Persistence Limits Under Vanishing Noise in Fault-Tolerant Quantum Systems Irreducible Maintenance Costs Independent of Physical Error Rates

Fault-tolerant quantum computation is often analyzed in the limit of vanishing physical noise, where logical error rates per operation can be made arbitrarily small. This limit is sometimes interpreted as implying that the physical cost of maintaining quantum information may likewise vanish. In this work, we show that this inference is incorrect for systems that preserve logical identity through sustained error correction. Even as physical noise approaches zero, the irreversible classical maintenance required to extract, process, and reset syndrome information imposes a non-vanishing thermodynamic cost. As a result, persistence limits on sustained quantum identity do not disappear in the ideal-noise limit. The constraint arises from irreversible identity maintenance rather than from noise suppression or imperfect hardware. This work is intentionally descriptive and non-operational, identifying a structural persistence bound without proposing mechanisms, architectures, or control strategies.