Silicon Spin Qubits Research Articles

Correcting on-chip distortion of control pulses with silicon spin qubits

Abstract In semiconductor quantum dot systems, pulse distortion is a significant source of coherent errors, which impedes qubit characterization and control. Here, we demonstrate two calibration methods using a two-qubit system as a detector to correct distortion and calibrate the transfer function of the control line. Both methods are straightforward to implement, robust against noise, and applicable to a wide range of qubit types. The two methods differ in correction accuracy and complexity. The first, the Coarse Predistortion (CPD) method, partially mitigates distortion. The second, the All Predistortion (APD) method, measures the transfer function and significantly enhances exchange oscillation uniformity. Both methods use exchange oscillation homogeneity as the metric and are suitable for any qubit driven by a diabatic pulse. We believe these methods will enhance qubit characterization accuracy and operation quality in future applications.

Integration of buried nanomagnet and silicon spin qubits in a one-dimensional fin structure

We adopt a buried nanomagnet (BNM) technology on a one-dimensional (1D) array of silicon spin qubits, and its availability was investigated using numerical simulations. The qubit array is formed in the center of the Si fin and the nanomagnet is buried in the lower lateral part of the qubits. The nanomagnet placed near the qubit generates a strong slanting magnetic field in the qubit, enabling X-gate operation approximately 15 times faster than in conventional cases. Furthermore, the formation of a BNM using a self-aligned process suppresses the dimensional variation of the nanomagnet caused by process variation, thereby mitigating the slanting field fluctuation and fidelity degradation. In addition, even for multiple qubits formed in the Si fin, the BNM with excess length generated a uniform slanting field, mitigating fidelity degradation and enabling all qubits to operate using a single-frequency microwave. Therefore, the proposed structure is useful for 1D integrated structures.

Full-Permutation Dynamical Decoupling in Triple-Quantum-Dot Spin Qubits

Dynamical decoupling of spin qubits in silicon can increase fidelity and can be used to extract the frequency spectra of noise processes. We demonstrate a full-permutation dynamical decoupling technique that cyclically exchanges the spins in a triple-quantum-dot qubit. This sequence not only suppresses both low-frequency charge-noise-induced and magnetic-noise-induced errors; it also refocuses leakage errors to first order, which is particularly interesting for encoded exchange-only qubits. For a specific construction, which we call “NZ1y,” the qubit is isolated from error sources to such a degree that we measure a remarkable exchange pulse error of 2.8×10−5. This sequence maintains a quantum state for roughly 18,000 exchange pulses, extending the qubit coherence from T2∗=2μs to T2=720μs. We experimentally validate an error model that includes 1/f charge noise and 1/f magnetic noise in two ways: by direct exchange-qubit simulation and by integration of the assumed noise spectra with derived filter functions, both of which reproduce the measured error and leakage with respect to a change of the repetition rate. Published by the American Physical Society 2024

High-Fidelity Spin Qubit Shuttling via Large Spin-Orbit Interactions

Shuttling spins with high fidelity is a key requirement to scale up semiconducting quantum computers, enabling qubit entanglement over large distances and favoring the integration of control electronics on-chip. To decouple the spin from the unavoidable charge noise, state-of-the-art spin shuttlers try to minimize the inhomogeneity of the Zeeman field. However, this decoupling is challenging in otherwise promising quantum computing platforms such as hole spin qubits in silicon and germanium, characterized by a large spin-orbit interaction and an electrically tunable qubit frequency. In this work, we show that, surprisingly, the large inhomogeneity of the Zeeman field stabilizes the coherence of a moving spin state, thus also enabling high-fidelity shuttling in these systems. We relate this enhancement in fidelity to the deterministic dynamics of the spin that filters out the dominant low-frequency contributions of the charge noise. By simulating several different scenarios and noise sources, we show that this is a robust phenomenon generally occurring at large field inhomogeneity. By appropriately adjusting the motion of the quantum dot, we also design realistic protocols enabling faster and more coherent spin shuttling. Our findings are generally applicable to a wide range of setups and could pave the way toward large-scale quantum processors. Published by the American Physical Society 2024

