A framework to evaluate the performance of Variational Quantum Algorithms

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.

💡 Research Summary

The paper addresses a pressing need in the NISQ era: a systematic, quantitative benchmark for Variational Quantum Algorithms (VQAs) applied to combinatorial optimization problems, specifically Quadratic Unconstrained Binary Optimization (QUBO). While VQAs such as QAOA and its variants have shown promise, existing performance assessments typically focus on single metrics—often the probability of sampling the global optimum (p_min) or the number of circuit evaluations (n_calls). These approaches neglect the inherently stochastic nature of VQAs and provide no unified decision rule for algorithm selection under realistic resource constraints.

To fill this gap, the authors propose a comprehensive evaluation framework built on three complementary metrics: feasibility (F), quality (Q), and reproducibility (R). Feasibility quantifies the a‑priori probability that a VQA will achieve a success probability above a user‑defined threshold p_threshold. Mathematically, F