Exploring Quantum Annealing Architectures: A Spin Glass Perspective
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929664132382720 |
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| author | Jaumà, Gabriel García-Ripoll, Juan José Pino, Manuel |
| author_facet | Jaumà, Gabriel García-Ripoll, Juan José Pino, Manuel |
| contents | We study the spin-glass transition in several Ising models of relevance for quantum annealers. We extract the spin-glass critical temperature by extrapolating the pseudo-critical properties obtained with Replica-Exchange Monte-Carlo for finite-size systems. We find a spin-glass phase for some random lattices (random-regular and small-world graphs) in good agreement with previous results. However, our results for the quasi-two-dimensional graphs implemented in the D-Wave annealers (Chimera, Zephyr, and Pegasus) indicate only a zero-temperature spin-glass state, as their pseudo-critical temperature drifts towards smaller values. This implies that the asymptotic runtime to find the low-energy configuration of those graphs is likely to be polynomial in system size, nevertheless, this scaling may only be reached for very large system sizes -- much larger than existing annealers -- as we observe an abrupt increase in the computational cost of the simulations around the pseudo-critical temperatures. Thus, two-dimensional systems with local crossings can display enough complexity to make unfeasible the search with classical methods of low-energy configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13065 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exploring Quantum Annealing Architectures: A Spin Glass Perspective Jaumà, Gabriel García-Ripoll, Juan José Pino, Manuel Quantum Physics We study the spin-glass transition in several Ising models of relevance for quantum annealers. We extract the spin-glass critical temperature by extrapolating the pseudo-critical properties obtained with Replica-Exchange Monte-Carlo for finite-size systems. We find a spin-glass phase for some random lattices (random-regular and small-world graphs) in good agreement with previous results. However, our results for the quasi-two-dimensional graphs implemented in the D-Wave annealers (Chimera, Zephyr, and Pegasus) indicate only a zero-temperature spin-glass state, as their pseudo-critical temperature drifts towards smaller values. This implies that the asymptotic runtime to find the low-energy configuration of those graphs is likely to be polynomial in system size, nevertheless, this scaling may only be reached for very large system sizes -- much larger than existing annealers -- as we observe an abrupt increase in the computational cost of the simulations around the pseudo-critical temperatures. Thus, two-dimensional systems with local crossings can display enough complexity to make unfeasible the search with classical methods of low-energy configurations. |
| title | Exploring Quantum Annealing Architectures: A Spin Glass Perspective |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2307.13065 |