Unveiling dynamical quantum error correcting codes via non-invertible symmetries
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911474265358336 |
|---|---|
| author | Radhakrishnan, Rajath Sharon, Adar Tantivasadakarn, Nathanan |
| author_facet | Radhakrishnan, Rajath Sharon, Adar Tantivasadakarn, Nathanan |
| contents | Dynamical stabilizer codes (DSCs) have recently emerged as a powerful generalization of static stabilizer codes for quantum error correction, replacing a fixed stabilizer group with a sequence of non-commuting measurements. This dynamical structure unlocks new possibilities for fault tolerance but also introduces new challenges, as errors must now be tracked across both space and time. In this work, we provide a physical and topological understanding of DSCs by establishing a correspondence between qudit Pauli measurements and non-invertible symmetries in 4+1-dimensional 2-form gauge theories. Sequences of measurements in a DSC are mapped to a fusion of the operators implementing these non-invertible symmetries. We show that the error detectors of a DSC correspond to endable surface operators in the gauge theory, whose endpoints define line operators, and that detectable errors are precisely those surface operators that braid non-trivially with these lines. Finally, we demonstrate how this framework naturally recovers the spacetime stabilizer code associated with a DSC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unveiling dynamical quantum error correcting codes via non-invertible symmetries Radhakrishnan, Rajath Sharon, Adar Tantivasadakarn, Nathanan High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Physics Dynamical stabilizer codes (DSCs) have recently emerged as a powerful generalization of static stabilizer codes for quantum error correction, replacing a fixed stabilizer group with a sequence of non-commuting measurements. This dynamical structure unlocks new possibilities for fault tolerance but also introduces new challenges, as errors must now be tracked across both space and time. In this work, we provide a physical and topological understanding of DSCs by establishing a correspondence between qudit Pauli measurements and non-invertible symmetries in 4+1-dimensional 2-form gauge theories. Sequences of measurements in a DSC are mapped to a fusion of the operators implementing these non-invertible symmetries. We show that the error detectors of a DSC correspond to endable surface operators in the gauge theory, whose endpoints define line operators, and that detectable errors are precisely those surface operators that braid non-trivially with these lines. Finally, we demonstrate how this framework naturally recovers the spacetime stabilizer code associated with a DSC. |
| title | Unveiling dynamical quantum error correcting codes via non-invertible symmetries |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2510.09565 |