Optimizing Circuit Reusing and its Application in Randomized Benchmarking

TL;DR

This paper develops a theoretical framework for optimizing circuit reusing in quantum experiments, minimizing measurement variance and cost, validated through randomized benchmarking and superconducting platform experiments.

Contribution

It introduces a method to determine the optimal reusing parameter R for quantum circuits, including a near-optimal strategy applicable without prior noise knowledge.

Findings

Optimal R minimizes variance for given cost.

Non-linear R-cost relationship observed experimentally.

Framework accurately predicts optimal R in superconducting experiments.

Abstract

Quantum learning tasks often leverage randomly sampled quantum circuits to characterize unknown systems. An efficient approach known as "circuit reusing," where each circuit is executed multiple times, reduces the cost compared to implementing new circuits. This work investigates the optimal reusing parameter that minimizes the variance of measurement outcomes for a given experimental cost. We establish a theoretical framework connecting the variance of experimental estimators with the reusing parameter R. An optimal R is derived when the implemented circuits and their noise characteristics are known. Additionally, we introduce a near-optimal reusing strategy that is applicable even without prior knowledge of circuits or noise, achieving variances close to the theoretical minimum. To validate our framework, we apply it to randomized benchmarking and analyze the optimal R for various typical noise channels. We further conduct experiments on a superconducting platform, revealing a non-linear relationship between R and the cost, contradicting previous assumptions in the literature. Our theoretical framework successfully incorporates this non-linearity and accurately predicts the experimentally observed optimal R. These findings underscore the broad applicability of our approach to experimental realizations of quantum learning protocols.