Bounds on Autonomous Quantum Error Correction

Oles Shtanko; Yu-Jie Liu; Simon Lieu; Alexey V. Gorshkov; Victor V. Albert

doi:10.22331/q-2025-07-22-1804

Bounds on Autonomous Quantum Error Correction

Oles Shtanko¹, Yu-Jie Liu^2,3, Simon Lieu^4,5, Alexey V. Gorshkov^4,5, and Victor V. Albert⁵

¹IBM Quantum, IBM Research – Almaden, San Jose, CA, USA
²Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany
³Munich Center for Quantum Science and Technology (MCQST), Munich, Germany
⁴Joint Quantum Institute, NIST/University of Maryland, College Park, MD, USA
⁵Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, USA

Published:	2025-07-22, volume 9, page 1804
Editor:	Ángela Capel
Eprint:	arXiv:2308.16233v2
Doi:	https://doi.org/10.22331/q-2025-07-22-1804
Citation:	Quantum 9, 1804 (2025).

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Abstract

Autonomous quantum memories are a way to passively protect quantum information using engineered dissipation that creates an “always-on'' decoder. We analyze Markovian autonomous decoders that can be implemented with a wide range of qubit and bosonic error-correcting codes, and derive several upper bounds and a lower bound on the logical error rate in terms of correction and noise rates. These bounds suggest that, in general, there is always a correction rate, possibly size-dependent, above which autonomous memories exhibit arbitrarily long coherence times. For any given autonomous memory, size dependence of this correction rate is difficult to rule out: we point to common scenarios where autonomous decoders that stochastically implement active error correction must operate at rates that grow with code size. For codes with a threshold, we show that it is possible to achieve faster-than-polynomial decay of the logical error rate with code size by using superlogarithmic scaling of the correction rate. We illustrate our results with several examples. One example is an exactly solvable global dissipative toric code model that can achieve an effective logical error rate that decreases exponentially with the linear lattice size, provided that the recovery rate grows proportionally with the linear lattice size.

► BibTeX data

@article{Shtanko2025boundsautonomous,
  doi = {10.22331/q-2025-07-22-1804},
  url = {https://doi.org/10.22331/q-2025-07-22-1804},
  title = {Bounds on {A}utonomous {Q}uantum {E}rror {C}orrection},
  author = {Shtanko, Oles and Liu, Yu-Jie and Lieu, Simon and Gorshkov, Alexey V. and Albert, Victor V.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1804},
  month = jul,
  year = {2025}
}

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