht⁷, Susan Coppersmith⁸, Mark Friesen⁴, Oana Cojocaru-Mirédin⁹, Lars Schreiber¹⁰, Dominique Bougeard¹¹
¹JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH & RWTH Aachen University, Aachen, Germany, ²Institute of Materials Physics, University of Münster, Münster, Germany; Tascon GmbH, Münster, Germany, ³I. Physikalisches Institut IA, RWTH Aachen University, Aachen, Germany, ⁴University of Wisconsin-Madison, Madison, Wisconsin, USA, ⁵Leibniz-Institut für Kristallzüchtung (IKZ), Berlin, Germany, ⁶Institute of Semiconductor Electronics, RWTH Aachen University, Aachen, Germany, ⁷Institute of Materials Physics, University of Münster, Münster, Germany, ⁸University of New South Wales, Sydney, Australia, ⁹I. Physikalisches Institut IA, RWTH Aachen University, Aachen, Germany; INATECH, Albert-Ludwigs Universität Freiburg, Freiburg im Breisgau, Germany, ¹⁰JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH & RWTH Aachen University, Aachen, Germany; ARQUE Systems GmbH, Aachen, Germany, ¹¹Institut für Experimentelle und Angewandte Physik, Fakultät für Physik, Universität Regensburg

Abstract:
We present isotope concentration depth profiles of a ²⁸Si/SiGe quantum well (QW) heterostructure analyzed with atom probe tomography (APT) and time-of-flight secondary-ion mass spectrometry. The profiles are then used as an input for a tight-binding model to predict realistic valley energy splittings. We have experimentally observed spin-echo dephasing times T₂ =128 μs and valley energy splittings E_VS around 200 μeV for single spin qubits in this molecular beam epitaxy (MBE) QW heterostructure previously. With APT, we find the concentration of nuclear spin-carrying ²⁹Si to be 50 ppm in the ²⁸Si QW.
The resolution limits of APT allow to uncover that both the top SiGe/²⁸Si and the bottom ²⁸Si/SiGe interfaces of the as-grown QW are shaped by epitaxial growth front segregation signatures on a few monolayer scale.
A post growth thermal treatment of the heterostructure - representative of the thermal budget experienced during qubit device processing – additionally indicates minimal thermally-driven, isotropic bulk diffusion, inducing a widening of the top SiGe/²⁸Si QW interface by about two monolayers, while the width of the bottom ²⁸Si/SiGe interface remains unchanged.
The tight-binding model including SiGe alloy disorder and the experimental APT concentration, suggests that the subtle combination of the slight thermally driven post growth diffusion and of a minimal Ge concentration around 0.3 % in the QW, as a result of a bottom ²⁸Si/SiGe QW interface segregation trailing edge, is instrumental for the observed large valley splitting of E_VS=200 μeV and the predicted probability of 62% to find E_VS>100 μeV in the annealed heterostructure.
Minimal Ge additions < 1 % hence seem to support high EVS without compromising coherence times. Note, that the probability to induce very small Ge additions into the QW during epitaxy gets more likely in thin QWs with diffused interfaces, which are used more and more for spin qubit devices.

04.09.2024, Wednesday, 14:20-16:00

On-chip Artificial Atomic Parametric Amplifier based on Semiconductor Quantum Dots
Yongqiang Xu, Rui Wu, Gang Cao, Guo-ping Guo
University of Science and Technology of China

Abstract:
In circuit quantum electrodynamics (circuit QED), superconducting microwave resonator is an important means for qubit readout. As one of the pivotal functional component, the parametric amplifier significantly enhances the performance of circuit QED-based readout. Quantum dot as an artificial atom, can serve as an ideal platform for the realization of an ultimate miniaturized parametric amplifier. It facilitates high fidelity readout, with advantages in convenient integration, strong tunability and resilience against magnetic fields.
Here, based on the interaction between a microwave cavity and a GaAs double quantum dot (DQD), we develop an artificial two-level atomic parametric amplifier. Harnessing the intrinsic nonlinearity of the DQD, a parametric gain of transmission exceeding 11~dB is achieved. Specifically, we exploit this on-chip amplifier to read out the other integrated DQD, demonstrating a significant enhancement in readout performance with a threefold increase in signal-to-noise ratio (SNR). Our results open a new avenue to develop on-chip quantum technologies for weak signal measurement.

Operating a coherent spin qubit all-electrically with high-Q gate-reflectometry for fast readout
Rafael Eggli¹, Taras Patlatiuk¹, Toni Berger¹, Eoin Kelly², Alexei Orekhov², Gian Salis², Richard Warburton¹, Dominik Zumbühl¹, Andreas Kuhlmann¹
¹University of Basel, ²IBM Research Zurich

Abstract:
Combining all electrical spin manipulation and in-situ gate-dispersive spin readout promises to be the road to high density, large scale spin qubit processors. The rapidly progressing hole spin qubit platforms in silicon and germanium provide purely electrical spin control at record-breaking speed. Superconducting off-chip inductors have been introduced to enhance the dispersive response by boosting the internal quality factor (Q) of the resonator and have enabled fast, high fidelity spin readout. However, demonstrating electrical spin manipulation in the presence of a high-Q resonator has been a long-standing challenge. A recent report (Kelly et al., APL, 2023) on the inadvertent ring-up of a superconducting high-Q dispersive sensor circuit caused by capacitive cross talk suggest resonator ringing to be a major obstacle when implementing electrical driving with such resonators, potentially limiting qubit coherence if qubit drive sequences spectrally overlap with the tank resonance frequency. This especially affects systems with strong spin-orbit interaction like silicon holes.
Here, we report on a silicon fin field-effect transistor hole spin qubit integrated with a niobium nitride nanowire inductor and coherently controlled all-electrically at 1.5 K. We investigate the mechanism by which resonator ring-up impacts qubit coherence and initialisation, by measuring the qubit in transport and contrasting data taken with first a low-Q wire wound surface-mount inductor and finally a high-Q inductor connected to the identical device and gate. We find a large parameter space for which resonator ring up causes a significant reduction in initialisation/readout efficacy, suggesting that primarily state preparation and measurement (SPAM) errors are introduced. Importantly, we find that the ring up does not limit our coherence time, indicating that efficient high-Q resonators in gate sensing are compatible with all-electrical spin control. These findings support the vision for large-scale, dense and hot qubit arrays based on all-electrical control with co-integrated gate-dispersive high-Q readout capabilities.

Spin Qubits with Scalable milli-kelvin CMOS Control
Sam Bartee¹, Will Gilbert², Kun Zuo¹, Kushal Das³, Tuomo Tanttu², Chih Huan Yang², Nard Stuyck², Sebastian Pauka³, Rocky Su⁴, Wee Han Lim², Santiago Serrano², Christopher Escott², Fay Hudson², Kohei Itoh⁵, Arne Laucht², Andrew Dzurak², David Reilly³
¹The University of Sydney, ²Diraq, ³Microsoft Quantum Sydney, ⁴UNSW, ⁵Keio University

Abstract:
A key virtue of spin qubits is their sub-micron footprint, enabling a single silicon chip to host the millions of qubits required to execute useful quantum algorithms with error correction. With each physical qubit needing multiple control lines however, a fundamental barrier to scale is the extreme density of connections that bridge quantum devices to their external control and readout hardware. A promising solution is to co-locate the control system proximal to the qubit platform at milli-kelvin temperatures, connected via miniaturized interconnects. Even so, heat and crosstalk from closely integrated control has potential to degrade qubit performance, particularly for two-qubit entangling gates based on exchange coupling that are sensitive to electrical noise. Here, we benchmark silicon MOS-style electron spin qubits controlled via heterogeneously-integrated cryo-CMOS circuits with a power envelope sufficiently low to enable scale-up. Demonstrating that cryo-CMOS can efficiently enable universal logic operations for spin qubits, we go on to show that mill-kelvin control has little impact on the performance of single- and two-qubit gates. Given the complexity of our milli- kelvin CMOS platform, with some 100-thousand transistors, these results open the prospect of scalable control based on the tight packaging of semiconductor qubits with a ‘chiplet style' control architecture.

