Quantum memory at nonzero temperature in a thermodynamically trivial system
arXiv:2403.10599 · doi:10.1038/s41467-024-55570-7
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.
32 pages, 9 figures, 1 table; v2 changes: added section on tree-codes, fixed typos; v3 changes: corrected a factor of e for cluster growth
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Cited by in corpus (8)
- Designing open quantum systems with known steady states: Davies generators and beyond
- Low-density parity-check codes as stable phases of quantum matter
- Solvable Quantum Circuits in Tree+1 Dimensions
- Single-shot preparation of hypergraph product codes via dimension jump
- Viewing protected superconducting qubits through the lens of the cat qubit
- On the energy barrier of hypergraph product codes
- Towards self-correcting quantum codes for neutral atom arrays
- Fracton models from product codes