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arXiv · 2601.18812

A framework to evaluate the performance of Variational Quantum Algorithms

Ernesto Mamedaliev·Vladyslav Libov·Albert Nieto-Morales·Oskar Słowik·Arit Kumar Bishwas
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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.

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Ernesto Mamedaliev, Vladyslav Libov, Albert Nieto-Morales, Oskar Słowik, Arit Kumar Bishwas. 2026-01-21. A framework to evaluate the performance of Variational Quantum Algorithms. https://arxiv.org/abs/2601.18812

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