Fast readout of planar Si-MOS quantum devices using gate-based sensing
Frederic Schlattner¹, Giovanni Oakes², David Ibberson², John Morton¹, Ross Leon², M. Fernando Gonzalez-Zalba²
¹UCL/Quantum Motion, ²Quantum Motion

Abstract:
Spins in planar metal-oxide-semiconductor (MOS) quantum dots are a promising platform to scale semiconductor quantum computing architectures. Particularly, they offer compatibility with semiconductor manufacturing lines and extensibility in two dimensions. As the technology scales up, techniques to ameliorate the impact of readout sensors on qubit connectivity need to be brought into place. Gate-based readout offers the advantage that the very same gates that define the qubit array can be used for sensing, resulting on a negligeable impact on qubit connectivity. However, gate-based readout has been hindered in planar MOS devices due to a low lever arm, lower quality factors and detrimental accumulation in the fanout regions.

In this work, we develop a methodology for gate-based readout of planar MOS quantum dots reaching a state-of-the-art minimum integration time of 300 ns for a SNR=1, corresponding to an electrical fidelity of >99.9% in just 2 µs and on a par with some of the best charge sensing demonstrations. We then show how the methodology can be used to read multiple quantum dots with just one gate/resonator enabling efficient and highly scalable readout.

Frequency-multiplexed readout of quantum dots with integrated cryo-CMOS current amplifiers
Baptiste Jadot¹, Quentin Schmidt¹, Brian Martinez¹, Thomas Houriez¹, Jean-Baptiste Casanova², Adrien Morel³, Tristan Meunier⁴, Gaël Pillonnet¹, Gérard Billiot¹, Aloysius Jansen⁵, Xavier Jehl⁵, Yvain Thonnart², Franck Badets¹
¹Univ. Grenoble Alpes, CEA, Leti, F-38000 Grenoble, France, ²Univ. Grenoble Alpes, CEA, List, F-38000 Grenoble, France, ³Univ. Savoie Mont Blanc, SYMME, F-74000 Annecy, France, ⁴Univ. Grenoble Alpes, CNRS, Institut Néel and Quobly, F-38000 Grenoble, France, ⁵Univ. Grenoble Alpes, CEA, IRIG, Pheliqs, F-38000 Grenoble, France

Abstract:
As spin-qubit based quantum cores increase in size, signal multiplexing techniques appear as a must-have to maintain a scalable approach. In particular, spin qubit readout techniques usually require the use of large inductors, circulators and amplifiers. Another approach is the use of current amplifiers with a high enough bandwidth (Fig. a) to probe the state of several frequency-multiplexed qubits. In this talk, we present a cryogenic capacitive trans-impedance amplifier (C-TIA) operating at 4K, able to measure up to 70 different channels with a readout fidelity of 99.99% in 8.5μs. Varying the frequency separation between channels, we study the threshold above which channel overlap is suppressed (Fig. b) and compare our approach to state of the art reflectometry techniques.
In a second part of the talk, we exploit this cryogenic amplifier to demonstrate the charge readout of two multiplexed single-electron transistors (SETs). These SETs are made from dual-gates FDSOI 28nm transistors with adapted dimensions. Under a strong back-biasing voltage, a quantum dot is formed between the two gates and Coulomb diamonds are observed. Using this small-scale demonstrator, we verify the metrics obtained by the circuit alone and probe the electrostatic environment of each SET independently at 4K.

05.09.2024, Thursday, 9:00-10:40

Optimal pulse control for Pauli spin blockade initialization and readout
Christian Ventura Meinersen, Stefano Bosco, Maximilian Rimbach-Russ
QuTech, TU Delft

Abstract:
Semiconductor spin qubits in electrostatically defined quantum dots have recently raised attention by demonstrating high-fidelity operations and proof-of-principle error correction algorithms [1, 2]. An essential component of quantum error correction is a reliable, yet fast, initialization and readout process. Fast readout is typically performed using Pauli spin blockade (PSB), where the spin information is converted into a charge degree of freedom using conditional hopping of an electron or hole inside a double quantum dot. The charge information can then be detected, for example, by a charge sensor. For initialization, the process is reversed.

A bottleneck for fast and high-fidelity PSB readout is a fast yet adiabatic population transfer of the spin states to the desired charge states by pulsing the electrostatic potential of the double quantum dot. On the one hand, a fully adiabatic transfer is slow and can further lead to significant errors through state leakage induced by noise, e.g. 1/f charge noise at the anti-crossing [3]. On the other hand, diabatic protocols are fast and potentially less prone to such errors but induce undesired transitions.

We theoretically study multiple shortcuts-to-adiabaticity strategies for population transfer and discuss transfer fidelities, speed, and feasibility. We particularly focus on a multi-level fast-quasiadiabatic pulse [4], which provides an optimized pulse for the detuning of the double quantum dot potential. Furthermore, we analyze the impact of charge noise by combining the Lindblad and filter function formalisms and compute the corresponding transfer fidelity. Our results show a drastic improvement in fidelity compared to the commonly implemented linear ramp (See Figure).

[1] van Riggelen et al., npj Quantum Inf 8, 1–7 (2022).
[2] Takeda et al., Nature 608, 682–686 (2022).
[3] Krzywda et al., Phys. Rev. B 104, 075439 (2021).
[4] Fehse et al., Phys. Rev. B 107, 245303 (2023).

Tomography of silicon spin qubits dressed in a global field
Kevin Guo¹, Ensar Vahapoglu², MengKe Feng², Amanda Seedhouse², Wee Han Lim², Fay Hudson², James Slack-Smith¹, Nicola Meggiato³, Andre Saraiva², Chih Yang², Arne Laucht², Andrew Dzurak², Jarryd Pla¹
¹UNSW, ²UNSW, Diraq, ³ETH Zürich

Abstract:
A spin-based quantum computer capable of running practical quantum algorithms will likely require an architecture which can be scaled to millions of qubits. Individually addressing and controlling many qubits presents a challenge in scalability due to qubit crosstalk. One possible solution utilizes a dielectric resonator to provide a uniform driving field used for global qubit control. By dressing the qubits in an on-resonance global field, all qubits are driven simultaneously with a single microwave source.
In this study, we demonstrate control of electron spin qubits in silicon driven by a dielectric resonator. We use gate set tomography (GST) to benchmark bare qubits and qubits dressed in both continuous-wave and sinusoidally modulating global fields (Fig. 1a), obtaining dressed single qubit gate fidelities exceeding 99% (Fig.1b). Crucially, the dressed identity gate error is four times smaller than the bare error, which is particularly relevant for common quantum algorithms where qubit idle time is high.
Finally, GST experiments are performed with introduced offsets in the Rabi and Larmor frequencies, finding that the dressed gates are more robust to variability in the Larmor frequency. Using a combination of GST and noise spectroscopy we posit potential sources of noise in the experimental setup and suggest improvements to further increase qubit fidelities. These results demonstrate the viability of dielectric resonators for global control in scalable silicon quantum computing architectures.

