Solving Larger Maximum Clique Problems Using Parallel Quantum Annealing
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929216158695424 |
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| author | Pelofske, Elijah Hahn, Georg Djidjev, Hristo N. |
| author_facet | Pelofske, Elijah Hahn, Georg Djidjev, Hristo N. |
| contents | Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave Systems, which we consider in this work, is sparsely connected and moderately sized (on the order of thousands of qubits), thus necessitating a minor-embedding of a logical problem onto the physical qubit hardware. The combination of relatively small hardware sizes and the necessity of a minor-embedding can mean that solving large optimization problems is not possible on current quantum annealers. In this research, we show that a hybrid approach combining parallel quantum annealing with graph decomposition allows one to solve larger optimization problem accurately. We apply the approach on the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_12165 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Solving Larger Maximum Clique Problems Using Parallel Quantum Annealing Pelofske, Elijah Hahn, Georg Djidjev, Hristo N. Quantum Physics Emerging Technologies Combinatorics Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave Systems, which we consider in this work, is sparsely connected and moderately sized (on the order of thousands of qubits), thus necessitating a minor-embedding of a logical problem onto the physical qubit hardware. The combination of relatively small hardware sizes and the necessity of a minor-embedding can mean that solving large optimization problems is not possible on current quantum annealers. In this research, we show that a hybrid approach combining parallel quantum annealing with graph decomposition allows one to solve larger optimization problem accurately. We apply the approach on the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges. |
| title | Solving Larger Maximum Clique Problems Using Parallel Quantum Annealing |
| topic | Quantum Physics Emerging Technologies Combinatorics |
| url | https://arxiv.org/abs/2205.12165 |