Title: Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters Show Chinese title

Title: 参数化Clifford电路中参数化旋转和Hadamard门的最优数量

Abstract: We present an efficient algorithm to reduce the number of non-Clifford gates in quantum circuits and the number of parametrized rotations in parametrized quantum circuits. The method consists in finding rotations that can be merged into a single rotation gate. This approach has already been considered before and is used as a pre-processing procedure in many optimization algorithms, notably for optimizing the number of Hadamard gates or the number of $T$ gates in Clifford$+T$ circuits. Our algorithm has a better complexity than similar methods and is particularly efficient for circuits with a low number of internal Hadamard gates. Furthermore, we show that this approach is optimal for parametrized circuits composed of Clifford gates and parametrized rotations with non-repeated parameters. For the same type of parametrized quantum circuits, we also prove that a previous procedure optimizing the number of Hadamard gates and internal Hadamard gates is optimal. This procedure is notably used in our low-complexity algorithm for optimally reducing the number of parametrized rotations. Show Chinese abstract

Abstract: 我们提出了一种高效的算法，用于减少量子电路中的非Clifford门数量以及参数化量子电路中的参数化旋转数量。该方法在于找到可以合并为单个旋转门的旋转。这种方法之前已经考虑过，并被用作许多优化算法中的预处理步骤，特别是在优化Hadamard门数量或Clifford$+T$电路中的$T$门数量时。我们的算法比类似方法具有更好的复杂度，并且对于内部Hadamard门数量较少的电路特别高效。此外，我们证明了对于由Clifford门和具有不重复参数的参数化旋转组成的参数化电路，这种方法是最佳的。对于同一类型的参数化量子电路，我们还证明了之前优化Hadamard门和内部Hadamard门数量的程序是最佳的。该程序尤其被用于我们用于最优减少参数化旋转数量的低复杂度算法中。