Dressed singlet-triplet qubit in germanium driven via resonant exchange interaction
Kostas Tsoukalas, Alexei Orekhov, Uwe Lüpke, Felix Schupp, Matthias Mergenthaler, Gian Salis, Patrick Harvey-Collard, Andreas Fuhrer
IBM Research

Abstract:
In a typical spin qubit device, the exchange interaction of two spins is tuned via a barrier gate that controls the wavefunction overlap between neighboring charges. This interaction can be changed with a baseband pulse on the barrier gate voltage to perform a SWAP-like gate operation. However, in most cases the splitting of the two antiparallel spins competes with the exchange and results in a rotation around a tilted axis. Driving the exchange at the frequency of the antiparallel spin splitting can recover a clean, orthogonal SWAP-like gate. In this work, we study this resonant exchange interaction of two neighboring hole spins in a germanium quantum dot array (Figure, left inset).

We first demonstrate coherent Rabi and full Bloch sphere control in the subspace spanned by the two antiparallel spin states (Figure, right inset). Through Clifford randomized benchmarking, we estimate an average gate fidelity above 99%. We then use the resonant interaction to create a continuously driven qubit in this antiparallel spin subspace, realizing a dressed singlet-triplet (S-T0) qubit. On this dressed qubit we demonstrate the ability to initialize, perform single qubit operations and readout while achieving substantially increased coherence times compared with the bare qubit.

Geometry of the dephasing sweet spots of spin-orbit qubits
Esteban Rodriguez-Mena¹, Marion Bassi¹, Boris Brun-Barriere¹, Simon Zilhmann¹, Lorenzo Mauro¹, Jose Carlos Abadillo-Uriel², Benoit Bertrand¹, Heimanu Niebojewski¹, Romain Maurand¹, Yann-Michel Niquet¹, Xavier Xehl¹, Vivien Schmitt¹, Silvano de Franceschi¹
¹CEA Grenoble, ²Instituto de Ciencia de Materiales de Madrid

Abstract:
Hole spin qubits in semiconductor quantum dots have attracted much attention as possible building blocks for quantum computers and simulators. They can be manipulated electrically thanks to strong intrinsic spin-orbit coupling without the need for extrinsic elements such as micro-magnets. This electrical addressability comes at the cost of a higher sensitivity to electrical and charge noise, limiting the dephasing time T^*₂. However, there may exist "dephasing sweet spots" where the qubit decouples (to first order) from the noise so that T^*₂ reaches a maximum.

Here we discuss the geometrical nature of the dephasing sweet spots of a spin-orbit qubit electrically coupled to one or more fluctuator(s). We show theoretically that the sweet spots usually draw lines (rather than points) on the unit sphere describing magnetic field orientation, providing more opportunities for optimal operation (see Fig a.). For that purpose, we characterize the qubit and its response to the fluctuator(s) by a Zeeman tensor G and its derivative(s) G' with respect to the fluctuating field(s). We discuss Si & Ge hole spin qubits as an illustration. Moreover, we experimentally probe the sweet lines in Si-MOS devices (see Fig b.), and demonstrate that their position can be tuned by gate voltages. We achieve efficient electric-dipole resonance on the sweet lines with a quality factor as high as 690, side by side with the values reported for electrons in silicon.

Our results provide guidelines for highly coherent operation of hole spin qubits regardless of the architecture, and insights for the design of devices more resilient to electrical noise.

Classification and magic magnetic field directions for spin-orbit-coupled double quantum dots
Aritra Sen¹, Gyorgy Frank², Baksa Kolok², Jeroen Danon³, András Pályi²
¹Budapest University of Technology and Economics (BME), ²Budapest University of Technology and Economics, ³Norwegian University of Science and Technology

Abstract:
The spin of a single electron confined in a semiconductor quantum dot is a natural qubit candidate. Fundamental building blocks of spin-based quantum computing have been demonstrated in double quantum dots with significant spin-orbit coupling (SOC), for example with holes in Silicon and Germanium. Here we show that spin-orbit-coupled double quantum dots can be categorised in six classes (A to F in the figure), according to a partitioning of the multidimensional space of their g tensors (g_L, g_R) which are in general real and non-symmetric. In particular, for charge carriers in the valence bands of Silicon and Germanium subject to significant SOC, the g tensors are highly anisotropic. We predict that the spin physics is highly simplified due to pseudospin conservation, whenever the external magnetic field is pointing to special directions ("magic directions"), where the number of special directions is determined by the class. The magic directions yield spin-relaxation, electron-shuttling sweetspots and simpler single spin readout using Pauli spin blockade. We also analyze the existence and relevance of "magic loops" in the space of magnetic-field directions, corresponding to equal local Zeeman splittings. Magic loops provide dephasing sweet spots and stopping points in Pauli spin blockade readout. All together each class determines physical characteristics of the double dot, i.e., features in transport, spectroscopy, and coherence measurements, as well as qubit control, shuttling, and readout experiments. These results present an important step toward precise interpretation and efficient design of spin-based quantum computing experiments in materials with strong spin-orbit coupling.

05.09.2024, Thursday, 11:10-12:30

Large Scale Characterization of Qarpet at mK temperatures
Asser Elsayed¹, Federico Poggiali¹, Alberto Tosato¹, Davide Degli Esposti², Lucas Stehouwer¹, Menno Veldhorst¹, Giordano Scappucci³
¹QuTech / TU Delft, ²QuTech /TU Delft, ³TU Delft, QuTech

Abstract:
Germanium spin qubits are emerging as a promising technology for spin-based quantum processors based on electrostatically defined quantum dots. Advancements in optimizing Ge-based materials and a deeper understanding of their fundamental physics are essential to drive progress. Traditional hero device-style measurements are no longer sufficient to drive the required progress. To meet these demands, large-scale cryogenic characterization and statistical analysis, integrated into the design cycle of Ge-based quantum devices, are imperative.
At the SiQEW 2023 we introduced Qarpet (in name of the tightly knit fabric of electrostatic gates defining a highly dense array of qubits). The Qarpet architecture is tailored for large-scale characterization of quantum dot qubits and features a cross-bar array of repeating unit cells, each comprising a sensing dot and qubit dots. The device preparation and bonding is engineered for individual control yet maximizing shared lines to minimize room temperature resource requirements. Following the proof of principle qubit demonstration, our efforts are now focusing on the comprehensive characterization of quantum dots. We showcase the operation of single-hole transistors for sensing dots and last-hole occupation for qubit dots, allowing to address uniformity over extensive length scales. We then provide a detailed statistical investigation of charge noise, further discuss the potential for high-volume qubit measurements, and present proof-of-concept results paving the way for future characterization endeavors.

An Industrial Triple Metal Gate Process for a 2D Shuttling Architecture
Wolfram Langheinrich¹, Pascal Muster¹, Sebastian Pregl¹, Felix Reichmann², Yuji Yamamoto², Varvara Brackmann³, Michael Friedrich³, Nikola Komerički⁴, Laura Diebel⁵, Dominique Bougeard⁵, Till Huckemann⁶, Lars Schreiber⁶, Hendrik Bluhm⁶
¹Infineon Technologies Dresden GmbH & Co. KG, ²IHP Leibniz-Institut für innovative Mikroelektronik, Frankfurt/Oder, Germany, ³Fraunhofer IPMS, Dresden, Germany, ⁴Fraunhofer IAF, Freiburg, Germany, ⁵Institut für Experimentelle und Angewandte Physik, Fakultät für Physik, Universität Regensburg, ⁶JARA Institute for Quantum Information

Abstract:
Scaling qubit numbers while improving gate fidelities is a general challenge for any quantum computing platform. In case of silicon-based spin qubits an obvious approach are cross-bar arrays, but they additionally suffer issues like wiring fan-out and crosstalk. A shuttling-based 2D-architecture is a promising alternative at the cost of increased fabrication complexity [1]. Therefore, a triple metal gate process on Si/SiGe heterostructures was developed within an industrial production line, enabling high yield and reliability for conveyor-mode shuttling devices with micrometer length. In order to achieve low defect density, pattern transfer is done using reactive ion etching, compared to lift-off techniques, typically used in research lab processes. Only one gate layer (Gate1) requires electron beam lithography, whereas the screening gate (Gate0) for the shuttling channel and the top gate (Gate2) use optical lithography. Furthermore, optimisation of the gate oxides is crucial, since charge noise and disorder will affect the shuttling fidelity. Room temperature characterisation of our CVD SiO₂ at MOS devices shows low interface trap densities as low as 10¹⁰ cm^-2. Low-frequency charge noise was measured at double quantum dots in the 50mK region, where one dot is operated as a SET. Values below 1 µeV/√Hz were achieved. The valley splitting energy was obtained via magneto-spectroscopy at the same device and values around 50 µeV were found. First results also show that single-electron shuttling is possible in devices fabricated with this process.

