Thermodynamics of quantum error correction : The entropy production of a measurement-free fault-tolerant bit-flip quantum memory.
Elisa Bossard
The aim of quantum error correction (QEC) is to counteract the decoherence of qubits,which arises from their unavoidable interaction with the environment. In this work, westudy the lower bound of entropy production in quantum error correction, asking the cen-tral question: Is it possible to fight decoherence in a reversible way?A previous work established that ideal quantum error correction can, in principle,be performed reversibly. In this work, however, we consider fault-tolerant quantum errorcorrection, which explicitly accounts for faults occurring during the correction processitself. We show that when noise affects the circuit during the error-correcting operations,quantum error correction can no longer be reversible, because of unused correlations thatmust be dissipated at each correction cycle.This result can be better understood by drawing an analogy with Maxwell’s demon.In quantum error correction, the goal is to remove entropy from the data qubits. Ancillaryqubits are used to record the occurrence of errors (syndrome diagnosis), and this infor-mation is then employed to correct them (recovery operation). At the end of each cycle,the ancillary qubits are reset in order to start a new cycle. This is closely analogous to aMaxwell demon, which uses a memory to store information about a system, exploits thatinformation to reduce the system’s entropy, and finally resets its memory, dissipating heatinto the environment in accordance with Landauer’s principle.In this analogy, the demon’s memory corresponds to the ancillary qubits, while thesystem corresponds to the data qubits. During syndrome diagnosis, information aboutthe errors is recorded in the ancillary qubits, creating some correlations between dataand ancillary qubits. In the recovery operation, these correlations are used to correctthe errors on the data qubits and thus reduce their entropy. At the end of the cycle, theancillary qubits are reset to |0⟩, which generates a heat flow to the environment as dictatedby Landauer’s principle.For ideal quantum error correction, this process can, in principle, be performed re-versibly, thereby reaching equality in Landauer’s bound.However, when errors occur on the ancillary qubits during the QEC process (in the lan-guage of Maxwell’s demon, when faults affect the demon’s memory before the feedbackstep) these errors propagate to the data qubits, creating unwanted correlations betweendata and ancillas. Such correlations generate an additional finite heat flow to the bath,that prevents reaching equality in Landauer’s principle.
•Dec 1, 2025•0 citations