Quantum memory at nonzero temperature in a thermodynamically trivial system

Yifan Hong, Jinkang Guo and Andrew Lucas ()
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Yifan Hong: University of Colorado
Jinkang Guo: University of Colorado
Andrew Lucas: University of Colorado

Nature Communications, 2025, vol. 16, issue 1, 1-8

Abstract: Abstract Passive error correction protects logical information forever (in the thermodynamic limit) by updating the system based only on local information and few-body interactions. A paradigmatic example is the classical two-dimensional Ising model: a Metropolis-style Gibbs sampler retains the sign of the initial magnetization (a logical bit) for thermodynamically long times in the low-temperature phase. Known models of passive quantum error correction similarly exhibit thermodynamic phase transitions to a low-temperature phase wherein logical qubits are protected by thermally stable topological order. Here, in contrast, we show that certain families of constant-rate classical and quantum low-density parity check codes have no thermodynamic phase transitions at nonzero temperature, but nonetheless exhibit ergodicity-breaking dynamical transitions: below a critical nonzero temperature, the mixing time of local Gibbs sampling diverges in the thermodynamic limit. Slow Gibbs sampling of such codes enables fault-tolerant passive quantum error correction using finite-depth circuits. This strategy is well suited to measurement-free quantum error correction, and may present a desirable experimental alternative to conventional quantum error correction based on syndrome measurements and active feedback.

Date: 2025
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DOI: 10.1038/s41467-024-55570-7

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