Robust Pretty Good Measurement via Hybrid Classical-Quantum Pseudoinverse Approximation and Circuit-Level Realization

Abstract:Pretty Good Measurement (PGM) is a near-optimal strategy for quantum state discrimination, but its practical realization becomes unstable when the ensemble operator is singular or ill-conditioned. We introduce a numerically robust PGM formulation based on the Moore-Penrose pseudoinverse, replacing the standard inverse square root with a threshold-regularized variant that remains well-defined across different spectral regimes. We develop a hybrid classical-quantum framework that combines pseudoinverse-based spectral preprocessing with quantum circuit realizations using block-encoding and spectral-transformation techniques. The framework incorporates support awareness, yielding physically meaningful measurement operators even in rank-deficient cases, and employs oblivious amplitude amplification to improve circuit-level success probabilities. Extensive numerical and circuit-level simulations show close agreement between theoretical predictions and quantum circuit outputs. Experiments on synthetic and real datasets, including ill-conditioned and degenerate scenarios, demonstrate stable discrimination performance where standard PGM becomes numerically unstable. The results establish a practical hybrid classical-quantum framework for robust quantum state discrimination and extend previous circuit-based implementations of the PGM testing stage toward pseudoinverse-aware measurement design.

arXiv:2606.13150 [quant-ph]

(or arXiv:2606.13150v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.13150 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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