Bounding experimental quantum error rates relative to fault-tolerant thresholds

Abstract

Rigorously establishing that the error in an experimental quantum operation is beneath the threshold for fault-tolerant quantum computation currently requires considering the worst-case error, which can be orders of magnitude smaller than the average gate infidelities routinely reported in experiments. We show that an improved bound on the worst-case error can be obtained by also considering the recently-introduced unitarity of the noise where the upper and lower bounds differ by a factor of $\approx 2.45$ for unital qubit channels. We prove that the contribution from the nonunital part of any noise map is at most on the order of the average gate infidelity and so is negligible relative to any coherent contribution. We also show that the "average" error rate when measurements are not restricted to an eigenbasis containing the state of the system exhibits the same scaling as the worst-case error, which, for coherent noise, is the square-root of the infidelity. We also obtain improved bounds for the diamond distance when the noise map is known (or approximately known).

12 pages, comments welcome. Improves on bounds involving the unitarity presented in arxiv.org/abs/1510.05653. v2: added discussion of the average gate error, simplified proofs and expositions and improved bounds

References in corpus (7)

• Randomized Benchmarking of Quantum Gates
• Robust randomized benchmarking of quantum processes
• Noise tailoring for scalable quantum computation via randomized compiling
• Direct Fidelity Estimation from Few Pauli Measurements
• Estimating the Coherence of Noise
• Comparing Experiments to the Fault-Tolerance Threshold
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Cited by in corpus (19)

• Noise tailoring for scalable quantum computation via randomized compiling
• Performance and structure of single-mode bosonic codes
• Silicon qubit fidelities approaching incoherent noise limits via pulse engineering
• Comparing Experiments to the Fault-Tolerance Threshold
• Performance of quantum error correction with coherent errors
• Recovering quantum gates from few average gate fidelities
• Gate-error analysis in simulations of quantum computers with transmon qubits
• Estimating the coherence of noise in quantum control of a solid-state qubit
• Estimating the fidelity of T gates using standard interleaved randomized benchmarking
• From randomized benchmarking experiments to gateset circuit fidelity: how to interpret randomized benchmarking decay parameters
• Unitarity estimation for quantum channels
• Entangling-gate error from coherently displaced motional modes of trapped ions
• Estimation of correlations and non-separability in quantum channels via unitarity benchmarking
• Combining $T_1$ and $T_2$ estimation with randomized benchmarking and bounding the diamond distance
• Lightweight Detection of a Small Number of Large Errors in a Quantum Circuit
• Supercomputer simulations of transmon quantum computers
• Measurement-based interleaved randomised benchmarking using IBM processors
• Relative resilience to noise of standard and sequential approaches to measurement-based quantum computation
• Robustly decorrelating errors with mixed quantum gates