Quantum memory at nonzero temperature in a thermodynamically trivial system
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...
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Nature Portfolio
2025-01-01
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| Series: | Nature Communications |
| Online Access: | https://doi.org/10.1038/s41467-024-55570-7 |
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| author | Yifan Hong Jinkang Guo Andrew Lucas |
| author_facet | Yifan Hong Jinkang Guo Andrew Lucas |
| author_sort | Yifan Hong |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-1dff2ce08f0a4ba790cb5a4f4f522d3a |
| institution | Kabale University |
| issn | 2041-1723 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Nature Communications |
| spelling | doaj-art-1dff2ce08f0a4ba790cb5a4f4f522d3a2025-01-05T12:40:37ZengNature PortfolioNature Communications2041-17232025-01-011611810.1038/s41467-024-55570-7Quantum memory at nonzero temperature in a thermodynamically trivial systemYifan Hong0Jinkang Guo1Andrew Lucas2Department of Physics and Center for Theory of Quantum Matter, University of ColoradoDepartment of Physics and Center for Theory of Quantum Matter, University of ColoradoDepartment of Physics and Center for Theory of Quantum Matter, University of ColoradoAbstract 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.https://doi.org/10.1038/s41467-024-55570-7 |
| spellingShingle | Yifan Hong Jinkang Guo Andrew Lucas Quantum memory at nonzero temperature in a thermodynamically trivial system Nature Communications |
| title | Quantum memory at nonzero temperature in a thermodynamically trivial system |
| title_full | Quantum memory at nonzero temperature in a thermodynamically trivial system |
| title_fullStr | Quantum memory at nonzero temperature in a thermodynamically trivial system |
| title_full_unstemmed | Quantum memory at nonzero temperature in a thermodynamically trivial system |
| title_short | Quantum memory at nonzero temperature in a thermodynamically trivial system |
| title_sort | quantum memory at nonzero temperature in a thermodynamically trivial system |
| url | https://doi.org/10.1038/s41467-024-55570-7 |
| work_keys_str_mv | AT yifanhong quantummemoryatnonzerotemperatureinathermodynamicallytrivialsystem AT jinkangguo quantummemoryatnonzerotemperatureinathermodynamicallytrivialsystem AT andrewlucas quantummemoryatnonzerotemperatureinathermodynamicallytrivialsystem |