Published June 13, 2023 | Published
Journal Article Open

Floquet Codes without Parent Subsystem Codes

  • 1. ROR icon Massachusetts Institute of Technology
  • 2. ROR icon University of California, Santa Barbara
  • 3. ROR icon California Institute of Technology
  • 4. ROR icon Harvard University

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.

Copyright and License

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

 

Acknowledgement

We are grateful to Ike Chuang, Aram Harrow, Ali Lavasani, Michael Vasmer, Ethan Lake, John Preskill, Sagar Vijay, Dave Aasen, and Dominic Williamson for useful discussions. We are especially grateful for insightful discussions with Ben Brown. N.T. is supported by the Walter Burke Institute for Theoretical Physics at Caltech. S.B. is supported by the National Science Foundation (NSF) Graduate Research Fellowship under Grant No. 1745302. This research was supported in part by the NSF under Grant No. NSF PHY-1748958, the Heising-Simons Foundation, and the Simons Foundation (216179, LB). We thank MIT Libraries for funding support. This work was also funded in part by NSF grant CCF-1729369.

Funding

N.T. is supported by the Walter Burke Institute for Theoretical Physics at Caltech. S.B. is supported by the National Science Foundation (NSF) Graduate Research Fellowship under Grant No. 1745302. This research was supported in part by the NSF under Grant No. NSF PHY-1748958, the Heising-Simons Foundation, and the Simons Foundation (216179, LB). We thank MIT Libraries for funding support. This work was also funded in part by NSF grant CCF-1729369.

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Created:
December 6, 2024
Modified:
December 6, 2024