标题： 高精度多量子比特Clifford+T综合通过单位对角化 显示英文标题

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

摘要： 资源高效的和高精度的量子电路近似综合，以Clifford+T门集表达，在容错量子计算中是至关重要的。 已知对于单量子比特RZ酉矩阵有高效最优方法，否则该问题通常难以处理。 基于搜索的方法，如模拟退火，只要可以容忍较低精度（Hilbert-Schmidt距离大于10^-2），可以经验性地生成一般多量子比特酉矩阵的低资源成本近似实现。 这些算法构建直接反转目标酉矩阵的电路。 我们则利用基于搜索的方法首先近似对角化一个酉矩阵，然后进行解析逆运算。 这使得困难的连续旋转被绕过，并在后处理步骤中处理。 当在来自实际量子算法的酉矩阵上评估时，我们的方法使综合算法的实现精度和运行时间提高了数量级。 在以前只能使用解析技术如量子香农分解进行综合的基准测试中，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 RZ 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 e>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.