A framework to evaluate the performance of Variational Quantum Algorithms

TL;DR

This paper presents a comprehensive framework for benchmarking Variational Quantum Algorithms on NISQ devices, focusing on performance metrics like feasibility, quality, and reproducibility, with visualization tools for trade-offs.

Contribution

It introduces a standardized evaluation framework with novel metrics and visualization tools, enabling systematic benchmarking and adaptive algorithm selection for VQAs.

Findings

Framework effectively compares VQAs on QUBO problems

Reproducibility quantified using Shannon entropy

Supports systematic benchmarking and resource-aware decisions

Abstract

Variational Quantum Algorithms (VQAs) are promising methods for solving combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) devices. However, benchmarking VQAs is difficult due to their stochastic behavior and the lack of standardized performance criteria. This work introduces a general framework for evaluating VQAs applied to Quadratic Unconstrained Binary Optimization (QUBO) problems. The framework uses three complementary metrics: feasibility, quality, and reproducibility. It also introduces a quality diagram that visualizes trade-offs between success probability and computational resources. Reproducibility is formalized using Shannon entropy, and a decision rule is defined for selecting algorithms under resource constraints. As a demonstration, the framework is applied to several VQAs using Conditional Value at Risk (CVaR) cost functions and different shot counts on a 16-qubit QUBO instance. The results show how the framework supports systematic benchmarking and provides a foundation for adaptive algorithm selection in hybrid quantum-classical workflows.