Stability of gapped quantum matter and error-correction with adiabatic noise
The codespace of a quantum error-correcting code can often be identified with the degenerate ground space within a gapped phase of quantum matter. We argue that the stability of such a phase is directly related to a set of coherent error processes against which this quantum error-correcting code (QE...
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American Physical Society
2025-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.023166 |
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| author | Ali Lavasani Sagar Vijay |
| author_facet | Ali Lavasani Sagar Vijay |
| author_sort | Ali Lavasani |
| collection | DOAJ |
| description | The codespace of a quantum error-correcting code can often be identified with the degenerate ground space within a gapped phase of quantum matter. We argue that the stability of such a phase is directly related to a set of coherent error processes against which this quantum error-correcting code (QECC) is robust: such a quantum code can recover from adiabatic noise channels, corresponding to random adiabatic drift of code states through the phase, with asymptotically perfect fidelity in the thermodynamic limit, as long as this adiabatic evolution keeps states sufficiently “close” to the initial ground space. We further argue that when specific decoders—such as minimum-weight perfect matching—are applied to recover this information, an error-correcting threshold is generically encountered within the gapped phase. In cases where the adiabatic evolution is known, we explicitly show examples in which quantum information can be recovered by using stabilizer measurements and Pauli feedback, even up to a phase boundary, though the resulting decoding transitions are in different universality classes from the optimal decoding transitions in the presence of incoherent Pauli noise. This provides examples where nonlocal, coherent noise effectively decoheres in the presence of syndrome measurements in a stabilizer QECC. |
| format | Article |
| id | doaj-art-34fe5a0d900941b79d242658e9762f36 |
| institution | DOAJ |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-34fe5a0d900941b79d242658e9762f362025-08-20T03:07:06ZengAmerican Physical SocietyPhysical Review Research2643-15642025-05-017202316610.1103/PhysRevResearch.7.023166Stability of gapped quantum matter and error-correction with adiabatic noiseAli LavasaniSagar VijayThe codespace of a quantum error-correcting code can often be identified with the degenerate ground space within a gapped phase of quantum matter. We argue that the stability of such a phase is directly related to a set of coherent error processes against which this quantum error-correcting code (QECC) is robust: such a quantum code can recover from adiabatic noise channels, corresponding to random adiabatic drift of code states through the phase, with asymptotically perfect fidelity in the thermodynamic limit, as long as this adiabatic evolution keeps states sufficiently “close” to the initial ground space. We further argue that when specific decoders—such as minimum-weight perfect matching—are applied to recover this information, an error-correcting threshold is generically encountered within the gapped phase. In cases where the adiabatic evolution is known, we explicitly show examples in which quantum information can be recovered by using stabilizer measurements and Pauli feedback, even up to a phase boundary, though the resulting decoding transitions are in different universality classes from the optimal decoding transitions in the presence of incoherent Pauli noise. This provides examples where nonlocal, coherent noise effectively decoheres in the presence of syndrome measurements in a stabilizer QECC.http://doi.org/10.1103/PhysRevResearch.7.023166 |
| spellingShingle | Ali Lavasani Sagar Vijay Stability of gapped quantum matter and error-correction with adiabatic noise Physical Review Research |
| title | Stability of gapped quantum matter and error-correction with adiabatic noise |
| title_full | Stability of gapped quantum matter and error-correction with adiabatic noise |
| title_fullStr | Stability of gapped quantum matter and error-correction with adiabatic noise |
| title_full_unstemmed | Stability of gapped quantum matter and error-correction with adiabatic noise |
| title_short | Stability of gapped quantum matter and error-correction with adiabatic noise |
| title_sort | stability of gapped quantum matter and error correction with adiabatic noise |
| url | http://doi.org/10.1103/PhysRevResearch.7.023166 |
| work_keys_str_mv | AT alilavasani stabilityofgappedquantummatteranderrorcorrectionwithadiabaticnoise AT sagarvijay stabilityofgappedquantummatteranderrorcorrectionwithadiabaticnoise |