Quantum memory at nonzero temperature in a thermodynamically trivial system

Fuente: arXiv
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Autores principales: Hong, Yifan, Guo, Jinkang, Lucas, Andrew
Formato: Preprint
Publicado: 2024
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author Hong, Yifan
Guo, Jinkang
Lucas, Andrew
author_facet Hong, Yifan
Guo, Jinkang
Lucas, Andrew
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2403_10599
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Quantum memory at nonzero temperature in a thermodynamically trivial system
Hong, Yifan
Guo, Jinkang
Lucas, Andrew
Quantum Physics
Statistical Mechanics
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.
title Quantum memory at nonzero temperature in a thermodynamically trivial system
topic Quantum Physics
Statistical Mechanics
url https://arxiv.org/abs/2403.10599