Robust Quantum Entanglement at (nearly) Room Temperature

TL;DR

This paper demonstrates the existence of topologically-ordered quantum systems at nearly room temperature whose thermal states are globally entangled and cannot be approximated by shallow circuits, advancing understanding of quantum entanglement in practical conditions.

Contribution

It proves a mixed-state analog of the NLTS conjecture for nearly optimal parameters, combining advanced quantum code constructions and local-decoding techniques.

Findings

Thermal Gibbs states at nearly constant temperature are globally entangled.

Existence of topologically-ordered systems with complex entanglement properties.

Quantum codes from high-dimensional manifolds enable these results.

Abstract

We formulate a mixed-state analog of the NLTS conjecture [FH14] by asking whether there exist topologically-ordered systems for which the thermal Gibbs state for constant temperature is globally-entangled in the sense that it cannot even be approximated by shallow quantum circuits. We then prove this conjecture holds for nearly optimal parameters: when the "inverse temperature" is almost a constant (temperature decays as 1/loglog(n))) and the Hamiltonian is nearly local (log(n)-local). The construction and proof combine quantum codes that arise from high-dimensional manifolds [Has17, LLZ19], the local-decoding approach to quantum codes [LTZ15, FGL18] and quantum locally-testable codes [AE15].