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.

翻译：$n$量子比特量子态的制备是众多量子算法的交叉子程序，降低其电路复杂度是一项重要挑战。文献中，Sun等人提出的量子态制备算法被证明是最优有界的，定义了在有/无辅助量子比特情况下渐近最优的宽度-深度权衡边界。本工作提出了一种更简洁的代数分解方法，将目标态实部与复部的制备过程分离，当存在$m$个辅助量子比特时，可在电路深度、总门数及CNOT门数量方面实现约简。该复杂度降低源于每个均匀控制门仅使用单一算子$Λ$，而非原始分解中的三个算子。利用PennyLane库，我们在模拟环境中实现并测试了这种用于稠密态与稀疏态（包括随机态和具有物理意义的量子态）的新型态制备算法。此外，我们将其性能与Möttönen等人提出的算法进行了对比——后者在无辅助量子比特情况下已成为量子态制备的事实标准，并由此揭示了若干具有发展前景的研究方向。