Optimally Stopped Variational Quantum Algorithms

TL;DR

This paper introduces an optimal stopping benchmark for variational quantum algorithms that evaluates both solution quality and optimization time, demonstrating improved performance through better cost functions.

Contribution

It presents a new benchmarking method for VQAs incorporating time as a cost, and shows how optimizing the classical cost function enhances VQA performance.

Findings

Optimal stopping provides a comprehensive VQA assessment.

Better classical cost functions improve VQA scaling.

Benchmarking reveals potential for improved quantum algorithm performance.

Abstract

Quantum processors promise a paradigm shift in high-performance computing which needs to be assessed by accurate benchmarking measures. In this work, we introduce a new benchmark for variational quantum algorithm (VQA), recently proposed as a heuristic algorithm for small-scale quantum processors. In VQA, a classical optimization algorithm guides the quantum dynamics of the processor to yield the best solution for a given problem. A complete assessment of scalability and competitiveness of VQA should take into account both the quality and the time of dynamics optimization. The method of optimal stopping, employed here, provides such an assessment by explicitly including time as a cost factor. Here we showcase this measure for benchmarking VQA as a solver for some quadratic unconstrained binary optimization. Moreover we show that a better choice for the cost function of the classical routine can significantly improve the performance of the VQA algorithm and even improving it's scaling properties.