Walsh-Transform Realization of Dense-to-Sparse Quantum State Preparation

Abstract:We propose a hybrid quantum state preparation method based on the Walsh--Hadamard transform within the dense-to-sparse quantum state preparation framework. The method approximately prepares structured classical data in a quantum circuit through an indirect approach. Instead of directly preparing the dense amplitude-encoded state, the method first transforms the classical data into the Walsh domain and prepares only the largest-magnitude coefficients using a sparse state-preparation algorithm. The original state can then be approximately recovered through a parallel layer of Hadamard gates. Since this reconstruction requires no CNOT gates and has circuit depth 1, the proposed method introduces no additional CNOT or circuit-depth overhead, and its quantum preparation cost is determined by the underlying sparse state-preparation algorithm. Numerical results on representative benchmark signals demonstrate that the proposed method enables accurate state preparation for signals admitting sparse or approximately sparse representations in the Walsh domain.

arXiv:2609.28760 [quant-ph]

(or arXiv:2609.28760v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.28760 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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