Distributionally Robust Variational Quantum Algorithms with Shifted Noise

TL;DR

This paper introduces a distributionally robust optimization approach for variational quantum algorithms to maintain performance under unknown, shifting noise conditions, enhancing their reliability in practical quantum computing scenarios.

Contribution

It formulates a novel distributionally robust optimization framework for VQAs that accounts for shifted noise, and demonstrates its effectiveness through numerical experiments.

Findings

Robust VQA parameters outperform non-robust ones under shifted noise.

The approach improves the reliability of VQAs like QAOA and VQE.

Numerical results show increased stability against noise shifts.

Abstract

Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is that quantum noise is highly unstable and thus it is likely to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step towards improving the reliability of VQAs influenced by shifted noise from the parameter optimization perspective.