标题： 高精度多量子比特Clifford+T综合通过酉对角化 显示英文标题

标题： High-Precision Multi-Qubit Clifford+T Synthesis by Unitary Diagonalization

摘要： 资源高效且高精度的近似合成在Clifford+T门集表示的量子电路中对于容错量子计算至关重要。 已知针对单量子比特$R_Z$么正变换的有效最优方法，否则该问题通常难以处理。 基于搜索的方法，如模拟退火，只要可以容忍低精度（Hilbert-Schmidt距离为$\epsilon \geq 10^{-2}$），可以经验性地生成一般多量子比特么正变换的低资源成本近似实现。 这些算法构建直接反转目标么正变换的电路。 我们则利用基于搜索的方法首先近似对角化一个么正变换，然后进行解析反转。 这使得困难的连续旋转被绕过，并在后处理步骤中处理。 当在来自真实量子算法的么正变换上评估时，我们的方法使合成算法的实现精度和运行时间提高数量级。 在之前只能使用解析技术如量子香农分解进行合成的基准测试中，对角化平均使用了95%更少的非Clifford门。 显示英文摘要

摘要： Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit $R_Z$ unitaries, otherwise the problem is generally intractable. Search-based methods, like simulated annealing, empirically generate low resource cost approximate implementations of general multi-qubit unitaries so long as low precision (Hilbert-Schmidt distances of $\epsilon \geq 10^{-2}$) can be tolerated. These algorithms build up circuits that directly invert target unitaries. We instead leverage search-based methods to first approximately diagonalize a unitary, then perform the inversion analytically. This lets difficult continuous rotations be bypassed and handled in a post-processing step. Our approach improves both the implementation precision and run time of synthesis algorithms by orders of magnitude when evaluated on unitaries from real quantum algorithms. On benchmarks previously synthesizable only with analytical techniques like the Quantum Shannon Decomposition, diagonalization uses an average of 95% fewer non-Clifford gates.