SYK thermal expectations are classically easy at any temperature
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911614555389952 |
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| author | Zlokapa, Alexander Kiani, Bobak T. |
| author_facet | Zlokapa, Alexander Kiani, Bobak T. |
| contents | Estimating thermal expectations of local observables is a natural target for quantum advantage. We give a simple classical algorithm that approximates thermal expectations for Gibbs states of local Hamiltonians, and we show it has quasi-polynomial cost $n^{O(\log (n/ε))}$ for all temperatures above a phase transition in the free energy. For many natural models, this coincides with the entire fast-mixing, quantumly easy phase. Our results apply to the Sachdev-Ye-Kitaev (SYK) model at any constant temperature due to its absence of a phase transition -- despite its entanglement, sign problem, and polynomial quantum circuit lower bounds. Beyond SYK, we rigorously establish a universal classically easy high-temperature phase for all local, bounded-degree Hamiltonians and show that it extends to temperatures strictly colder than the death of entanglement transition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22619 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SYK thermal expectations are classically easy at any temperature Zlokapa, Alexander Kiani, Bobak T. Quantum Physics Data Structures and Algorithms Estimating thermal expectations of local observables is a natural target for quantum advantage. We give a simple classical algorithm that approximates thermal expectations for Gibbs states of local Hamiltonians, and we show it has quasi-polynomial cost $n^{O(\log (n/ε))}$ for all temperatures above a phase transition in the free energy. For many natural models, this coincides with the entire fast-mixing, quantumly easy phase. Our results apply to the Sachdev-Ye-Kitaev (SYK) model at any constant temperature due to its absence of a phase transition -- despite its entanglement, sign problem, and polynomial quantum circuit lower bounds. Beyond SYK, we rigorously establish a universal classically easy high-temperature phase for all local, bounded-degree Hamiltonians and show that it extends to temperatures strictly colder than the death of entanglement transition. |
| title | SYK thermal expectations are classically easy at any temperature |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2602.22619 |