Quantum memory at nonzero temperature in a thermodynamically trivial system
- URL: http://arxiv.org/abs/2403.10599v1
- Date: Fri, 15 Mar 2024 18:00:03 GMT
- Title: Quantum memory at nonzero temperature in a thermodynamically trivial system
- Authors: Yifan Hong, Jinkang Guo, Andrew Lucas,
- Abstract summary: We show that constant-rate classical and quantum low-density parity check codes have no $textitthermodynamic$ phase transitions at nonzero temperature.
We conjecture that the circuit complexity of preparing extensive-energy states may diverge without crossing any thermodynamic transition.
Fault-tolerant passive decoders may be amenable to measurement-free quantum error correction.
- Score: 1.1606619391009658
- License: http://creativecommons.org/licenses/by/4.0/
- 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 constant-rate classical and quantum low-density parity check codes have no $\textit{thermodynamic}$ phase transitions at nonzero temperature, but nonetheless exhibit $\textit{ergodicity-breaking}$ dynamical transitions: below a critical nonzero temperature, the mixing time of local Gibbs sampling diverges in the thermodynamic limit. We conjecture that the circuit complexity of preparing extensive-energy states may diverge without crossing any thermodynamic transition. Fault-tolerant passive decoders, inspired by Gibbs samplers, may be amenable 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.
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