Quantum memory at nonzero temperature in a thermodynamically trivial system — Andrew Lucas

Quantum memory at nonzero temperature in a thermodynamically trivial system — Andrew Lucas (Boulder)

Passive error correction protects logical information forever (in the thermodynamic limit) by updating the system based only on instantaneous 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, such as the four-dimensional toric code, similarly exhibit thermodynamic phase transitions to a low-temperature phase wherein logical qubits are protected by thermally stable topological order. Here, in contrast, I describe constant-rate classical and quantum low-density parity check codes which 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. This result suggests that NLTS can be a property of thermodynamically trivial phases of matter. Fault-tolerant passive “decoding" inspired by Gibbs sampling is amenable to measurement-free quantum error correction, and may be a desirable experimental alternative to conventional quantum error correction based on syndrome measurements and active feedback.