Q-PIPE A Practical Quantum Phase Encoding Method

Abstract: A major hurdle in Quantum Image Processing (QIMP) is efficiently transferring classical, high-dimensional image data into quantum states. Current methods face trade-offs: amplitude encoding (FRQI) is computationally expensive in gate complexity and limited arithmetic capabilities, while basis encoding (NEQR) incurs heavy initialization overhead scaling with image resolution and intensity bit-depth. Frequency-domain approaches further demand complex transformations for basic pixel-wise arithmetic and extensive post-processing to reconstruct pixel information. To address the lack of practical phase encodings, we introduce Q-PIPE (Quantum-Gray Phase Injection for Pixel Encoding). Exploiting the quantum phase kickback mechanism and optimized spatial traversal via a Gray-code sequence, Q-PIPE efficiently maps continuous intensity values into the computational basis with an elementary gate count of $O(qN)$ a $O(\text{log}N)$ improvement over standard basis encoding. Operating directly in the phase domain enables native computation of finite differences without deep arithmetic circuits. Classical readout vulnerabilities, including phase aliasing and spectral leakage, are mitigated by mapping inputs to $[-π, π]$ and introducing a probability threshold equation that scales inversely with the dimension of the spatial register. A proof-of-concept performing Quantum Edge Detection (QED) via directional derivatives demonstrates strong accuracy, yielding exact reconstructions for quantized inputs and low Mean Absolute Error (MAE) for continuous data across multiple benchmark datasets. Ultimately, Q-PIPE establishes a highly parallelizable, NISQ-compatible subroutine that advances quantum computer vision while reducing input/output (I/O) data-loading overhead in broader Quantum Machine Learning (QML) workflows.