Floquet Codes without Parent Subsystem Codes
Name
PRXQuantum.4.020341.pdf
Size
8.25 MB
Format
Adobe PDF
Checksum (MD5)
4047d65679a1392215a20e90d7e973a0
Author(s)
Davydova, Margarita
Tantivasadakarn, Nathanan
Balasubramanian, Shankar
Date Issued
June 13, 2023
Publisher
American Physical Society (APS)
Citation
Davydova, Margarita, Tantivasadakarn, Nathanan and Balasubramanian, Shankar. 2023. "Floquet Codes without Parent Subsystem Codes." 4 (2).
Version
Final published version
Abstract
We propose a new class of error-correcting dynamic codes in two and three dimensions that has no explicit connection to any parent subsystem code. The two-dimensional code, which we call the CSS (Calderbank-Shor-Steane) honeycomb code, is geometrically similar to that of the honeycomb code by Hastings and Haah and also dynamically embeds an instantaneous toric code. However, unlike the honeycomb code, it possesses an explicit CSS structure and its gauge checks do not form a subsystem code. Nevertheless, we show that our dynamic protocol conserves logical information and possesses a threshold for error correction. We generalize this construction to three dimensions and obtain a code that fault tolerantly alternates between realizing two type-I fracton models, the checkerboard and the X-cube model. Finally, we show the compatibility of our CSS honeycomb-code protocol and the honeycomb code by showing the possibility of randomly switching between the two protocols without information loss while still measuring error syndromes. We call this more general aperiodic structure “dynamic tree codes,” which we also generalize to three dimensions. We construct a probabilistic finite automaton prescription that generates dynamic tree codes correcting any single-qubit Pauli errors and can be viewed as a step toward the development of practical fault-tolerant random codes.
Subjects
General Physics and Astronomy
Mathematical Physics
Applied Mathematics
Electronic, Optical and Magnetic Materials
Electrical and Electronic Engineering
General Computer Science
MIT Department
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Center for Theoretical Physics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/prxquantum.4.020341
