Monolithic Quantum Error Correction in the Presence of Distinguishability
arXiv preprint (2026)
In short
Codes stored inside a single atom, molecule or oscillator rely on the environment being unable to tell which state an error came from. We show that small energy shifts leak this information gradually rather than all at once, and we work out how often errors must be checked to stay ahead of the leak.
Why it matters
Fault-tolerant quantum computers need far fewer resources when their building blocks are less noisy. One way to build better blocks is monolithic encoding, where a qubit is stored in the many levels of a single system, such as a bosonic mode, an atom or a molecule, so that the dominant noise is already correctable. Our earlier Æ codes are one example.
These codes rely on errors being indistinguishable. For example, when an atom emits a photon, the photon has to look the same whichever code state it came from, so that it reveals only that a decay happened and nothing about the stored information. In real devices, small Zeeman or Stark shifts and anharmonicities pull these transition frequencies slightly apart. The emitted photons then carry “which-path” information to the environment.
What we did
We studied how error correction degrades as errors become distinguishable. We used two models: an exactly solvable four-level system, and a canonical spontaneous-emission noise model for atoms and molecules built from angular-momentum selection rules. We found that a small energy shift does not ruin a code at once. Which-path information leaks out gradually, on a timescale set by the inverse of the shift, and the fidelity lost grows with both the decay rate and the size of the shift.
This defines a checking time: how often the syndrome has to be measured to keep a target fidelity. The checking time gets shorter as the emitted photons become more separated in frequency. If syndromes are extracted fast enough, recovery is again nearly perfect. Distinguishability is therefore a practical limit on monolithic error correction, and fast syndrome extraction is a way around it.
Related
Cite
@misc{jain2026monolithic,
title = {Monolithic Quantum Error Correction in the Presence of Distinguishability},
author = {Jain, Shubham P. and Hudson, Eric R. and Campbell, Wesley C. and Gorshkov, Alexey V. and Albert, Victor V.},
year = {2026},
eprint = {2609.26946},
archivePrefix = {arXiv},
primaryClass = {quant-ph}
}