Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.06023 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909728455524352 |
|---|---|
| author | Ruba, Blazej Yang, Bowen |
| author_facet | Ruba, Blazej Yang, Bowen |
| contents | We study translationally invariant Pauli stabilizer codes with qudits of arbitrary, not necessarily uniform, dimensions. Using homological methods, we define a series of invariants called charge modules. We describe their properties and physical meaning. The most complete results are obtained for codes whose charge modules have Krull dimension zero. This condition is interpreted as mobility of excitations. We show that it is always satisfied for translation invariant 2D codes with unique ground state in infinite volume, which was previously known only in the case of uniform, prime qudit dimension. For codes all of whose excitations are mobile we construct a $p$-dimensional excitation and a $(D-p-1)$-form symmetry for every element of the $p$-th charge module. Moreover, we define a braiding pairing between charge modules in complementary degrees. We discuss examples which illustrate how charge modules and braiding can be computed in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_06023 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Homological invariants of Pauli stabilizer codes Ruba, Blazej Yang, Bowen Mathematical Physics Strongly Correlated Electrons Commutative Algebra We study translationally invariant Pauli stabilizer codes with qudits of arbitrary, not necessarily uniform, dimensions. Using homological methods, we define a series of invariants called charge modules. We describe their properties and physical meaning. The most complete results are obtained for codes whose charge modules have Krull dimension zero. This condition is interpreted as mobility of excitations. We show that it is always satisfied for translation invariant 2D codes with unique ground state in infinite volume, which was previously known only in the case of uniform, prime qudit dimension. For codes all of whose excitations are mobile we construct a $p$-dimensional excitation and a $(D-p-1)$-form symmetry for every element of the $p$-th charge module. Moreover, we define a braiding pairing between charge modules in complementary degrees. We discuss examples which illustrate how charge modules and braiding can be computed in practice. |
| title | Homological invariants of Pauli stabilizer codes |
| topic | Mathematical Physics Strongly Correlated Electrons Commutative Algebra |
| url | https://arxiv.org/abs/2204.06023 |