标题： 一种用于最优门合成的低复杂度数值方法 显示英文标题

标题： A reduced complexity numerical method for optimal gate synthesis

摘要： 尽管量子计算机有潜力高效解决某些被已知经典方法认为难以解决的问题，但量子电路的设计仍然是计算上困难的。 已知最优门设计问题等价于相关最优控制问题的求解，而该问题的求解同样计算密集。 因此，在本文中，我们引入了一类数值方法（称为无维度灾难的max-plus技术）的应用，这些方法确定最优控制从而合成所需的酉门。 该技术在量子系统中的应用复杂度增长取决于控制集近似的基数，而不是基于空间网格化方法的复杂度增长，后者在之前文献中被使用，其复杂度随着空间维度的增长而大幅增加。 该技术通过获得$SU(4)$上的门合成近似解来演示——这是一个基于网格的方法无法计算解决的问题。 显示英文摘要

摘要： Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate design problem is equivalent to the solution of an associated optimal control problem, the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality free techniques) that determine the optimal control thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, used in previous literature. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on $SU(4)$- a problem that is computationally intractable by grid based approaches.