Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911080590082048 |
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| author | Zhang, Hao Kamenev, Alex |
| author_facet | Zhang, Hao Kamenev, Alex |
| contents | Finding an exact ground state of a three-dimensional (3D) Ising spin glass is proven to be an NP-hard problem (i.e., at least as hard as any problem in the nondeterministic polynomial-time (NP) class). Given validity of the exponential time hypothesis, its computational complexity was proven to be no less than $2^{N^{2/3}}$, where $N$ is the total number of spins. Here, we report results of extensive experimentation with D-Wave 3D annealer with $N\le 5627$. We found exact ground states (in a probabilistic sense) for typical realizations of 3D spin glasses with the efficiency, which scales as $2^{N/ β}$ with $β\approx 10^3$. Based on statistical analysis of low-energy states, we argue that with an improvement of annealing protocols and device noise reduction, $β$ can be increased even further. This suggests that, for $N<β^3$, annealing devices provide most efficient way to find an exact ground state. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_01107 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer Zhang, Hao Kamenev, Alex Disordered Systems and Neural Networks Quantum Physics Finding an exact ground state of a three-dimensional (3D) Ising spin glass is proven to be an NP-hard problem (i.e., at least as hard as any problem in the nondeterministic polynomial-time (NP) class). Given validity of the exponential time hypothesis, its computational complexity was proven to be no less than $2^{N^{2/3}}$, where $N$ is the total number of spins. Here, we report results of extensive experimentation with D-Wave 3D annealer with $N\le 5627$. We found exact ground states (in a probabilistic sense) for typical realizations of 3D spin glasses with the efficiency, which scales as $2^{N/ β}$ with $β\approx 10^3$. Based on statistical analysis of low-energy states, we argue that with an improvement of annealing protocols and device noise reduction, $β$ can be increased even further. This suggests that, for $N<β^3$, annealing devices provide most efficient way to find an exact ground state. |
| title | Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer |
| topic | Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2501.01107 |