An optimal hybrid quantum-classical representation for robust photonic image processing on NISQ devices

Abstract

Quantum image processing (QIP) promises significant advantages for computer vision, but its realization on Noisy Intermediate-Scale Quantum (NISQ) devices is hampered by a fundamental trade-off between qubit efficiency and measurement robustness. This work introduces a novel hybrid quantum-classical representation that optimizes this trade-off for discrete-variable photonic quantum hardware using path-encoded qubits. Through a dual optimization approach combining simulation-based ablation study and mathematical optimization with bootstrap validation (1000 resamples), we derive an optimal operating point of α=0.393±0.019\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha = 0.393 \pm 0.019$$\end{document} (95% CI: 0.355−0.424). This value is universal: it balances qubit count against measurement fidelity under the assumed NISQ hardware characteristics and is independent of the specific image content. Our architecture requires only Q=⌈log2(N2)⌉+4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q = \lceil \log _2(N^2) \rceil + 4$$\end{document} qubits for an N×N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N \times N$$\end{document} image, achieving logarithmic scaling while maintaining measurement fidelity between 0.92−0.97 on simulated NISQ hardware. We provide complete photonic circuit designs utilizing path encoding, including resource estimates for optical components. Comprehensive performance analysis demonstrates a 38% improvement in error resilience over FRQI, while using only one additional control qubit compared to NEQR under equivalent color depth (3 bits, 8 levels). For applications where 8-level color is sufficient, this modest overhead is offset by superior measurement robustness and noise tolerance. Measurement distribution analysis confirms well-separated operational modes with minimal overlap, indicating excellent discrimination capability. This work establishes a practical and scalable framework for implementing QIP on imminent discrete-variable photonic quantum processors.