论文标题
通过SDP优化量子电路参数
Optimizing quantum circuit parameters via SDP
论文作者
论文摘要
近年来，参数化的量子电路已成为设计量子算法以进行优化问题的主要工具。充分利用给定参数化电路家族的挑战在于在非凸面景观中找到一组良好的参数，该参数可以指数增长到参数的数量。 我们引入了一个新框架，以优化参数化量子电路：回路参数的圆形SDP解决方案。在此框架内，我们提出了一种算法，该算法为量子优化问题产生近似解决方案，称为量子最大切割。圆形算法在多项式时间内运行到参数数量，而不论基础相互作用图是什么。 量子最大切割的通用实例所得的0.562-Approximation算法改善了先前已知的最佳算法，该算法的近似值比小于0.54。
In recent years, parameterized quantum circuits have become a major tool to design quantum algorithms for optimization problems. The challenge in fully taking advantage of a given family of parameterized circuits lies in finding a good set of parameters in a non-convex landscape that can grow exponentially to the number of parameters. We introduce a new framework for optimizing parameterized quantum circuits: round SDP solutions to circuit parameters. Within this framework, we propose an algorithm that produces approximate solutions for a quantum optimization problem called Quantum Max Cut. The rounding algorithm runs in polynomial time to the number of parameters regardless of the underlying interaction graph. The resulting 0.562-approximation algorithm for generic instances of Quantum Max Cut improves on the previously known best algorithms, which give approximation ratios of less than 0.54.
