Abstract
The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error that has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomized benchmarking and related protocols are not sensitive to the full impact of coherent errors and therefore do not reliably predict the global performance of quantum algorithms, leaving us unprepared to validate the accuracy of future large-scale quantum computations. Randomized compiling is a protocol designed to overcome these performance limitations by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of algorithmic performance from error rates measured via cycle benchmarking. In this work, we demonstrate significant performance gains under randomized compiling for the four-qubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. Additionally, we accurately predict algorithm performance using experimentally measured error rates. Our results demonstrate that randomized compiling can be utilized to leverage and predict the capabilities of modern-day noisy quantum processors, paving the way forward for scalable quantum computing.Received 13 May 2021Accepted 3 September 2021DOI:https://doi.org/10.1103/PhysRevX.11.041039Published 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 algorithmsQuantum benchmarkingQuantum controlQuantum information with solid state qubitsQuantum Information
Highlights
The accuracy of quantum algorithms is limited by different types of errors
We show that Randomized compiling [20] (RC) effectively reduces and stabilizes the otherwise unpredictable impact of actual performance-limiting coherent errors in the quantum Fourier transform [31] (QFT) algorithm and in random circuits of variable depth sampled from a universal gate set
A histogram of the total variation distance (TVD) improvement for two, three, and four-qubit random input quantum Fourier transform [31] (QFT) results can be seen in Fig. 3(e), showing that the vast majority of circuits are improved under RC by an average of dTV;bare=dTV;RC ≈ 1.9
Summary
The accuracy of quantum algorithms is limited by different types of errors. Interactions between qubits and the surrounding environment result in incoherent (i.e., nonunitary or irreversible) errors, leading to purity-decreasing processes such as the decoherence of a quantum state. The average-case and worst-case infidelities of a single computational gate can differ by orders of magnitude in the presence of coherent errors, as has been explicitly demonstrated for the quantum processor used in this work using simultaneous gate-set tomography [15]. RC significantly mitigates the impact of coherent errors, as indicated by a reduction in the TVD from dTV;bare 1⁄4 0.170ð8Þ to dTV;RC 1⁄4 0.029ð2Þ in the fjþi; j−ig basis, from dTV;bare 1⁄4 0.069ð4Þ to dTV;RC 1⁄4 0.060ð1Þ in the fj þ ii; j − iig basis, and from dTV;bare 1⁄4 0.073ð8Þ to dTV;RC 1⁄4 0.008ð2Þ in the fj0i; j1ig (computational) basis This improvement is not captured by the bare (F 1⁄4 0.862) and RC (F 1⁄4 0.879) state fidelities, which are approximately equal. Quantum processors continue to decrease, paving the way for more robust large-scale quantum computation
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