Low-Density Parity-Check Codes as Stable Phases of Quantum Matter
Phases of matter with robust ground-state degeneracy, such as the quantum toric code, are known to be capable of robust quantum information storage. Here, we address the converse question: given a quantum error-correcting code, when does it define a stable gapped quantum phase of matter, whose groun...
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American Physical Society
2025-08-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/361k-nj4b |
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| author | Chao Yin Andrew Lucas |
| author_facet | Chao Yin Andrew Lucas |
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| collection | DOAJ |
| description | Phases of matter with robust ground-state degeneracy, such as the quantum toric code, are known to be capable of robust quantum information storage. Here, we address the converse question: given a quantum error-correcting code, when does it define a stable gapped quantum phase of matter, whose ground-state degeneracy is robust against perturbations in the thermodynamic limit? We prove that a low-density parity-check (LDPC) code defines such a phase, robust against all few-body perturbations, if its code distance grows at least logarithmically in the number of degrees of freedom, and it exhibits “check soundness.” Many constant-rate quantum LDPC expander codes have such properties, and define stable phases of matter with a constant zero-temperature entropy density, violating the third law of thermodynamics. Our results also show that quantum toric-code phases are robust to spatially nonlocal few-body perturbations. Similarly, phases of matter defined by classical codes are stable against symmetric perturbations. In the classical setting, we present improved locality bounds on the quasiadiabatic evolution operator between two nearby states in the same code phase. |
| format | Article |
| id | doaj-art-d1dffef31992499b9a97c580f1a53a1f |
| institution | DOAJ |
| issn | 2691-3399 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj-art-d1dffef31992499b9a97c580f1a53a1f2025-08-20T03:07:37ZengAmerican Physical SocietyPRX Quantum2691-33992025-08-016303032910.1103/361k-nj4bLow-Density Parity-Check Codes as Stable Phases of Quantum MatterChao YinAndrew LucasPhases of matter with robust ground-state degeneracy, such as the quantum toric code, are known to be capable of robust quantum information storage. Here, we address the converse question: given a quantum error-correcting code, when does it define a stable gapped quantum phase of matter, whose ground-state degeneracy is robust against perturbations in the thermodynamic limit? We prove that a low-density parity-check (LDPC) code defines such a phase, robust against all few-body perturbations, if its code distance grows at least logarithmically in the number of degrees of freedom, and it exhibits “check soundness.” Many constant-rate quantum LDPC expander codes have such properties, and define stable phases of matter with a constant zero-temperature entropy density, violating the third law of thermodynamics. Our results also show that quantum toric-code phases are robust to spatially nonlocal few-body perturbations. Similarly, phases of matter defined by classical codes are stable against symmetric perturbations. In the classical setting, we present improved locality bounds on the quasiadiabatic evolution operator between two nearby states in the same code phase.http://doi.org/10.1103/361k-nj4b |
| spellingShingle | Chao Yin Andrew Lucas Low-Density Parity-Check Codes as Stable Phases of Quantum Matter PRX Quantum |
| title | Low-Density Parity-Check Codes as Stable Phases of Quantum Matter |
| title_full | Low-Density Parity-Check Codes as Stable Phases of Quantum Matter |
| title_fullStr | Low-Density Parity-Check Codes as Stable Phases of Quantum Matter |
| title_full_unstemmed | Low-Density Parity-Check Codes as Stable Phases of Quantum Matter |
| title_short | Low-Density Parity-Check Codes as Stable Phases of Quantum Matter |
| title_sort | low density parity check codes as stable phases of quantum matter |
| url | http://doi.org/10.1103/361k-nj4b |
| work_keys_str_mv | AT chaoyin lowdensityparitycheckcodesasstablephasesofquantummatter AT andrewlucas lowdensityparitycheckcodesasstablephasesofquantummatter |