Figure: Short conveyor-mode shuttling device with two SETs left and right. The dark-field TEM shows four claviature gates for adiabatically moving a single electron.

A 300mm Silicon-Based Platform for Quantum Computing Device Technologies
Bart Raes, Clement Godfrin, Ruoyu Li, George Simion, Stefan Kubicek, Sofie Beyne, Shana Massar, Yann Canvel, Julien Jussot, Roger Loo, Yosuke Shimura, Massimo Mongillo, Danny Wan, Kristiaan De Greve
Imec

Abstract:
Silicon spin qubits have emerged as leading contenders for large-scale quantum computing, owing to their extended coherence times and compatibility with CMOS technology. At IMEC, we have devised a comprehensive strategy to systematically optimize all process parameters, leveraging industrial 300mm fabrication processes, to enhance qubit performance. The scalability and high reproducibility inherent in 300mm processes enable a deterministic exploration of qubit metrics and their sensitivity to process parameters, crucial for advancing qubit quality.

We showcase the efficacy of our approach by presenting the latest findings, focusing on fully integrated qubit structures, on our electron SiMOS, hole SiMOS and Si/SiGe platforms. We will discuss, among others, high fidelity (99-99.9%), high speed operation and readout, and the overall approach into scaling up our qubit platforms.

Fidelity of Si/SiGe spin qubits fabricated by an industrial 300 mm process
Viktor Adam¹, Thomas Koch¹, Daniel Schroller¹, Bart Raes², Julian Ferrero¹, Stefan Kubicek², Shana Massar², Ruoyu Li², Clement Godfrin², Danny Wan², Kristiaan De Greve², Wolfgang Wernsdorfer¹
¹Karlsruhe Institute of Technology (KIT), Germany, ²Interuniversity Microelectronics Centre (imec), Belgium

Abstract:
Silicon spin qubits are one of the most promising candidates for large-scale quantum computing due to their long coherence times and compatibility with existing industrial complementary metal-oxide-semiconductor (CMOS) fabrication processes. The Si/SiGe heterostructure aims to decouple the qubits from the semiconductor-oxide interface, known as the main source of charge noise, but often features low valley-splitting values and is more challenging in terms of heterostructure growth.

In this work, we demonstrate the operation of natural Si/SiGe spin qubit devices, fabricated in a 300 mm semiconductor manufacturing facility using a combination of optical and e-beam lithography with an industry compatible process. A Co-µ magnet generates a magnetic field gradient that enables us to drive the qubits at MHz rate via the electric dipole spin resonance (EDSR) drive line and to address both qubits individually via their respective resonance frequency. We measure valley-splittings of 85 µeV and charge noise values of 1 µeV/√Hz. Furthermore, we observe spin relaxation times above 1 s and qubit coherence times around 1 µs, which are common for natural silicon quantum wells. Finally, we present qubit drives of several MHz and a single gate fidelity above 99%.

06.09.2024, Friday, 9:00-10:40

The Qube: a lattice of vertically and laterally coupled quantum dots
Hanifa Tidjani¹, Michael Chan², Dario Denora², Jann Hinnerk-Ungerer³, Alexander Ivlev², Alberto Tosato², Corentin Déprez², Lucas Stehouwer², Amir Sammack⁴, Stefan Oosterhout⁴, Giordano Scappucci², Menno Veldhorst²
¹QuTech, TU Delft, ²TU Delft, ³Harvard University, ⁴TNO

Abstract:
Quantum dot based spin qubits have made rapid developments in the complexity of devices, with scaling of qubits being a priority. Approaches towards the scale up of quantum dot qubits are primarily based on one or two-dimensional planar arrays. Here, introduce the third spatial dimension by increasing the number of quantum wells, forming a three-dimensional quantum dot lattice in a Ge/SiGe heterostructure. To achieve this, we show that on a bilayer heterostructure a single top plunger gate can be used to form a vertically-coupled double quantum dot, both in transport and in charge sensing[1]. We demonstrate independent control of the occupation of the vertically aligned quantum dots by virtualizing to the surrounding gates. This virtualization is facilitated by differing gate-to-dot capacitances due to the separation of the quantum wells in the vertical z-direction, resulting in differences in electrostatic confinement. By accumulating under two plunger gates, we form a 2x2 quantum dot array, aligned on the x-z plane[2]. Despite a small interlayer separation of 4nm, we control the occupation and tune to the (1,1,1,1) regime. Expanding this to a device with four plunger gates (a) and a larger interlayer separation of 10nm (b), we form a 3D lattice of quantum dots (c). Confinement plays an important role in operating the lower layer. When strongly confined, only the upper quantum well is occupied, and in this regime we form lateral singlet-triplet qubits. The expansion of the quantum dot devices to the third spatial dimension presents an exciting opportunity to extend the framework of gate-defined semiconductor quantum dots beyond planar implementations, for the development of scalable quantum computation and simulation.

A hole spin qubit on a planar silicon 300 mm CMOS platform
Isaac Vorreiter¹, Joseph Hillier², Scott Liles³, Jonathan Huang¹, Aaquib Shamim³, Stefan Kubicek⁴, Clement Godfrin⁴, Danny Wan⁴, Ruoyu Li⁴, Bart Raes⁴, Kristiaan De Greve⁴, Alex Hamilton¹
¹UNSW, ²QED group, School of Physics, University of New South Wales, Sydney NSW, 2052, Australia, ³University of New South Wales, ⁴imec, KU Leuven

Abstract:
Spin qubits implemented within Group-IV semiconductor hole quantum dots are demonstrating favourable properties as building blocks for scalable quantum processors [1-5]. Holes possess a strong intrinsic spin-orbit interaction which enables fast all-electrical spin control via electric-dipole spin resonance (EDSR), allowing for the implementation of ‘spin-orbit' qubits. Implementing spin-orbit qubits within 2D planar MOS structures provides the benefits of flexible integration, enabling the creation of densely packed 2D tunnel-coupled arrays or sparse arrays [6]. However, spin-orbit qubits realised in 2D-like planar MOS silicon have not been extensively studied, and as such their single and two qubit properties are not well-characterised in these systems.

Here we demonstrate a hole-spin spin-orbit qubit in a planar silicon double quantum dot. Furthermore, we demonstrate Rabi frequencies reaching 15 MHz and controllable two-qubit exchange of order 40 MHz. We investigate the qubit control and fidelity as a function of magnetic field, demonstrating strategies for operating these qubits in the presence of strong spin-orbit interaction. Additionally, the device was fabricated using a 300mm integration flow [7] compatible with foundry-based fabrication processes. Our results affirm industrially fabricated 2D MOS silicon quantum dots as feasible platforms for implementing spin-orbit qubits.

