SYK thermal expectations are classically easy at any temperature

Alexander Zlokapa, Bobak T. Kiani (Feb 27 2026).

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

Arxiv: https://arxiv.org/abs/2602.22619