Provable bounds for noise-free expectation values computed from noisy samples

TL;DR

This paper investigates how noise affects the accuracy of expectation values in quantum computing, providing bounds and methods to mitigate noise impact, validated through experiments on real quantum hardware.

Contribution

It introduces a formal framework to quantify sampling overhead and derive provable bounds on noise-free expectation values from noisy samples in quantum computing.

Findings

Sampling overhead relates to layer fidelity in noisy quantum processors.

Conditional Value at Risk can be used to bound expectation values.

Experimental results on a 127-qubit quantum computer align with theoretical predictions.

Abstract

In this paper, we explore the impact of noise on quantum computing, particularly focusing on the challenges when sampling bit strings from noisy quantum computers as well as the implications for optimization and machine learning applications. We formally quantify the sampling overhead to extract good samples from noisy quantum computers and relate it to the layer fidelity, a metric to determine the performance of noisy quantum processors. Further, we show how this allows us to use the Conditional Value at Risk of noisy samples to determine provable bounds on noise-free expectation values. We discuss how to leverage these bounds for different algorithms and demonstrate our findings through experiments on a real quantum computer involving up to 127 qubits. The results show a strong alignment with theoretical predictions.