High-fidelity spin qubit operation and algorithmic initialization above 1 K

The encoding of qubits in semiconductor spin carriers has been recognized as a promising approach to a commercial quantum computer that can be lithographically produced and integrated at scale1–10. However, the operation of the large number of qubits required for advantageous quantum applications11–13 will produce a thermal load exceeding the available cooling power of cryostats at millikelvin temperatures. As the scale-up accelerates, it becomes imperative to establish fault-tolerant operation above 1 K, at which the cooling power is orders of magnitude higher14–18. Here we tune up and operate spin qubits in silicon above 1 K, with fidelities in the range required for fault-tolerant operations at these temperatures19–21. We design an algorithmic initialization protocol to prepare a pure two-qubit state even when the thermal energy is substantially above the qubit energies and incorporate radiofrequency readout to achieve fidelities up to 99.34% for both readout and initialization. We also demonstrate single-qubit Clifford gate fidelities up to 99.85% and a two-qubit gate fidelity of 98.92%. These advances overcome the fundamental limitation that the thermal energy must be well below the qubit energies for the high-fidelity operation to be possible, surmounting a main obstacle in the pathway to scalable and fault-tolerant quantum computation.

Pipeline quantum processor architecture for silicon spin qubits

We propose a quantum processor architecture, the qubit ‘pipeline’, in which run-time scales additively as functions of circuit depth and run repetitions. Run-time control is applied globally, reducing the complexity of control and interconnect resources. This simplification is achieved by shuttling N-qubit states through a large layered physical array of structures which realise quantum logic gates in stages. Thus, the circuit depth corresponds to the number of layers of structures. Subsequent N-qubit states are ‘pipelined’ densely through the structures to efficiently wield the physical resources for repeated runs. Pipelining thus lends itself to noisy intermediate-scale quantum (NISQ) applications, such as variational quantum eigensolvers, which require numerous repetitions of the same or similar calculations. We illustrate the architecture by describing a realisation in the naturally high-density and scalable silicon spin qubit platform, which includes a universal gate set of sufficient fidelity under realistic assumptions of qubit variability.

High-fidelity initialization and control of multiple nuclear spin qubits in silicon.

High-fidelity initialization and control of multiple nuclear spin qubits in silicon.

Impact of measurement backaction on nuclear spin qubits in silicon

Impact of measurement backaction on nuclear spin qubits in silicon

Compressed Gate Characterization for Quantum Devices with Time-Correlated Noise

As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate-set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one- and two-qubit gates can be compressed by 10× and 100×, respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two-qubit interleaved randomized benchmarking fidelities of 99.8% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large arrays of quantum devices with non-Markovian noise. Published by the American Physical Society 2024

Noise-correlation spectrum for a pair of spin qubits in silicon

Noise-correlation spectrum for a pair of spin qubits in silicon

Feedback-based active reset of a spin qubit in silicon

Feedback control of qubits is a highly demanded technique for advanced quantum information protocols such as fault-tolerant quantum error correction. Here we demonstrate active reset of a silicon spin qubit using feedback control. The active reset is based on quantum non-demolition (QND) readout of the qubit and feedback according to the readout results, which is enabled by hardware data processing and sequencing. We incorporate a cumulative readout technique to the active reset protocol, enhancing initialization fidelity above a limitation imposed by the single-shot QND readout fidelity. An analysis of the reset protocol implies a pathway to achieve the initialization fidelity sufficient for fault-tolerant quantum computation. These results provide a practical approach to high-fidelity qubit operations in realistic devices.

Interface and electromagnetic effects in the valley splitting of Si quantum dots

The performance and scalability of silicon spin qubits depend directly on the value of the conduction band valley splitting (VS). In this work, we investigate the influence of electromagnetic fields and the interface width on the VS of a quantum dot in a Si/SiGe heterostructure. We propose a new three-dimensional theoretical model within the effective mass theory for the calculation of the VS in such heterostructures that takes into account the concentration fluctuation at the interfaces and the lateral confinement. With this model, we predict that the electric field is an important parameter for VS engineering, since it can shift the probability distribution away from small VSs for some interface widths. We also obtain a critical softness of the interfaces in the heterostructure, above which the best option for spin qubits is to consider an interface as wide as possible.

Nonlinear Response and Crosstalk of Electrically Driven Silicon Spin Qubits

Frequency multiplexing of operations is an attractive strategy to control multiple qubits simultaneously in a spin-based quantum processor with relatively few control lines. However, high-fidelity operation demands good spectral addressability and noncontextual spin dynamics. The authors explore an unexpected crosstalk mechanism, in which the Rabi frequency of one spin changes markedly depending on the simultaneous operation of another. They also connect this behavior to another surprising feature: the nonlinear scaling of Rabi frequency with resonant driving amplitude. These results provide insight into the challenges that such state-of-the-art control methods will face.

