Quantum Annealing Algorithms for Estimating Ising Partition Functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908891764228096 |
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| author | Li, Haowei Yao, Zhiyuan Qiu, Xingze |
| author_facet | Li, Haowei Yao, Zhiyuan Qiu, Xingze |
| contents | Estimating partition functions of Ising spin glasses is a cornerstone of statistical physics and computational science, yet it remains classically challenging due to its $\#$P-hard complexity. While Jarzynski's equality offers a theoretical pathway, its practical application is crippled at low temperatures by rare, divergent statistical fluctuations. Here, we introduce a quantum protocol that overcomes this fundamental limitation by synergizing reverse quantum annealing with optimized nonequilibrium initial distributions. Our method dramatically suppresses the estimator variance, achieving saturation in the low-temperature regime where existing methods fail. Numerical benchmarks on the Sherrington-Kirkpatrick spin glass and the 3-SAT problem demonstrate that our protocol reduces computational scaling exponents by over an order of magnitude (e.g., from $\sim 8.5$ to $\sim 0.5$), despite retaining exponential system-size dependence. Crucially, our protocol circumvents stringent adiabatic constraints, making it feasible for near-term quantum devices like superconducting qubits, trapped ions, and Rydberg atom arrays. This work provides a methodological framework for quantum-enhanced estimation in spin glass thermodynamics and beyond by harnessing non-adiabatic quantum dynamics to address a classically difficult problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_21666 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Annealing Algorithms for Estimating Ising Partition Functions Li, Haowei Yao, Zhiyuan Qiu, Xingze Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Computational Physics Estimating partition functions of Ising spin glasses is a cornerstone of statistical physics and computational science, yet it remains classically challenging due to its $\#$P-hard complexity. While Jarzynski's equality offers a theoretical pathway, its practical application is crippled at low temperatures by rare, divergent statistical fluctuations. Here, we introduce a quantum protocol that overcomes this fundamental limitation by synergizing reverse quantum annealing with optimized nonequilibrium initial distributions. Our method dramatically suppresses the estimator variance, achieving saturation in the low-temperature regime where existing methods fail. Numerical benchmarks on the Sherrington-Kirkpatrick spin glass and the 3-SAT problem demonstrate that our protocol reduces computational scaling exponents by over an order of magnitude (e.g., from $\sim 8.5$ to $\sim 0.5$), despite retaining exponential system-size dependence. Crucially, our protocol circumvents stringent adiabatic constraints, making it feasible for near-term quantum devices like superconducting qubits, trapped ions, and Rydberg atom arrays. This work provides a methodological framework for quantum-enhanced estimation in spin glass thermodynamics and beyond by harnessing non-adiabatic quantum dynamics to address a classically difficult problem. |
| title | Quantum Annealing Algorithms for Estimating Ising Partition Functions |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2504.21666 |