MetaMorphQ: Physics-Based Metamorphic Testing of Variational Quantum Circuits

2026-06-27

AI Summary

This work addresses the challenge of reliably testing variational quantum eigensolvers (VQE) in the absence of known ground-state energies, a scenario where conventional testing methods suffer from high false-positive rates. The authors propose a metamorphic testing framework grounded in quantum mechanical invariants, uniquely integrating physical symmetries and algebraic properties into quantum software validation. By exploiting intrinsic invariants arising from parameterized rotation gates and diagonal Hamiltonians, the approach verifies circuit correctness without requiring oracle knowledge of the true ground-state energy. Demonstrated on 500 benchmark circuits—including those generated by humans and large language models—the method achieves zero false positives and substantially outperforms convergence-based testing, with a Youden’s J statistic of 0.57 compared to 0.02.

Abstract

Variational Quantum Eigensolvers (VQEs) are central to quantum computing, yet testing them remains challenging due to the oracle problem: the ground-state energy they compute is itself unknown. Existing approaches, such as convergence-based testing, are unreliable and yield high false-positive rates due to optimisation instability. We propose METAMORPHQ, a metamorphic testing framework that derives test oracles directly from quantum mechanical properties of VQE circuits. Exploiting algebraic properties of parametrised rotation gates and diagonal Hamiltonians, we define five physics-based invariants that hold for any correct circuit and can be verified at initialisation without ground-truth outputs. Evaluated on 500 benchmark circuits with 2,469 mutants, METAMORPHQ achieves zero false positives and significantly improves diagnostic effectiveness (Youden's J = 0.57 vs. 0.02 for convergence testing). These results demonstrate that physics-derived invariants provide a practical, oracle-free foundation for testing quantum software, enabling reliable validation of both human- and LLM-generated circuits.

Problem

• Variational Quantum Eigensolvers
• oracle problem
• metamorphic testing
• quantum software testing
• false positives

Innovation

• metamorphic testing
• variational quantum circuits
• physics-based invariants
• oracle-free validation
• quantum software testing