Figure: a) False-colour SEM image of the device, where the quantum dots are formed under the plunger gates P1 and P2, with confinement provided by the barrier gates B1, B2 and the C-gate. An adjacent single-hole transistor is use for charge sensing and readout. b) Charge stability diagram in the few-hole, weakly-coupled regime where spin readout is performed. c) Rabi oscillations as a function of frequency detuning showing a typical chevron pattern.
[1] Nat Commun 7,13575,(2016).
[2] 17,1072–1077,(2022).
[3] Nat. Nanotechnol. 16,308–312,(2021).
[4] Nat Electron 5,178–183,(2022).
[5] Nature 577,487–491,(2020).
[6] npj Quantum Inf 3,34,(2017).
[7] 2021 Symposium on VLSI Circuits, Kyoto, Japan, 2021,pp.1-2

Fully autonomous tuning of a spin qubit
Jonas Schuff¹, Miguel Carballido², Madeleine Kotzagiannidis³, Juan Carlos Calvo³, Marco Caselli³, Jacob Rawling³, David Craig¹, Barnaby van Straaten¹, Brandon Severin¹, Federico Fedele¹, Simon Svab², Pierre Chevalier Kwon², Rafael Eggli², Taras Patlatiuk², Nathan Korda³, Dominik Zumbühl², Natalia Ares¹
¹University of Oxford, ²University of Basel, ³Mind Foundry

Abstract:
Spanning over two decades, the study of qubits in semiconductors for quantum computing has yielded significant breakthroughs. However, the development of large-scale semiconductor quantum circuits is still limited by challenges in efficiently tuning and operating these circuits. Identifying optimal operating conditions for these qubits is complex, involving the exploration of vast parameter spaces. This presents a real 'needle in the haystack' problem, which, until now, has resisted complete automation due to device variability and fabrication imperfections. In this study, we present the first fully autonomous tuning of a semiconductor qubit, from a grounded device to Rabi oscillations, a clear indication of successful qubit operation. We demonstrate this automation, achieved without human intervention, in a Ge/Si core/shell nanowire device. Our approach integrates deep learning, Bayesian optimization, and computer vision techniques. We expect this automation algorithm to apply to a wide range of semiconductor qubit devices, allowing for statistical studies of qubit quality metrics. As a demonstration of the potential of full automation, we characterise how the Rabi frequency and g-factor depend on barrier gate voltages for one of the qubits found by the algorithm. Twenty years after the initial demonstrations of spin qubit operation, this significant advancement is poised to finally catalyze the operation of large, previously unexplored quantum circuits.

Automated real-time gate virtualization of a 10 quantum dot array
Anantha Rao¹, Donovan Buterakos², Valentin John³, Cécile Yu³, Stefan Oosterhout⁴, Lucas Stehouwer³, Giordano Scappucci³, Menno Veldhorst³, Francesco Borsoi³, Justyna Zwolak²
¹University of Maryland, ²NIST, ³QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands, ⁴Netherlands Organisation for Applied Scientific Research (TNO), Delft, The Netherlands

Abstract:
Arrays of gate-defined quantum dots are potential candidates for realizing scalable multi-qubit devices and efficiently performing quantum computation. As the capacitive coupling between different voltage gates leads to cross-talk, implementing virtual gates is crucial for achieving orthogonal control of all the qubit's parameters, such as energies and couplings. However, determining efficiently and accurately the compensations on each layer of virtual gates frameworks is challenging and requires iterative procedures. In our work, we propose and test in real-time an automated method for defining multiple layers of virtual gates using machine learning techniques. Earlier methods relied on automatic detection of the slope of transition lines from individual two-dimensional charge stability diagrams (2DCSD). However, we show that such strategies are prone to errors, particularly due to effects such as slow loading via decoupled reservoirs that lead to "latchy" transitions. In our simple and robust approach, we combine machine learning and traditional curve-fitting to define virtual barrier gates. Our algorithm identifies the locations and tracks the trajectories of charge interdots in 2DCSDs while stepping a barrier gate voltage [Fig. 1(B), see Fig. 1(D) for trajectory of charge interdot 6 shown in the first plot in Fig. 1(B)]. The slope of the linear fit in Fig.1(D) is used to extract the required compensation for the virtual plunger gates preventing the movement of the interdot as barrier voltage is varied [Fig. 1(C)]. With our approach, we autonomously virtualize a state-of-the-art hole-based 10 quantum dot system [Fig. 1(A)], with 12 barrier gates and 10 plunger gates defined on planar germanium, producing a 10x12 virtual matrix in under an hour, leading to a factor of 10x to 1000x reduction in time with respect to manual operations.

Investigating phonon-induced frequency shifts in semiconductor spin qubits
Irina Heinz¹, Jeroen Danon², Guido Burkard¹
¹University of Konstanz, ²Norwegian University of Science and Technology

Abstract:
Spin qubits have proven to be a feasible candidate for quantum computation and benefit from the advanced device manufacturing in semiconductor industry making them a good candidate for scalable quantum computation [1]. Compared to superconducting platforms spin qubits can operate at higher temperatures up to hundreds of mK. However, recent experiments [2,3] show a non-trivial dependence of the spin qubit frequency on the temperature. In this work we aim to gain insight into the underlying physics causing frequency shifts in the low-temperature limit and to understand the interaction between qubit and phonons.

[1] G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Semiconductor spin qubits, Rev. Mod. Phys. 95, 025003 (2023)
[2] B. Undseth, X. Xue, M. Mehmandoost, M. Rimbach-Russ, P. T. Eendebak, N. Samkharadze, A. Sammak, V. V. Dobrovitski, G. Scappucci, and L. M. K. Vandersypen, Nonlinear Response and Crosstalk of Electrically Driven Silicon Spin Qubits, Phys. Rev. Appl. 19, 044078 (2023)
[3] B. Undseth, O. Pietx-Casas, E. Raymenants, M. Mehmandoost, M. T. Mądzik, S. G. J. Philips, S. L. de Snoo, D. J. Michalak, S. V. Amitonov, L. Tryputen, B. P. Wuetz, V. Fezzi, D. D. Esposti, A. Sammak, G. Scappucci, and L. M. K. Vandersypen, Hotter is Easier: Unexpected Temperature Dependence of Spin Qubit Frequencies, Phys. Rev. X 13, 041015 (2023)

06.09.2024, Friday, 11:10-12:30

Remote quantum state transfer using spin-photon vacuum Rabi oscillations
Xiao Xue¹, Jurgen Dijkema¹, Patrick Harvey-Collard², Maximilian Rimbach-Russ¹, Tobias Bonsen¹, Sander de Snoo¹, Guoji Zheng¹, Amir Sammak¹, Giordano Scappucci¹, Lieven Vandersypen¹
¹QuTech, TU Delft, ²IBM Research Zurich

Abstract:
With the demonstrations of strong spin-photon couplings in semiconductor and distant two-qubit logic mediated by virtual microwave photons, circuit quantum electrodynamics becomes a promising approach to link spin qubits in spatially separated quantum modules. Here, we use a real microwave photon which is on resonance with two spin qubits that are 250 µm apart to coherently transfer a quantum state between them.
First, we report the first observation of vacuum Rabi oscillations between spin qubits and microwave photons. The oscillations can be rapidly switched on and off by a simple voltage pulse on the double quantum dot detuning. The oscillation frequencies match the observed avoided crossing of the energy levels in spectroscopy measurements.
Second, we utilize consecutive vacuum Rabi oscillations of the two spin qubits to transfer quantum states from one to the other. The quantum state is first transferred coherently from one qubit to the photonic state in the resonator with a half-period vacuum Rabi oscillation, and then similarly transferred to the second qubit.
These experiments provide new avenues for scaling quantum networks on a chip.

