Understanding Stabilizer Codes Under Local Decoherence Through a General Statistical Mechanics Mapping
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911790240104448 |
|---|---|
| author | Lyons, Anasuya |
| author_facet | Lyons, Anasuya |
| contents | We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we construct a mapping from the $n$th moment of the decohered ground state density matrix to a classical statistical mechanics model. We demonstrate that various measures of information capacity -- (i) quantum relative entropy, (ii) coherent information, and (iii) entanglement negativity -- map to thermodynamic quantities in the statistical mechanics model and can be used to characterize the decoding phase transition. As examples, we analyze the 3D toric code and X-cube model, deriving bounds on their optimal decoding thresholds and gaining insight into their information properties under decoherence. Additionally, we demonstrate that the SM mapping acts an an "ungauging" map; the classical models that describe a given code under decoherence also can be gauged to obtain the same code. Finally, we comment on correlated errors and non-CSS stabilizer codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Understanding Stabilizer Codes Under Local Decoherence Through a General Statistical Mechanics Mapping Lyons, Anasuya Quantum Physics Statistical Mechanics Strongly Correlated Electrons We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we construct a mapping from the $n$th moment of the decohered ground state density matrix to a classical statistical mechanics model. We demonstrate that various measures of information capacity -- (i) quantum relative entropy, (ii) coherent information, and (iii) entanglement negativity -- map to thermodynamic quantities in the statistical mechanics model and can be used to characterize the decoding phase transition. As examples, we analyze the 3D toric code and X-cube model, deriving bounds on their optimal decoding thresholds and gaining insight into their information properties under decoherence. Additionally, we demonstrate that the SM mapping acts an an "ungauging" map; the classical models that describe a given code under decoherence also can be gauged to obtain the same code. Finally, we comment on correlated errors and non-CSS stabilizer codes. |
| title | Understanding Stabilizer Codes Under Local Decoherence Through a General Statistical Mechanics Mapping |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2403.03955 |