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Local stabilizer codes in three dimensions without string logical operators
Open accessAbstract
We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have stringlike logical operators, which make the codes non-self-correcting. We introduce a notion of ``logical string segments'' to avoid difficulties in defining one-dimensional objects in discrete lattices. We prove that every stringlike logical operator of our code can be deformed to a disjoint union of short segments, each of which is in the stabilizer group. The code has surfacelike logical operators whose partial implementation has unsatisfied stabilizers along its boundary.
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Cites
Quantum Error Correction and Orthogonal Geometry
Calderbank, A. R., Rains, E. M., Shor, P. W., & Sloane, N. J. A. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.405 · Cited by 811
Cited by
Quantum error correction for quantum memories
Terhal, B. M. (2015) · Reviews of Modern Physics · doi:10.1103/revmodphys.87.307 · Cited by 1,354
Fracton topological order, generalized lattice gauge theory, and duality
Vijay, S., Haah, J., & Fu, L. (2016) · Physical Review B · doi:10.1103/physrevb.94.235157 · Cited by 553
Self-citationNandkishore, R. M., & Hermele, M. (2019) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031218-013604 · Cited by 517
Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians
Sala, P., Rakovszky, T., Verresen, R., Knap, M., & Pollmann, F. (2020) · Physical Review X · doi:10.1103/physrevx.10.011047 · Cited by 432
Quantum Low-Density Parity-Check Codes
Breuckmann, N. P., & Eberhardt, J. N. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040101 · Cited by 328
Metadata
- Authors
- Haah, J.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2011-04-22
- Volume
- 83
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2097361916
- Cited by
- 690
- References
- 1
- FWCI
- 16.26
- Type
- journal article
- Language
- en
- Open access
- green
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