Error-Tolerant Quantum State Discrimination: Optimization and Quantum Circuit Synthesis

TL;DR

This paper introduces error-tolerant quantum state discrimination strategies, combining optimization, hybrid frameworks, and circuit synthesis to enhance performance under noise and facilitate implementation on current quantum hardware.

Contribution

It proposes novel error-tolerant QSD methods, a unified framework for trade-offs, and a hardware-efficient circuit synthesis approach, supported by an open-source toolkit.

Findings

Developed CrossQSD with tunable confidence bounds.

Optimized measurement distributions via FitQSD.

Created a circuit synthesis framework for efficient hardware implementation.

Abstract

We develop error-tolerant quantum state discrimination(QSD) strategies that maintain reliable performance under moderate noise. Two complementary approaches are proposed: CrossQSD, which generalizes unambiguous discrimination with tunable confidence bounds to balance accuracy and efficiency, and FitQSD, which optimizes the measurement outcome distribution to approximate that of the ideal noiseless case. Furthermore, we provide a unified hybrid-objective QSD framework that continuously interpolates between minimum-error discrimination (MED) and FitQSD, allowing flexible trade-offs among competing objectives. The associated optimization problems are formulated as convex programs and efficiently solved via disciplined convex programming or, in many cases, semidefinite programming. Additionally, a circuit synthesis framework based on a modified Naimark dilation and isometry synthesis enables hardware-efficient implementations with substantially reduced qubit and gate resources. An open-source toolkit automates the full optimization and synthesis workflow, providing a practical route to QSD on current quantum devices.