Hong Yifan, Guo Jinkang, Lucas Andrew
Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO, USA.
Nat Commun. 2025 Jan 2;16(1):316. doi: 10.1038/s41467-024-55570-7.
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.
被动纠错通过仅基于局部信息和少体相互作用来更新系统，从而永远（在热力学极限下）保护逻辑信息。一个典型的例子是经典二维伊辛模型：在低温相中，采用梅特罗波利斯风格的吉布斯采样器能在热力学长时间内保持初始磁化强度（一个逻辑比特）的符号。已知的被动量子纠错模型同样表现出向低温相的热力学相变，其中逻辑量子比特受到热稳定拓扑序的保护。相比之下，我们在此表明，某些恒定速率的经典和量子低密度奇偶校验码族在非零温度下没有热力学相变，但仍表现出遍历性破坏的动力学相变：在低于临界非零温度时，局部吉布斯采样的混合时间在热力学极限下发散。对此类码进行缓慢的吉布斯采样能够使用有限深度电路实现容错被动量子纠错。这种策略非常适合无测量量子纠错，并且可能为基于综合征测量和主动反馈的传统量子纠错提供一种理想的实验替代方案。
