Nonlinear Response and Crosstalk of Electrically Driven Silicon Spin Qubits
Brennan Undseth, Xiao Xue, Mohammad Mehmandoost, Maximilian Rimbach-Russ, Pieter T. Eendebak, Nodar Samkharadze, Amir Sammak, V. V. Dobrovitski, Giordano Scappucci, Lieven M. K. Vandersypen
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.
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.
In electric dipole spin resonance (EDSR), a single spin is electrically driven in the field gradient produced by a micromagnet. While EDSR has enabled high fidelity gate operations in many devices, there are reports of unexpected non-linearities in the Rabi frequency as a function of microwave drive amplitude. We carefully measure the response of Loss-DiVincenzo (LD) single spin qubits to resonant drives as well as simultaneous resonant and off-resonant drives, as would be encountered in a realistic quantum processor. With the microwave amplitude carefully calibrated, we find that the Rabi frequency scales linearly with drive amplitude, even when all three spins are driven simultaneously. We also determine that heating-induced resonance frequency shifts from off-resonant drives are comparable to typical temporal drifts. Our results indicate that the previously observed nonlinear response is not a general feature of LD spin qubits.
Electron spins trapped in quantum dots have recently proven to be a promising technology for the implementation of qubits, already demonstrating high fidelity single- and two-qubits gates. The next step towards fault-tolerant quantum computing is to increase the number of so-called spin qubits on the processor. However, this poses several challenges, one of which being how to implement single-qubit gates in multi-qubit systems, with high fidelity. This work focused on two aspects. The first one was to identify the physical phenomena and limitations that hinder the realisation of high fidelity single-qubit gates in multi-qubit environments. The second objective was to investigate, implement and optimise methods in order to minimise the impact of these perturbing phenomena. The identified perturbing effects include unwanted driving between a pulse and the neighbouring qubits, as well as frequency shifts induced by drive-spin coupling and non-ideal pulse in experimental setups. Crosstalk was addressed using pulse shaping (i.e. amplitude or phase modulation of the driving pulse to tailor its spectral characteristics and reduce the energy transmitted at unwanted frequencies). The performance of shapes taken from both NMR and signal processing literature was investigated, for various pulse parameters, through an extensive grid search. In addition, a frequency correction algorithm was devised: off-resonant drive frequencies are selected so that the shifted qubits are resonantly driven. It currently accounts for two phenomena: the AC Stark and Bloch-Siegert shifts. The algorithm furthermore tracks the changes caused by the time-dependent characteristics of the shaped pulses. The proposed frequency correction algorithm was shown to almost entirely negate the effects of the considered shifts, leading to unitary fidelity improvements by up to 55%. In addition, pulse shaping was demonstrated to noticeably improve the fidelity of simultaneous single-qubit rotations compared to unshaped driving. Rotations with fidelities as high as 99.98% were obtained for pi/2 rotations on two-qubits systems. Moreover, shapes whose Fourier transform is narrow and sharp, associated with low Rabi frequencies, were demonstrated to generally provide the highest fidelities of the tested configurations. Lastly, the trends and guidelines highlighted by these results were shown to scale to systems with larger numbers of qubits. The correction techniques investigated in this work have proven promising for the implementation of high fidelity single-qubit gates in multi-qubit systems. In particular, the guidelines for selecting a well-performing pulse shape should also be useful for the design of optimised driving schemes, regardless of the number of qubits involved. Additionally, the proposed frequency shift correction algorithm is expected to be able to handle arbitrary shifts, and so to be easily adaptable to use in experiments.
Abstract Silicon spin qubits offer a promising path to scalable quantum computing due to their compatibility with industrial semiconductor manufacturing. A key requirement for scaling quantum processors is the ability to perform high-fidelity operations in parallel across many qubits. However, simultaneous control remains a major challenge in silicon devices, as fidelities typically degrade under parallel operation. Here we identify microwave-drive-induced a.c.-Stark shifts as the dominant source of this degradation in a five-qubit silicon spin array. We address this by introducing a scalable mitigation protocol based solely on pairwise phase calibrations. Using tailored control pulses on a shared control line, we achieve primitive X and Y gate fidelities well above 99.99% for each qubit individually, with some approaching 99.999%. Furthermore, these fidelities are preserved above 99.99% during simultaneous operation of up to three qubits. During parallel five-qubit operation, fidelities remain above the widely targeted fault-tolerant threshold of 99.9%. By maintaining high-fidelity control during simultaneous operation, shared qubit-control lines can support the development of large-scale semiconductor quantum processors.
