Variational (matrix) product states for combinatorial optimization
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915692789366784 |
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| author | Preisser, Guillermo Keever, Conor Mc Lubasch, Michael |
| author_facet | Preisser, Guillermo Keever, Conor Mc Lubasch, Michael |
| contents | To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansatzes. We perform variational energy minimization with respect to a quantum annealing Hamiltonian and utilize randomness by embedding the approaches in the metaheuristic iterated local search (ILS). The resulting quantum-inspired ILS algorithms are benchmarked on maximum cut problems of up to 50000 variables. We show that they can outperform traditional (M)PS methods, classical ILS, the quantum approximate optimization algorithm and other variational quantum-inspired solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20613 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational (matrix) product states for combinatorial optimization Preisser, Guillermo Keever, Conor Mc Lubasch, Michael Quantum Physics Computational Physics To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansatzes. We perform variational energy minimization with respect to a quantum annealing Hamiltonian and utilize randomness by embedding the approaches in the metaheuristic iterated local search (ILS). The resulting quantum-inspired ILS algorithms are benchmarked on maximum cut problems of up to 50000 variables. We show that they can outperform traditional (M)PS methods, classical ILS, the quantum approximate optimization algorithm and other variational quantum-inspired solvers. |
| title | Variational (matrix) product states for combinatorial optimization |
| topic | Quantum Physics Computational Physics |
| url | https://arxiv.org/abs/2512.20613 |