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arXiv 2602.06535quant-phcs.DScs.ET
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代数简化以改进最优有界的量子态准备算法

Algebraic Reduction to Improve an Optimally Bounded Quantum State Preparation Algorithm

University of Parma（帕尔马大学）

Giacomo Belli, Michele Amoretti

备注：
15 pages, 13 figures, 5 tables
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AI总结：

本研究通过代数简化改进了量子态准备算法，减少电路深度、总门数和CNOT计数，提高了效率并拓展了应用范围。

摘要：

n个量子比特态的准备是许多量子算法中的通用子程序，减少其电路复杂度的努力是一个重大挑战。在文献中，Sun等人提出的量子态准备算法已被证明是最佳有界的，定义了有无辅助量子比特的渐进最优宽度-深度折中界限。在本工作中，提出了一种更简单的代数分解，将所需态的实部准备与复部分开，当有m个辅助量子比特可用时，这导致了电路深度、总门数和CNOT计数的减少。这种复杂度的降低是由于每个均匀控制门使用单个操作符Λ，而不是原始分解中的三个。使用PennyLane库，该新的态准备算法已在模拟环境中实现了对密集和稀疏量子态（包括随机和物理感兴趣的态）的测试。此外，其性能已与Möttönen等人算法进行了比较，后者是无辅助量子比特情况下准备量子态的事实标准，突显了有趣的发展方向。

英文摘要：

The preparation of $n$-qubit quantum states is a cross-cutting subroutine for many quantum algorithms, and the effort to reduce its circuit complexity is a significant challenge. In the literature, the quantum state preparation algorithm by Sun et al. is known to be optimally bounded, defining the asymptotically optimal width-depth trade-off bounds with and without ancillary qubits. In this work, a simpler algebraic decomposition is proposed to separate the preparation of the real part of the desired state from the complex one, resulting in a reduction in terms of circuit depth, total gates, and CNOT count when $m$ ancillary qubits are available. The reduction in complexity is due to the use of a single operator $Λ$ for each uniformly controlled gate, instead of the three in the original decomposition. Using the PennyLane library, this new algorithm for state preparation has been implemented and tested in a simulated environment for both dense and sparse quantum states, including those that are random and of physical interest. Furthermore, its performance has been compared with that of Möttönen et al.'s algorithm, which is a de facto standard for preparing quantum states in cases where no ancillary qubits are used, highlighting interesting lines of development.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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