Thermodynamics of Ahn--Doherty--Landahl Continuous Quantum Error Correction

Juan Garcia-Nila; Pedro B. Melo; Lucas Johns

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arXiv · 2609.39597

Thermodynamics of Ahn--Doherty--Landahl Continuous Quantum Error Correction

Juan Garcia-Nila·Pedro B. Melo·Lucas Johns

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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.

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BibTeX RIS

Juan Garcia-Nila, Pedro B. Melo, Lucas Johns. 2026-09-30. Thermodynamics of Ahn--Doherty--Landahl Continuous Quantum Error Correction. https://arxiv.org/abs/2609.39597

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