Strong Charge-Photon Coupling in Planar Ge with Granular Aluminium Superconducting Resonators
Marian Janik¹, Kevin Roux¹, Carla Borja Espinosa¹, Oliver Sagi¹, Abdulhamid Baghdadi¹, Thomas Adletzberger¹, Andrea Ballabio², Marc Botifoll³, Alba Garzon Manjon³, Jordi Arbiol⁴, Daniel Chrastina², Giovanni Isella², Ioan Pop⁵, Georgios Katsaros¹
¹ISTA, Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria, ²L-NESS, Physics Department, Politecnico di Milano, via Anzani 42, 22100, Como, Italy, ³ICN2, Catalan Institute of Nanoscience and Nanotechnology CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Catalonia, Spain, ⁴ICN2, Catalan Institute of Nanoscience and Nanotechnology CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Catalonia, Spain; ICREA, Catalan Institution for Research and Advanced Studies, Passeig de Lluís Companys 23, 08010 Barcelona, Catalonia, Spain, ⁵IQMT, Institute for Quantum Materials and Technology, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany; PHI, Physikalisches Institut, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany

Abstract:
Charges and spins confined in quantum dots (QDs) coherently coupled to a microwave photon in a superconducting resonator are interesting for quantum computation, quantum optics, or analog quantum simulations. Reaching a sizeable coupling strength exceeding loss rates is intrinsically challenging in these systems due to the small dipole moment of charges confined in QDs. Since it can be compensated with high-impedance resonators, they have received notable attention in the past decade. Nevertheless, previous QD circuit quantum electrodynamics implementations have not exceeded the impedance of ∼ 3.8 kΩ, leaving opportunities for significant improvement. The large kinetic inductance of granular aluminium (grAl) could provide an order-of-magnitude enhancement.

Here, we report an in situ resistance control of grAl evaporation, which allows us to reproducibly fabricate grAl coplanar waveguide resonators with characteristic impedances reaching Z = 22.3 ± 0.3 kΩ due to the large sheet kinetic inductance up to L_k ≅ 3 nH/☐. Magnetic field resilience of B_⊥^max = 281 ± 1 mT and B_∥^max = 3.5 ± 0.05 T is achieved for 100 nm-narrow superinductors. We implement these resonators with QDs in planar germanium and reach the strong hole-photon coupling regime with a rate of g_c = 566 ± 2 MHz and a cooperativity of C = 251 ± 8.

The demonstrated properties make grAl resonators suitable for boosting the spin-photon coupling strength, a crucial requirement for fast, high-fidelity, long-distance two-qubit gates.

Lifetime and coherence of a cQED hole spin qubit
Leo Noirot¹, Simon Zihlmann², Cecile Yu³, Etienne Dumur², Romain Maurand⁴
¹CEA Grenoble Lateqs, ²CEA Grenoble, ³TU Delft, ⁴CEA

Abstract:
Spins in semiconductor quantum dots constitute a promising platform for scalable quantum information processing. Coupling them strongly to the photonic modes of superconducting microwave resonators would enable fast non-demolition readout and long-range, on-chip connectivity, well beyond nearest-neighbor quantum interactions. As the field of spin circuit quantum electro-dynamic (cqed) is growing, new experiments showed spin-photon coupling rates as high as 330 MHz and a 2-qubit gate mediated by a photonic interaction. However, up to now, all of the semiconductor spin-cqed devices have showed fast decoherence and relaxation, hindering the high fidelity control and readout usually achieved for spin qubits.

We present here an experimental study of a hole spin qubit embedded in a Si double quantum dot, strongly coupled to a microwave cavity thanks to the intrinsic spin-orbit interaction (SOI) of holes in Si. We measure relaxation (Fig. a) and dephasing (Fig. b) as a function of magnetic field and gate voltage (not provided here), therefore controlling the spin-photon coupling as well as the spin's energy through the magnetic-field dependence of the SOI and gate-dependence of the electric dipole. We span its energy over a range of 10GHz, crossing several cavity modes and identify photon emission (multimode Purcell) as the limiting mechanism for lifetime. The dephasing shows signs of charge-noise induced dephasing as its magnetic-field dependence follows the second-order electrical susceptibility of the qubit at the charge sweet-spot. Accordingly, the Ramsey dephasing time is maximal at the sweet-spot while it degrades strongly away from it. Surprisingly however, the Echo dephasing time is minimal at the sweet-spot and increases away from it. This trend is qualitatively in agreement with a dephasing induced by thermal photons or it could be the consequence of the interplay between first and second order coupling to charge noise. Further studies are needed to fully clarify the situation.

Microsecond-lived quantum states in a carbon-based circuit in cQED
Benoit Neukelmance¹, Hue Benjamin², Quentin Schaeverbeke³, Lucas Jarjat⁴, Arnaud Théry⁴, Jules Craquelin⁴, William Legrand⁵, Cubaynes Tino⁴, Gulibusitan Abulizi³, Jeanne Becdelievre³, Mariah El Abassi³, Joseph Sulpizio³, Davide Stefani³, Audrey Cottet⁶, Matthieu Desjardins³, Kontos Takis⁷, Matthieu Delbecq⁸
¹1) Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, Paris, France; 2) C12 Quantum Electronics, Paris, France, ²1) aboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, Paris, France; 2) C12 Quantum Electronics, Paris, France, ³C12 Quantum Electronics, Paris, France, ⁴Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, Paris, France, ⁵1)Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, Paris, France; 2) C12 Quantum Electronics, Paris, France, ⁶1) Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, Paris, France; 3) Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, Université PSL, CNRS, Sorbonne Université, Paris, France, ⁷1) aboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, Paris, France; 3) Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, Université PSL, CNRS, Sorbonne Université, Paris, France, ⁸1) Laboratoire de Physique de l'École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, Paris, France; 3) Laboratoire de Physique et d'Etude des Matériaux, ESPCI Paris, Université PSL, CNRS, Sorbonne Université, Paris, France; 4) Institut universitaire de France (IUF)

Abstract:
Electron spins in quantum dots represent an attractive path towards the realization of quantum processors due to the high spin resilience to environmental noise and the large electric dipole allowed by the DQD. While multi-qubit gates are commonly mediated through nearest-neighbor exchange interaction, achieving coherent long-range coupling between spins remains a major challenge for such architectures. Enabling spin-photon interaction is thus appealing.

Here, we manipulate the quantum state of an ultra-clean suspended carbon nanotube double quantum dot with ferromagnetic contacts embedded in a microwave cavity. By performing quantum manipulations in the time domain via the cavity photons, we demonstrate coherence times T₂* of the order of 1 μs as shown by the Ramsey fringes experiment shown in panel 1. This is two orders of magnitude larger than what was ever measured in any carbon quantum circuit and one order of magnitude larger than silicon based quantum dots in comparable environment. Thanks to a peculiar Rabi chevrons pattern, we are able to infer precisely the spectrum of our double quantum dot. In particular it allows us to understand why our transition exhibits a very weak dispersion with detuning ε_δ as shown in panel 2 (dashed line is theory). This regime is favorable to drastically reduce charge noise dephasing. Combining the regime we achieved with a high impedance resonator to boost the bare electron-photon coupling should enable high fidelity two-qubit gates in future works. Overall this holds promise for carbon as a contender host material for spin qubits in circuit quantum electrodynamics.

06.09.2024, Friday, 14:00-15:40

Fabrication and characterization of multi-rail Si/SiGe exchange-only spin qubits in the SLEDGE architecture
Jacob Blumoff
HRL Laboratories LLC

Abstract:
Si/SiGe exchange-only spin qubits encoded in a decoherence-free subsystem (DFS) are a compelling platform for quantum computing because of their compatibility with advanced fabrication techniques and their exclusive use of baseband pulses for control. Using the Single-Layer Etch-Defined Gate-Electrode (SLEDGE) architecture, which implements a CMOS-like separation between active front-end gates and electrical routing layers, we recently demonstrated high-fidelity two-qubit DFS-encoded gates in a single-rail device. Scaling to multi-rail geometries, where qubits are connected to more than two neighbors, is an essential step towards quantum fault tolerance because it improves robustness and connectivity. We report on the fabrication of a two-rail, six-dot device with three distinct back-end routing layers. We also discuss the electrostatic tune-up, the initial parametric characterization, and the single-qubit randomized benchmarking performance of this device.

