Walsh变换实现稠密到稀疏量子态制备
Walsh-Transform Realization of Dense-to-Sparse Quantum State Preparation
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中文总结 AI 辅助
提出一种基于Walsh-Hadamard变换的混合量子态制备方法，通过间接制备稀疏系数并利用Hadamard门重建，实现稠密到稀疏量子态的高效制备，无额外CNOT开销。
中文摘要 AI 辅助
我们提出了一种基于Walsh-Hadamard变换的混合量子态制备方法，该方法在稠密到稀疏量子态制备框架内工作。该方法通过间接途径在量子电路中近似制备结构化经典数据。不是直接制备稠密的振幅编码态，而是首先将经典数据变换到Walsh域，并使用稀疏态制备算法仅制备最大幅值系数。然后，通过一层并行的Hadamard门可以近似恢复原始态。由于这种重建不需要CNOT门且电路深度为1，所提出的方法不引入额外的CNOT或电路深度开销，其量子制备成本由底层的稀疏态制备算法决定。在代表性基准信号上的数值结果表明，所提出的方法能够对在Walsh域中具有稀疏或近似稀疏表示的信号实现精确的态制备。
英文摘要
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.
