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arXiv · 2602.22619

SYK thermal expectations are classically easy at any temperature

Alexander Zlokapa·Bobak T. Kiani
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Abstract

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 $n^{O(\log (n/\epsilon))}$ 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.

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Alexander Zlokapa, Bobak T. Kiani. 2026-02-26. SYK thermal expectations are classically easy at any temperature. https://arxiv.org/abs/2602.22619

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