Non-variational Quantum Combinatorial Optimisation

• URL: http://arxiv.org/abs/2404.03167v2
• Date: Thu, 1 Aug 2024 03:33:45 GMT
• Title: Non-variational Quantum Combinatorial Optimisation
• Authors: Tavis Bennett, Lyle Noakes, Jingbo Wang,
• Abstract summary: This paper introduces a non-variational quantum algorithm designed to solve a wide range of optimisation problems. The algorithm's versatility is demonstrated through its application to various problems. For each problem instance, the algorithm finds a globally optimal solution with a small number of iterations.
• Score: 3.6538093004443155
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces a non-variational quantum algorithm designed to solve a wide range of combinatorial optimisation problems, including constrained and non-binary problems. The algorithm leverages an engineered interference process achieved through repeated application of two unitaries; one inducing phase-shifts dependent on objective function values, and the other mixing phase-shifted probability amplitudes via a continuous-time quantum walk (CTQW) on a problem-specific graph. The algorithm's versatility is demonstrated through its application to various problems, namely those for which solutions are characterised by either a vector of binary variables, a vector of non-binary integer variables, or permutations (a vector of integer variables without repetition). An efficient quantum circuit implementation of the CTQW for each of these problem types is also discussed. A penalty function approach for constrained problems is also introduced, including a method for optimising the penalty function. The algorithm's performance is demonstrated through numerical simulation for randomly generated instances of the following problems (and problem sizes): weighted maxcut (18 vertices), maximum independent set (18 vertices), k-means clustering (12 datapoints, 3 clusters), capacitated facility location (12 customers, 3 facility locations), and the quadratic assignment problem (9 locations). For each problem instance, the algorithm finds a globally optimal solution with a small number of iterations.

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