期刊
出版社
IEEE COMPUTER SOC
DOI: 10.1109/QCE52317.2021.00030
关键词
-
资金
- Laboratory Directed Research and Development program of Los Alamos National Lahoratory [20200671DU20190495DR]
The study introduces a new quantum optimization algorithm, Th-QAOA, and combines it with the Grover Mixer operator to obtain GM-Th-QAOA. Results show that GM-Th-QAOA outperforms non-thresholded GM-QAOA in terms of approximation ratios across a range of optimization problems and experimental design parameters.
We propose and study Th-QAOA (pronounced Threshold QAOA), a variation of the Quantum Alternating Operator Ansatz (QAOA) that replaces the standard phase separator operator, which encodes the objective function, with a threshold function that returns a value 1 for solutions with an objective value above the threshold and a 0 otherwise. We vary the threshold value to arrive at a quantum optimization algorithm. We focus on a combination with the Grover Mixer operator; the resulting GM-Th-QAOA can be viewed as a generalization of Grover's quantum search algorithm and its minimum/maximum finding cousin to approximate optimization. Our main findings include: (i) we provide intuitive arguments and show empirically that the optimum parameter values of GM-Th-QAOA (angles and threshold value) can be found with O(log(p) x log M) iterations of the classical outer loop, where p is the number of QAOA rounds and M is an upper bound on the solution value (often the number of vertices or edges in an input graph), thus eliminating the notorious outer-loop parameter finding issue of other QAOA algorithms; (ii) GM-Th-QAOA can be simulated classically with little effort up to 100 qubits through a set of tricks that cut down memory requirements; (iii) somewhat surprisingly, GM-Th-QAOA outperforms non-thresholded GM-QAOA in terms of approximation ratios achieved. This third result holds across a range of optimization problems (MaxCut, Max k-VertexCover, Max k-DensestSubgraph, MaxBisection) and various experimental design parameters, such as different input edge densities and constraint sizes.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据