Quantum memory at nonzero temperature in a thermodynamically trivial system
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908579381903360 |
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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 |