Thermodynamics of Ahn--Doherty--Landahl Continuous Quantum Error Correction
Abstract
Continuous quantum error correction (CQEC) replaces discrete syndrome measurements and recovery operations with continuous syndrome extraction and real-time Hamiltonian feedback. Here we investigate the thermodynamic resources required by this process by formulating measurement-based continuous quantum error correction as an information engine. We distinguish the system-side power associated with energy transfer between the feedback field and the protected system from the controller-side power associated with the feedback Hamiltonian. The framework is first developed for the one-qubit Ahn-Doherty-Landahl (ADL) protocol and subsequently extended to the three-qubit repetition code under continuous stabilizer monitoring. Numerical simulations show that increasing the feedback strength improves the steady-state fidelity and reduces the conditional-state entropy, while both energetic contributions continue to increase in magnitude after the fidelity begins to saturate. These results expose a direct tradeoff between logical stabilization and the energetic resources required for continuous feedback, closely related to previously established energy--precision tradeoffs in quantum measurement and quantum-Zeno stabilization.
Related
- Access Resources and Stability of Error-Correction Capabilities in Continuous Strategic Codes
- Quantum-Coherent Thermodynamics: Leaf Typicality via Minimum-Variance Foliation
- Second Law of Thermodynamics in Closed Quantum Many-Body Systems
- Statistical thermodynamics of the quantum spin-s XXZ Heisenberg model in the Weiss limit
- Wasserstein-2 gradient flows and the geometry of entropy production in classical and quantum stochastic thermodynamics
BibTeX
@misc{garcianila2026thermodynamics,
title = {{Thermodynamics of Ahn--Doherty--Landahl Continuous Quantum Error Correction}},
author = {Juan Garcia-Nila and Pedro B. Melo and Lucas Johns},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39597},
eprint = {2609.39597},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39597},
}
RIS
TY - UNPB
TI - Thermodynamics of Ahn--Doherty--Landahl Continuous Quantum Error Correction
AU - Juan Garcia-Nila
AU - Pedro B. Melo
AU - Lucas Johns
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39597
UR - https://arxiv.org/abs/2609.39597
AB - Continuous quantum error correction (CQEC) replaces discrete syndrome measurements and recovery operations with continuous syndrome extraction and real-time Hamiltonian feedback. Here we investigate the thermodynamic resources required by this process by formulating measurement-based continuous quantum error correction as an information engine. We distinguish the system-side power associated with energy transfer between the feedback field and the protected system from the controller-side power associated with the feedback Hamiltonian. The framework is first developed for the one-qubit Ahn-Doherty-Landahl (ADL) protocol and subsequently extended to the three-qubit repetition code under continuous stabilizer monitoring. Numerical simulations show that increasing the feedback strength improves the steady-state fidelity and reduces the conditional-state entropy, while both energetic contributions continue to increase in magnitude after the fidelity begins to saturate. These results expose a direct tradeoff between logical stabilization and the energetic resources required for continuous feedback, closely related to previously established energy--precision tradeoffs in quantum measurement and quantum-Zeno stabilization.
ER -