2024/03/28 by Bo‐Hung Chen, Chen, Bo-Hung, Dah-Wei Chiou +3
Computer Science · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2403.19172
openalex publication_date 2024/03/28 · openalex created_date 2024/03/30 · openalex updated_date 2026/07/28
This paper addresses the challenge of preparing mixed quantum states -- both arbitrary states in general and highly sparse ones in particular -- an area that has received far less attention than the preparation of pure states. We present two classes of circuit-synthesis methods: one based on constructing the density matrix as a mixture of pure states and the other based on purification. To improve both preprocessing efficiency and the complexity of the resulting circuits, we propose a novel strategy based on the Cholesky decomposition, which offers significant advantages, especially when the target density matrix is highly or extremely sparse. Furthermore, by exploiting incomplete Cholesky decomposition with threshold dropping, we introduce a practical approach for constructing high-fidelity approximations of the target density matrix. This approach enables substantial reductions in circuit complexity at the cost of negligible or only mild fidelity loss.