The growing interest in quantum computers has triggered various approaches for the realization of a large-scale quantum processor that can eventually outperform classical high-performance computers. Quantum computers are attracting increasing attention for their potential to enormously accelerate the simulation of quantum systems and the solution of optimization problems, promising an immense impact, particularly in fields such as chemistry, medicine, and cybersecurity. Although it is still a long way to a practical quantum device, the progress over the last decades has shown encouraging results for a so far limited number of quantum bits, or qubits for short, which represent the computational units of the processor. One promising platform for the implementation of qubits is the spin of charge carriers in semiconductor quantum dots. Especially the use of purified silicon as a host material has significantly improved the performance of quantum operations. Advanced fabrication techniques from the established semiconductor industry in principle allow for the manufacturing of a large number of qubits on a small chip, making them specifically competitive from the perspective of scalability. In this thesis, we investigate challenges for electron spin qubits, particularly in the context of scaling to large qubit arrays for quantum computation. We evaluate the performance of quantum gates, present error mitigation strategies, and propose new quantum operations for two particular spin qubit implementations. In a dense array of Loss-DiVincenzo spin qubits on a chip, quantum information can be electrically controlled by microwave pulses. For neighboring qubits, capacitive couplings of nearby electrodes lead to crosstalk that affects the quantum computation. The first examination in this thesis addresses the effect of crosstalk on idling and operating spin qubits due to an interfering microwave drive. After the analysis and characterization of the performance, we suggest mitigation protocols for different constellations of important quantum gates, which can be easily implemented experimentally. We further show how to reduce crosstalk in a two-qubit gate using an asymmetric driving scheme, resulting in an enormous improvement of the gate performance, and may be used to generally overcome the obstacle of crosstalk. An additional source of errors in spin qubit registers originates from the finite residual exchange interaction between neighboring qubits. It arises due to a finite overlap of the electron wave functions and is caused by the limited speed at which the applied voltages can be controlled. We evaluate the fidelity of doing quantum operations under these circumstances with a varying number of neighboring qubits and present robust mitigation schemes with a decent performance also in the presence of noise. Besides crosstalk, another crucial observation in experiments using microwaves is the heating caused by the delivery of high-power radio frequency pulses to the quantum chip and results in a change of the qubit properties. We therefore investigate the impact of phonons on the energy levels in spin qubits to identify a temperature-dependent correction to the qubit state splitting. As microwave pulses are associated with potential errors, exchange-only qubits represent a promising alternative to achieve universal quantum computation only using baseband control. Therefore, we shift our focus towards exchange-only qubits and outline the main error sources in these systems, including residual exchange interactions between spins, charge noise from the applied voltages, and magnetic fluctuations in the material. A consequential complication of this implementation is that the quantum information can leak out of the qubit states. This effect, however, can be reduced in the presence of a finite magnetic field, as we will demonstrate in this thesis. The gate construction for exchange-only qubits usually requires more pulse steps than in the previous qubit type. Nevertheless, if exchange interactions are switched on simultaneously, this can result in faster quantum gates, as we demonstrate in this thesis. Especially the discovery of a quantum operation that introduces relative phases between computational and leakage states can be of interest for the construction of two-qubit gates and will be discussed in an example for a special operation space.
Exchange coupling and microwave drives are widely used control mechanisms for spin qubits. However, the influence of exchange coupling on microwave-driven spin dynamics is not fully understood. We report simultaneous drive measurements of two spin qubits as a function of exchange coupling and drive power. When the Rabi frequency exceeds exchange, we observe a beating pattern in the Rabi oscillations. In the opposite limit, two exchange-split patterns emerge in the Rabi chevrons. We find that these exchange-induced effects are suppressed when the difference in the Rabi frequencies exceeds the exchange coupling. A theoretical model is developed that reproduces the main features in our data.
Maintaining or even improving gate performance with growing numbers of parallel controlled qubits is a vital requirement for fault-tolerant quantum computing.For superconducting quantum processors, though isolated one-or two-qubit gates have been demonstrated with high fidelity, implementing these gates in parallel commonly shows worse performance.Generally, this degradation is attributed to various crosstalks between qubits, such as quantum crosstalk due to residual inter-qubit coupling.An understanding of the exact nature of these crosstalks is critical to figuring out respective mitigation schemes and improved qubit architecture designs with low crosstalk.Here we give a theoretical analysis of quantum crosstalk impact on simultaneous gate operations in a qubit architecture, where fixed-frequency transmon qubits are coupled via a tunable bus, and sub-100-ns controlled-Z (CZ) gates can be realized by applying a baseband flux pulse on the bus.Our analysis shows that for microwave-driven single-qubit gates, the dressing from the qubit-qubit coupling can cause non-negligible cross-driving errors when qubits operate near frequency collision regions.During CZ gate operations, although unwanted nearest-neighbor interactions are nominally turned off, sub-MHz parasitic next-nearest-neighbor interactions involving spectator qubits can still exist, causing considerable leakage or control error when one operates qubit systems around these parasitic resonance points.To ensure high-fidelity simultaneous operations, a request could be raised to figure out a better way to balance the gate error from target qubit systems themselves and the error from nonparticipating spectator qubits.Overall, our analysis suggests that towards useful quantum processors, the qubit architecture should be examined carefully in the context of high-fidelity simultaneous gate operations in a scalable qubit lattice.