An Optimal Hybrid Quantum-Classical Representation for Robust Photonic Image Processing on NISQ Devices

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 (95% CI: 0.355-0.424). Our architecture requires only 𝑸 = I log ₂ ( 𝑵 ² )] + 4 qubits for an 𝑵 × 𝑵 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 and a 27% reduction in qubit requirements over NEQR for typical image operations. 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.