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

• URL: http://arxiv.org/abs/2606.13150v1
• Date: Thu, 11 Jun 2026 10:26:28 GMT
• Title: Robust Pretty Good Measurement via Hybrid Classical-Quantum Pseudoinverse Approximation and Circuit-Level Realization
• Abstract summary: We introduce a numerically robust PGM formulation based on the Moore-Penrose pseudoinverse.<n>We develop a hybrid classical-quantum framework that combines pseudoinverse-based spectral preprocessing with quantum circuit realizations.
• Score: 0.46976113832881716
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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