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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.03167 |
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| _version_ | 1866913454445559808 |
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| author | Bennett, Tavis Noakes, Lyle Wang, Jingbo |
| author_facet | Bennett, Tavis Noakes, Lyle Wang, Jingbo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-variational Quantum Combinatorial Optimisation Bennett, Tavis Noakes, Lyle Wang, Jingbo Quantum Physics Computational Physics 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. |
| title | Non-variational Quantum Combinatorial Optimisation |
| topic | Quantum Physics Computational Physics |
| url | https://arxiv.org/abs/2404.03167 |