Time-Reversal Selection Rules for Quantum Error Correction
Quantum Physics
2026-08-06 v1
Abstract
We apply time-reversal symmetry to quantum codes and show that it imposes parity selection rules on the physical error algebra. A time-reversal-invariant logical qubit on an odd number of spins is a Kramers doublet, forcing every even-weight Pauli to act as a scalar. Consequently, all even-weight Knill--Laflamme conditions hold automatically, so single-qubit error detection implies correction. We then reinterpret the Rains shadow enumerator through time reversal: each coefficient is a sum of error-resolved overlaps between a code and its time-reversed image.
Cite
@article{arxiv.2608.06304,
title = {Time-Reversal Selection Rules for Quantum Error Correction},
author = {Eric Kubischta and Ian Teixeira},
journal= {arXiv preprint arXiv:2608.06304},
year = {2026}
}