High-fidelity coupling between nuclear spin registers via electron exchange
Junliang Wang Wang, Hermann Edlbauer, Ian Thorvaldson, Christian Moehle, Billy Pappas, A F M Saiful Haque Misha, Michael Jones, Fabian Pena, Yousun Chung, Joris G. Keizer, Ludwik Kranz, Michelle Y. Simmons
Silicon Quantum Computing

Abstract:
Nuclear spin qubits in silicon exhibit extremely long coherence times exceeding seconds, making them an excellent candidate for quantum computation [1]. Scanning tunnelling microscopy (STM) enables the fabrication of atomically engineered nuclear-spin registers with sub-nm precision, which are readily operable with single- and two-qubit gate fidelity above the fault-tolerant threshold [2]. A key challenge for scaling-up is the ability to couple nuclear spin registers whilst maintaining high fidelity. Here, we demonstrate such a highly efficient quantum link using exchange-coupled electron spins that are located on neighbouring nuclear spin registers. Applying interleaved randomized benchmarking to these electron spins, we report a CNOT gate fidelity exceeding 99%. By controlling the nuclear spins in both registers [3], we engineer the energy difference between the electron spin qubits and explore its impact on the CNOT gate fidelity. Establishing a highly efficient link between nuclear spin registers, our results continue to pave the way towards a large-scale silicon quantum processor.

References:
[1] J. T. Muhonen et al., Nature Nanotechnology 9 (2014)
[1] I. Thorvaldson et al., arXiv:2404.08741 (2024)
[2] J. Reiner et al., Nature Nanotechnology (2024)

Engineering the excited state spectra of Si/SiGe quantum dots.
Tom Watson, Daniel Keith, Sam Neyens, Otto Zietz, Andrew Wagner, Ekmel Ercan, Joelle Corrigan, John Rooney, Peter Bavdaz, Rambert Nahm, David Kohen, Nathan Bishop, Stephanie Bojarski, Jeanette Roberts, James Clarke
Intel Corporation

Abstract:
A key challenge for building larger spin-based quantum computers is to maintain high uniformity across the qubit array. For Si/SiGe spin qubits, one of the main sources of non-uniformity are low-lying excited states in quantum dots that result in poor readout and initialization fidelity. In addition, these states can lead to issues with spin shuttling and exchange-based gate operations. For one electron in a quantum dot, the lowest excited state is due to the valley degree of freedom and is determined by the atomistic details of the Si quantum well. Adding a second electron results in singlet/triplet states where the splitting is determined by both the valley and orbital degree of freedom and how strongly they couple.

In this talk, we discuss the techniques we employ for the fast millikelvin characterization of quantum dot excited states to build statistically relevant data sets to compare different wafers. With these techniques, we show that we can increase the mean valley splitting of our quantum dots from Ev = 60ueV (σEv = 40ueV) to Ev = 230ueV ( σEv =130ueV) by introducing a small percentage of Ge (~2%) into the silicon quantum well. Furthermore, we show that despite high valley splittings, the singlet/triplet splitting can still be strongly suppressed due to confinement effects and valley-orbit coupling.

Efficient 3D TCAD simulations of two-qubit gates in semiconductor quantum dots
Pericles Philippopoulos¹, Mohammad Mostaan², Raphaël Prentki¹, Thomas Baker³, Marek Korkusinski⁴, Felix Beaudoin⁵
¹Nanoacademic Technologies, ²Nanoacademic Technologies, Simon Fraser University, ³University of Victoria, ⁴National Research Council of Canada, ⁵Nanoacademic Technologies Inc.

Abstract:
The design and engineering of classical semiconductor chips often relies on a mature set of computational tools. Among these tools are technology computer-aided design (TCAD) software, used to predict device performance and trends before fabrication. As we move toward using semiconductors for quantum technologies like spin qubits, it seems plausible that we will need to adopt best practices from classical electronics. However, due to fundamental differences in operating principles between classical and quantum hardware, specialized quantum TCAD tools must be developed.

In recent years, spin-qubit systems in quantum-dot arrays have been scaled up to the 10-particle regime. In this regime, using 3D TCAD simulations to accurately model quantum operations on each qubit (e.g., single-qubit gates and readout) and pairs of qubits (e.g., two-qubit gates) becomes imperative to mitigate the significant costs of experimental rounds of design, fabrication, and characterization. Additionally, realistic 3D finite-element simulations of these systems are challenging due to mesh complexity and poor scaling of accurate many-body solvers with respect to particle number and size of the single-particle basis.

In this presentation, we will present computationally efficient approaches to simulate two-qubit gates in electron or hole quantum-dot systems with realistic 3D geometries. As illustrated in the figure, our approach encompasses the following key simulation steps: arbitrary 3D geometry definition (a), simulation of device electrostatics, computation of tunnel splittings (b) and envelope functions [(c) and (d)] from a single-particle effective Schrödinger equation, many-body simulations yielding charge stability diagrams and the exchange interaction strength (e), and time-dependent simulations of two-qubit gates under realistic noise sources (f). These results will be presented for practically relevant device geometries such as Fully Depleted Silicon On Insulator (FD-SOI) transistors. Leveraging recent advances in Coulomb interaction calculations and many-body physics, this work paves the way for high-throughput two-qubit gate simulation workflows for quantum-dot arrays.

Baseband control of single-electron silicon spin qubits in two-dimensions
Brennan Undseth¹, Florian Unseld¹, Yuta Matsumoto¹, Eline Raymenants¹, Oriol Pietx-Casas¹, Saurabh Karwal², Sergey Amitonov², Amir Sammak², Giordano Scappucci¹, Lieven Vandersypen¹
¹Delft University of Technology, ²Netherlands Organization for Applied Scientific Research (TNO)

Abstract:
Micromagnet-enabled electric-dipole spin resonance (EDSR) is an established means of high-fidelity single-spin control in silicon. However, the resulting architectural limitations have restrained state-of-the-art quantum processors to one-dimensional arrays, and heating effects from the associated microwave dissipation exacerbates crosstalk for multi-qubit operations. In contrast, spin control based on hopping spins has recently emerged as a compelling primitive for high-fidelity baseband control in sparse hole arrays in germanium [1]. In this work, we commission a ²⁸Si/SiGe 2x2 quantum dot array both as a 4-qubit quantum processor using established EDSR techniques and as a 2-qubit device using hopping spins in a low magnetic field regime. This control method is previously unexplored in the silicon platform but benefits from engineerable micromagnet-dominated stray fields that induce a measurable tip in quantization axis between adjacent quantum dots. The figure illustrates how the measured spin fraction after a particular shuttling sequence can be used to infer the tip when fit to the expected unitary evolution. We can directly compare the two modes of operation in terms of fidelity, coherence, and crosstalk. We find that the shuttling gate fidelity of 99.7% is on par with the benchmarked resonant gate while offering a shorter gate time. Lowering the external field to the shuttling regime nearly doubles the measured T₂^Hahn suggesting a reduced coupling to charge noise. Finally, the shuttling gate circumvents the transient pulse-induced resonance shift. These results establish new opportunities for engineering spin qubit arrays in silicon.

