Quantum Walk Dictionary Learning for Classical Image Representation: A Hybrid Framework

Abstract

Abstract Quantum computing offers novel paradigms for data representation and signal processing, yet traditional Quantum Image Representation (QIP) models often face significant challenges regarding qubit resources and state preparation complexity. This paper introduces a hybrid quantum-classical framework that utilizes Discrete-Time Quantum Walks (DTQW) as a generative mechanism for construction of classical dictionary learning. The core contribution of this work lies in the spectral and informational characterization of the quantum-generated basis. A comparative analysis against industry-standard benchmarks, including the Discrete Cosine Transform (DCT) and Haar Wavelet Transform (WAV), reveals that the DTQW basis operates in a high-entropy representational regime, achieving a maximum normalized Shannon entropy ( $$H/H_{max} \approx 1.0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>H</mml:mi> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>1.0</mml:mn> </mml:mrow> </mml:math> ). This property facilitates a delocalized or “holographic” distribution of signal energy across the entire coefficient spectrum. Furthermore, we show that applying unitary quantum operator to the position register enables visually interpretable image transformations through a computationally efficient coefficient reuse mechanism. This research shifts the focus from traditional compression-centric imaging toward a robustness-centric quantum-assisted paradigm, offering promising applications in secure communication and resilient image representation.