Blueprint of a Scalable Spin Qubit Shuttle Device for Coherent Mid-Range Qubit Transfer in Disordered Si/SiGe/SiO2

Silicon spin qubits stand out due to their very long coherence times, compatibility with industrial fabrication, and prospect to integrate classical control electronics. To achieve a truly scalable architecture, a coherent mid-range link that moves the electrons between qubit registers has been suggested to solve the signal fan-out problem. Here, we present a blueprint of such a link of 10 μm length, called a spin qubit shuttle, which is based on connecting an array of gates into a small number of sets. To control these sets, only a few voltage control lines are needed and the number of these sets and thus the number of required control signals is independent of the length of this link. We discuss two different operation modes for the spin qubit shuttle: a qubit conveyor, i.e., a potential minimum that smoothly moves laterally, and a bucket brigade, in which the electron is transported through a series of tunnel-coupled quantum dots by adiabatic passage. We find the former approach more promising considering a realistic Si/SiGe device, including potential disorder from the charged defects at the Si/SiO2 layer, as well as typical charge noise. Focusing on the qubit transfer fidelity in the conveyor shuttling mode, we discuss in detail motional narrowing, the interplay between orbital and valley excitation and relaxation in the presence of g factors that depend on orbital and valley state of the electron, and effects from spin hotspots. We find that a transfer fidelity of 99.9% is feasible in Si/SiGe at a speed of approximately 10m/s, if the average valley splitting and its inhomogeneity stay within realistic bounds. Operation at low global magnetic field approximately equal to 20mT and material engineering towards high valley splitting is favorable for reaching high fidelities of transfer.12 MoreReceived 10 March 2022Revised 18 October 2022Accepted 15 February 2023DOI:https://doi.org/10.1103/PRXQuantum.4.020305Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum information with solid state qubitsQuantum transportSpin coherenceSpin relaxationSurface & interfacial phenomenaPhysical SystemsQuantum dotsSemiconductor compoundsCondensed Matter, Materials & Applied PhysicsQuantum Information

Acceptor-based qubit in silicon with tunable strain

Long coherence time and compatibility with semiconductor fabrication make spin qubits in silicon an attractive platform for quantum computing. In recent years, hole spin qubits are being developed as they have the advantages of weak coupling to nuclear spin noise and strong spin-orbit coupling (SOC), in constructing high-fidelity quantum gates. However, there are relatively few studies on the hole spin qubits in a single acceptor, which requires only low density of the metallic gates. In particular, the investigation of flexible tunability using controllable strain for fault-tolerant quantum gates of acceptor-based qubits is still lacking. Here, we study the tunability of electric dipole spin resonance (EDSR) of acceptor-based hole spin qubits with controllable strain. The flexible tunability of LH-HH splitting and spin-hole coupling (SHC) with the two kinds of strain can avoid high electric field at the "sweet spot", and the operation performance of the acceptor qubits could be optimized. Longer relaxation time or stronger EDSR coupling at low electric field can be obtained. Moreover, with asymmetric strain, two "sweet spots" are induced and may merge together, and form a second-order "sweet spot". As a result, the quality factor $Q$ can reach $10^{4}$ for single-qubit operation, with high tolerance for the electric field variation. Furthermore, the two-qubit operation of acceptor qubits based on dipole-dipole interaction is discussed for high-fidelity two-qubit gates. The tunability of spin qubit properties in acceptor via strain could provide promising routes for spin-based quantum computing.

Probing Low-Frequency Charge Noise in Few-Electron CMOS Quantum Dots

Charge noise is one of the main sources of environmental decoherence for spin qubits in silicon, presenting a major obstacle in the path towards highly scalable and reproducible qubit fabrication. Here we demonstrate in-depth characterization of the charge noise environment experienced by a quantum dot in a CMOS-fabricated silicon nanowire. We probe the charge noise for different quantum dot configurations, finding that it is possible to tune the charge noise over two orders of magnitude, ranging from $1\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{eV}}^{2}/\mathrm{Hz}$ to $100\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{eV}}^{2}/\mathrm{Hz}$. In particular, we show that the top interface and the reservoirs are the main sources of charge noise, and their effect can be mitigated by controlling the quantum dot extension. Additionally, we demonstrate a method for the measurement of the charge noise experienced by a quantum dot in the few-electron regime. We measure a comparatively high charge noise value of $40\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{eV}}^{2}/\mathrm{Hz}$ at the first electron, and demonstrate that the charge noise is highly dependent on the electron occupancy of the quantum dot.

