Randomized Benchmarking Beyond Groups

Abstract

Randomized benchmarking (RB) is the gold standard for experimentally evaluating the quality of quantum operations. The current framework for RB is centered on groups and their representations, but this can be problematic. For example, Clifford circuits need up to $O(n^2)$ gates, and thus Clifford RB cannot scale to larger devices. Attempts to remedy this include new schemes such as linear cross-entropy benchmarking (XEB), cycle benchmarking, and non-uniform RB, but they do not fall within the group-based RB framework. In this work, we formulate the \emph{universal randomized benchmarking (URB) framework} which does away with the group structure and also replaces the recovery gate plus measurement component with a general ``post-processing'' POVM. Not only does this framework cover most of the existing benchmarking schemes, but it also gives the language for and helps inspire the formulation of new schemes. We specifically consider a class of URB schemes called \emph{twirling schemes}. For twirling schemes, the post-processing POVM approximately factorizes into an intermediate channel, inverting maps, and a final measurement. This leads us to study the twirling map corresponding to the gate ensemble specified by the scheme. We prove that if this twirling map is strictly within unit distance of the Haar twirling map in induced diamond norm, the probability of measurement as a function of gate length is a single exponential decay up to small error terms. The core technical tool we use is the matrix perturbation theory of linear operators on quantum channels.

36 pages

References in corpus (5)

• 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
• Randomized Benchmarking of Multi-Qubit Gates

Cited by in corpus (6)

• Benchmarking universal quantum gates via channel spectrum
• One Gate Scheme to Rule Them All: Introducing a Complex Yet Reduced Instruction Set for Quantum Computing
• Operational Markovianization in Randomized Benchmarking
• Linear Cross Entropy Benchmarking with Clifford Circuits
• Group twirling and noise tailoring for multi-qubit controlled phase gates
• Benchmarking of universal qutrit gates