[1] Wang, C., John, V., Tidjani, H., et al. Operating semiconductor quantum processors with hopping spins. arXiv:2402.18382

06.09.2024, Friday, 16:10-17:30

Er sites in Si for quantum information processing
Alexey Lyasota¹, Ian Berkman², Gabriele de Boo², John Bartholomew³, Shao Lim⁴, Brett Johnson⁵, Jeffrey McCallum⁴, Bin-Bin Xu², Shouyi Xie², Rose Ahlefeldt⁶, Matthew Sellars⁶, Chunming Yin⁷, Sven Rogge²
¹Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, ²Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia, ³Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia; The University of Sydney Nano Institute, The University of Sydney, Sydney, New South Wales 2006, Australia, ⁴Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of Melbourne, Victoria 3010, Australia, ⁵School of Science, RMIT University, Victoria 3001, Australia, ⁶Centre of Excellence for Quantum Computation and Communication Technology, Research School of Physics, Australian National University, Canberra, Australian Capital Territory 0200, Australia, ⁷Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia; Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China

Abstract:
Rare-earth ions in a solid-state host exhibit low homogeneous broadening and long spin coherence at cryogenic temperatures, making them promising for a range of quantum applications, such as optical quantum memories and optical-microwave transductions. Emitters with long electron spin and optical coherence in Si, a leading material platform for electronic and photonic technologies, are especially attractive for quantum applications.
Here, we report on the observation of eight Er sites in Si that have both long optical coherence and electron spin lifetime. We measured 1 ms spin coherence for two sites in a nuclear spin-free silicon crystal (<0.01% 29Si), which appeared to be instrumentally limited. Using Alternating-Phase CPMG sequence, we extended the spin coherence of one of the sites to 40 ms. Measurements with naturally abundant Si revealed that the Er electron spin coherence was limited by coupling to 29Si nuclear spins. The measured homogeneous linewidths of all 8 sites are below 100 kHz, and inhomogeneous broadening approaches 100 MHz [1]. These results were achieved for Er implanted from 200 and 700 nm from 28Si surface at 1016 cm-3 level. The Er homogeneous linewidth and spin coherence were addressed using optical comb-based spectral hole burning and optically detected magnetic resonance techniques. To enhance Er emission collection efficiency, samples were directly positioned atop specially fabricated superconducting single photon detectors and resonantly excited via fibre optics. The demonstration of a long spin coherence time and narrow optical linewidth in multiple sites show that Er in 28Si is an exceptional candidate for future quantum information and communication applications and can be used for single photon frequency multiplexing schemes.

[1] Ian R. Berkman et al, arXiv:2307.10021v2 (2023).

Creation and manipulation of Schrödinger cat states of a nuclear spin qudit in silicon
Xi Yu¹, Benjamin Wilhelm¹, Danielle Holmes¹, Arjen Vaartjes¹, Daniel Schwienbacher¹, Martin Nurizzo¹, Anders Kringhoj¹, Mark van Blankenstein¹, Alexander Jakob², Pragati Gupta³, Fay Hudson⁴, Kohei Itoh⁵, Andrew Dzurak¹, Barry Sanders³, David Jamieson², Andrea Morello¹
¹School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, NSW 2052, Australia, ²School of Physics, University of Melbourne, Melbourne, VIC 3010, Australia, ³Institute for Quantum Science and Technology, University of Calgary, Alberta T3A 0E1, Canada, ⁴Diraq Pty. Ltd., Sydney, NSW, Australia, ⁵School of Fundamental Science and Technology, Keio University, Kohoku-ku, Yokohama, Japan

Abstract:
High-dimensional quantum systems are a valuable resource for quantum information processing. They can be used to encode error-correctable logical qubits, for instance in continuous-variable states of oscillators such as microwave cavities or the motional modes of trapped ions. Powerful encodings include ‘Schrödinger cat' states, superpositions of widely displaced coherent states. Recent proposals suggest encoding logical qubits in high-spin atomic nuclei, which can host hardware-efficient versions of continuous-variable codes on a finite-dimensional system.

Here we demonstrate the creation and manipulation of Schrödinger cat states using the spin-7/2 nucleus of a single antimony atom, embedded in a silicon nano-electronic device. We use a coherent multi-frequency control scheme to produce spin rotations that preserve the SU(2) symmetry of the 8-level qudit. These SU(2)-covariant rotations (CR) constitute logical Pauli operations for logical qubits encoded in the Schrödinger cat states. Together with the set of `virtual-SNAP' gates, which impart an arbitrary phase on each qudit level, the CR are used to generate the cat state (see the pulse sequence in figure a). After the generation protocol, We measure an equal superposition of the two spin-coherent states with opposite magnetization (figure b) and the Wigner function of the cat states (figure d) exhibits parity oscillations with a contrast up to 0.982(5) (figure c), and state fidelities up to 0.913(2).

Furthermore, a strong orientation-dependent lifetime of the spin-7/2 cat state is observed, with T2* values of 15.0(6) ms for cat states parallel to the spin quantization axis and 49(2) ms for perpendicular orientations. These findings hold promise for encoding logical qubits into perpendicular cat states, leveraging inherent biases in physical noise affecting nuclear spins.

These results demonstrate high-fidelity preparation and logical control of nonclassical resource states and underscore the feasibility of quantum error correction on a single atomic site within a semiconductor platform.

Inferring the shape of a few-hole Ge quantum dot from magnetospectroscopy data
Mitchell Brickson, Andrew Miller, N Jacobson, Tzu-Ming Lu, Dwight Luhman, Andrew Baczewski
Sandia National Laboratories

Abstract:
The magnetic properties of hole quantum dots in Ge are sensitive to their shape due to the interplay between strong spin-orbit coupling and strong confinement. We show that the inclusion of the split-off band, surrounding SiGe layers, and hole-hole interactions have a strong influence on calculations of the effective g factor of a lithographic quantum dot in a Ge/SiGe heterostructure. Comparing predictions from such a detailed model to raw magnetospectroscopy data, we apply maximum-likelihood estimation to infer the shape of a quantum dot with up to four holes. We expect that methods like this will be useful in assessing qubit-to-qubit variability critical to further scaling quantum computing technologies based on spins in semiconductors.

Magnon propagation and localization in a 2x4 Ge quantum dot array
Daniel Jirovec¹, Pablo Cova-Fariña², Stephan Oosterhout³, Tzu-Kan Hsiao¹, Xin Zhang¹, Elizaveta Morozova¹, Amir Sammak⁴, Giordano Scappucci¹, Menno Veldhorst¹, Lieven Vandersypen¹
¹TU Delft/ QuTech, ²TU Delft/QuTech, ³TNO / QuTech, ⁴TNO/ QuTech

Abstract:
Semiconductor-based quantum dot arrays are versatile platforms for analog quantum simulations, potentially offering insights into classically intractable many-body quantum phenomena with fewer resources compared to digital processors. The ability to engineer a variety of interesting regimes has led to the demonstration of exotic phases of matter, from Mott insulators and Nagaoka ferromagnetism to implementations of a Heisenberg spin-chain and signatures of resonating valence bonds. However, for quantum advantage, large scale systems and new tuning strategies are required. Here, we present advancements in this direction in a 2x4 Ge-based quantum dot array. We apply new tuning methods to the observation of magnon dynamics in a disordered system, where magnons represent spin excitations traveling through the array via nearest-neighbor exchange interactions, amidst disorder provided by random effective g-factors in each dot, typical for holes in Ge.

With our improved gate design, we achieve exchange tunability up to 500 MHz, surpassing disorder by a factor of 50 at our operating magnetic field, while mitigating exchange crosstalk through a novel compensation method. By optimizing ramp-times and idling points, we leverage the Hamiltonian's features to initialize target spin-states and extract single-site spin-up probabilities across the array. This enables us to track magnon evolution in tailored configurations as depicted in the figure showing a quantum walk in weakly coupled double dots. By increasing exchange we observe a transition from localization to free propagation, a phase transition reminiscent of many-body localization, a phenomenon of significant recent interest.

Our experiment bridges single qubit properties with many-body physics concepts, indicating progress towards large-scale analog simulators and realistic near-term applications of semiconductor quantum dot systems. Furthermore, we anticipate that the techniques demonstrated here will be directly transferable to digital spin qubit processors, expanding their capabilities.