A general framework for randomized benchmarking

Abstract

Randomized benchmarking (RB) refers to a collection of protocols that in the past decade have become central methods for characterizing quantum gates. These protocols aim at efficiently estimating the quality of a set of quantum gates in a way that is resistant to state preparation and measurement errors. Over the years many versions have been developed, however, a comprehensive theoretical treatment of RB has been missing. In this work, we develop a rigorous framework of RB general enough to encompass virtually all known protocols as well as novel, more flexible extensions. Overcoming previous limitations on error models and gate sets, this framework allows us, for the first time, to formulate realistic conditions under which we can rigorously guarantee that the output of any RB experiment is well-described by a linear combination of matrix exponential decays. We complement this with a detailed analysis of the fitting problem associated with RB data. We introduce modern signal processing techniques to RB, prove analytical sample complexity bounds, and numerically evaluate performance and limitations. In order to reduce the resource demands of this fitting problem, we introduce novel, scalable post-processing techniques to isolate exponential decays, significantly improving the practical feasibility of a large set of RB protocols. These post-processing techniques overcome shortcomings in efficiency of several previously proposed methods such as character benchmarking and linear-cross entropy benchmarking. Finally, we discuss, in full generality, how and when RB decay rates can be used to infer quality measures like the average fidelity. On the technical side, our work substantially extends the recently developed Fourier-theoretic perspective on RB by making use of the perturbation theory of invariant subspaces, as well as ideas from signal processing.

61 pages, 7 figures, replaced by final version in PRX Quantum

References in corpus (14)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Randomized Benchmarking of Quantum Gates
• Robust randomized benchmarking of quantum processes
• Characterization of addressability by simultaneous randomized benchmarking
• Symmetrised Characterisation of Noisy Quantum Processes
• Theory of quantum system certification: a tutorial
• Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing
• Statistical analysis of randomized benchmarking
• Matchgate benchmarking: Scalable benchmarking of a continuous family of many-qubit gates
• Rolling quantum dice with a superconducting qubit
• Benchmarking near-term quantum computers via random circuit sampling
• Compressive Spectral Estimation with Single-Snapshot ESPRIT: Stability and Resolution
• Randomized Benchmarking, Correlated Noise, and Ising Models
• A framework for randomized benchmarking over compact groups

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