SYK thermal expectations are classically easy at any temperature

• URL: http://arxiv.org/abs/2602.22619v1
• Date: Thu, 26 Feb 2026 04:48:32 GMT
• Title: SYK thermal expectations are classically easy at any temperature
• Authors: Alexander Zlokapa, Bobak T. Kiani,
• Abstract summary: We give a simple classical algorithm that approximates thermal expectations.<n>We show it has quasi-polynomial cost $nO(log n/)$ for all temperatures above a phase transition in the free energy.
• Score: 49.788604174558564
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Estimating thermal expectations of local observables is a natural target for quantum advantage. We give a simple classical algorithm that approximates thermal expectations, 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 -- including when the thermal state is highly entangled and satisfies polynomial quantum circuit lower bounds, a sign problem, and nontrivial instance-to-instance fluctuations. Our analysis of the SYK model relies on the replica trick to control the complex zeros of the partition function.

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