Theory of mirror benchmarking and demonstration on a quantum computer

TL;DR

This paper introduces mirror benchmarking as a method to evaluate quantum computer performance, providing a theoretical foundation and experimental validation on Honeywell hardware, with a focus on noise coherence estimation.

Contribution

It offers a simple proof of exponential decay in mirror benchmarking under certain noise assumptions and demonstrates its application on real quantum hardware.

Findings

Exponential decay of survival probability with circuit length observed

Decay rate linked to noise unitarity and quadratic error functions

Performance curves for different qubit numbers and depths presented

Abstract

A new class of protocols called mirror benchmarking was recently proposed to measure the system-level performance of quantum computers. These protocols involve circuits with random sequences of gates followed by mirroring, that is, inverting each gate in the sequence. We give a simple proof that mirror benchmarking leads to an exponential decay of the survival probability with sequence length, under the uniform noise assumption, provided the twirling group forms a 2-design. The decay rate is determined by a quantity that is a quadratic function of the error channel, and for certain types of errors is equal to the unitarity. This result yields a new method for estimating the coherence of noise. We present data from mirror benchmarking experiments run on the Honeywell System Model H1. This data constitutes a set of performance curves, indicating the success probability for random circuits as a function of qubit number and circuit depth.