标题： 无辅助量子比特的近似多控制单量子比特门的对数深度分解 显示英文标题

标题： Logarithmic Depth Decomposition of Approximate Multi-Controlled Single-Qubit Gates Without Ancilla Qubits

摘要： 量子算子的合成涉及将通用量子门分解为给定量子设备支持的门集。 多控制门是这一过程中的关键组件。 在本工作中，我们提出了使用单个辅助量子位的多控制NOT门的改进分解方法，其深度为对数级，相比之前的工作，还减少了电路深度中的常数因子。 我们通过识别条件清洁量子位的存在，优化了之前提出的多目标、多控制特殊酉SU(2)门的分解方法。 此外，我们引入了无需使用辅助量子位的多控制近似酉U(2)门的最佳已知分解方法。 该方法在保持可调误差参数的同时显著减少了整体电路深度和CNOT数量，为合成大型控制酉门提供了更高效和可扩展的解决方案。 我们的方法特别适用于NISQ和容错量子架构。 本项目开发的所有软件均可免费获得。 显示英文摘要

摘要： The synthesis of quantum operators involves decomposing general quantum gates into the gate set supported by a given quantum device. Multi-controlled gates are essential components in this process. In this work, we present improved decompositions of multi-controlled NOT gates with logarithmic depth using a single ancilla qubit, while also reducing the constant factors in the circuit depth compared to previous work. We optimize a previously proposed decomposition of multi-target, multi-controlled special unitary SU(2) gates by identifying the presence of a conditionally clean qubit. Additionally, we introduce the best-known decomposition of multi-controlled approximate unitary U(2) gates without using ancilla qubits. This approach significantly reduces the overall circuit depth and CNOT count while preserving an adjustable error parameter, yielding a more efficient and scalable solution for synthesizing large controlled-unitary gates. Our method is particularly suitable for both NISQ and fault-tolerant quantum architectures. All software developed in this project is freely available.