Realizable time crystal of four silicon quantum dot qubits

We demonstrate that exciting possible realizations of quantum Floquet matter are within reach for modern silicon spin qubits based in quantum dots, most notably the discrete time crystal (DTC). This is significant given that spin qubits have fallen behind other qubit architectures in terms of size and control. However, silicon spin qubits are especially well suited to this task as the charge noise that usually foils gate operations can now be leveraged as an asset in this time-crystal realization. We illustrate differences between prethermal phenomena and true time-crystalline spatiotemporal order. We demonstrate that even for a spin chain of four qubits, rich regime structures can be established by observing signatures of the discrete time crystal and the Floquet symmetry-protected topological regime both distinct from the thermal regime. We also analyze the persistence of these signatures at longer chain lengths, showing that the DTC lifetime grows exponentially with the system length and that these signatures may even be detectable for chains as small as three qubits. We also discuss the effects of longer pulse durations and the effectiveness of pulse sequences for converting the exchange interaction to an Ising model. Our theoretical predictions are well suited for immediate experimental implementations using currently existing quantum dot spin qubit systems.

Device structure and fabrication process for silicon spin qubit realizing process-variation-robust SWAP gate operation

In this study, we propose technologies for the device structure, gate fabrication process, and back-bias-assisted operation of Si spin qubits to realize the high robustness of the two-qubit SWAP gate operation against process variations. We performed quantum device simulations for MOS-type two-qubit devices and verified the benefits of these technologies on the SWAP gate fidelity. We clarified that these technologies significantly improve the robustness of the SWAP gate operation against process variations and achieve a 6σ-yield SWAP gate operation with 99% fidelity, assuming device size fluctuation of the International Roadmap for Devices and Systems (IRDS) target for 2022. The proposed technologies provide a solution for completing a universal quantum gate set for realizing universal quantum computers with silicon.

High-Fidelity CNOT Gate for Donor Electron Spin Qubits in Silicon

Epitaxial atom-based spin qubits in silicon exhibit excellent properties, and benefit from the outstanding scalability of that material platform. As silicon spin-based qubits now start to meet the 99% fault-tolerance threshold, the authors show how the nuclear spins inherent to the local magnetic environment can be engineered as atomic magnets to boost the fidelities of two-qubit logic gates. Modeling indicates that two-qubit CNOT gate fidelities as high as 99.98% are realistic, through silicon purification and careful engineering. This work provides a roadmap for atom qubits in silicon, showing how to optimize two-qubit gates at both the design and measurement stages.

Universal logic with encoded spin qubits in silicon

Quantum computation features known examples of hardware acceleration for certain problems, but is challenging to realize because of its susceptibility to small errors from noise or imperfect control. The principles of fault tolerance may enable computational acceleration with imperfect hardware, but they place strict requirements on the character and correlation of errors1. For many qubit technologies2–21, some challenges to achieving fault tolerance can be traced to correlated errors arising from the need to control qubits by injecting microwave energy matching qubit resonances. Here we demonstrate an alternative approach to quantum computation that uses energy-degenerate encoded qubit states controlled by nearest-neighbour contact interactions that partially swap the spin states of electrons with those of their neighbours. Calibrated sequences of such partial swaps, implemented using only voltage pulses, allow universal quantum control while bypassing microwave-associated correlated error sources1,22–28. We use an array of six 28Si/SiGe quantum dots, built using a platform that is capable of extending in two dimensions following processes used in conventional microelectronics29. We quantify the operational fidelity of universal control of two encoded qubits using interleaved randomized benchmarking30, finding a fidelity of 96.3% ± 0.7% for encoded controlled NOT operations and 99.3% ± 0.5% for encoded SWAP. The quantum coherence offered by enriched silicon5–9,16,18,20,22,27,29,31–37, the all-electrical and low-crosstalk-control of partial swap operations1,22–28 and the configurable insensitivity of our encoding to certain error sources28,33,34,38 all combine to offer a strong pathway towards scalable fault tolerance and computational advantage.