Enhancing Quantum Expectation Values via Exponential Error Suppression and CVaR Optimization

TL;DR

This paper introduces a combined framework of Virtual Channel Purification and CVaR optimization to enhance the accuracy of quantum expectation values in noisy systems, providing analytical bounds and practical guidance.

Contribution

It develops conditions for comparing CVaR values from different distributions and applies these to VCP, establishing bounds that improve expectation value estimations under noise.

Findings

CVaR comparison conditions for quantum estimations

Analytical bounds for VCP effectiveness in noisy environments

Numerical examples demonstrating improved expectation values

Abstract

Precise quantum expectation values are crucial for quantum algorithm development, but noise in real-world systems can degrade these estimations. While quantum error correction is resource-intensive, error mitigation strategies offer a practical alternative. This paper presents a framework that combines Virtual Channel Purification (VCP) technique with Conditional Value-at-Risk (CVaR) optimization to improve expectation value estimations in noisy quantum circuits. Our contributions are twofold: first, we derive conditions to compare CVaR values from different probability distributions, offering insights into the reliability of quantum estimations under noise. Second, we apply this framework to VCP, providing analytical bounds that establish its effectiveness in improving expectation values, both when the overhead VCP circuit is ideal (error-free) and when it adds additional noise. By introducing CVaR into the analysis of VCP, we offer a general noise-characterization method that guarantees improved expectation values for any quantum observable. We demonstrate the practical utility of our approach with numerical examples, highlighting how our bounds guide VCP implementation in noisy quantum systems.