Quantum Framework for Wavelet Shrinkage

TL;DR

This paper introduces a quantum framework for wavelet shrinkage that uses controlled decoherence to suppress noise, integrating classical denoising concepts into quantum circuits with practical demonstrations.

Contribution

It presents a novel quantum approach to wavelet shrinkage using decoherence, unifying statistical adaptivity and unitarity in quantum circuits, with experimental validation.

Findings

Quantum decoherence can be harnessed for noise suppression.

Quantum circuits can emulate classical wavelet shrinkage.

Practical implementations are demonstrated on NISQ devices.

Abstract

This paper develops a unified framework for quantum wavelet shrinkage, extending classical denoising ideas into the quantum domain. Shrinkage is interpreted as a completely positive trace-preserving process, so attenuation of coefficients is carried out through controlled decoherence rather than nonlinear thresholding. Phase damping and ancilla-driven constructions realize this behavior coherently and show that statistical adaptivity and quantum unitarity can be combined within a single circuit model. The same physical mechanisms that reduce quantum coherence, such as dephasing and amplitude damping, are repurposed as programmable resources for noise suppression. Practical demonstrations implemented with Qiskit illustrate how circuits and channels emulate coefficientwise attenuation, and all examples are provided as Jupyter notebooks in the companion GitHub repository. Encoding schemes for amplitude, phase, and hybrid representations are examined in relation to transform coherence and measurement feasibility, and realizations suited to current noisy intermediate-scale quantum devices are discussed. The work provides a conceptual and experimental link between wavelet-based statistical inference and quantum information processing, and shows how engineered decoherence can act as an operational surrogate for classical shrinkage.