论文标题
QAOA的Grover混合器：将复杂性从混音器设计转移到状态准备
Grover Mixers for QAOA: Shifting Complexity from Mixer Design to State Preparation
论文作者
论文摘要
我们提出了GM-QAOA，这是使用类似Grover的选择性相位移动混合操作员的量子交替运算符ANSATZ（QAOA）的变体。 GM-QAOA在任何NP优化问题上都可以有效地准备所有可行解决方案的同等叠加；它旨在在约束优化问题上表现特别好，在这种情况下，并非所有可能的变量分配都是可行的解决方案。 GM-QAOA具有以下功能：（i）它不容易受到哈密顿模拟误差（例如Trotterterization错误），因为可以使用标准门集精确地实现其运算符，并且（II）具有相同客观值的解决方案总是以相同的幅度对其进行采样。 我们说明了GM-QAOA在几个优化问题类别上的潜力：对于基于排列的优化问题，例如旅行销售人员问题，我们提出了一种有效的算法，以准备所有可能的$ n $数字的叠加，并定义为$ O（n^2）$ qubits;对于硬约束$ k $ - vertex cover问题，以及用于离散投资组合重新平衡的应用程序，我们表明GM-QAOA的表现优于现有的QAOA接近。
We propose GM-QAOA, a variation of the Quantum Alternating Operator Ansatz (QAOA) that uses Grover-like selective phase shift mixing operators. GM-QAOA works on any NP optimization problem for which it is possible to efficiently prepare an equal superposition of all feasible solutions; it is designed to perform particularly well for constraint optimization problems, where not all possible variable assignments are feasible solutions. GM-QAOA has the following features: (i) It is not susceptible to Hamiltonian Simulation error (such as Trotterization errors) as its operators can be implemented exactly using standard gate sets and (ii) Solutions with the same objective value are always sampled with the same amplitude. We illustrate the potential of GM-QAOA on several optimization problem classes: for permutation-based optimization problems such as the Traveling Salesperson Problem, we present an efficient algorithm to prepare a superposition of all possible permutations of $n$ numbers, defined on $O(n^2)$ qubits; for the hard constraint $k$-Vertex-Cover problem, and for an application to Discrete Portfolio Rebalancing, we show that GM-QAOA outperforms existing QAOA approaches.
