Interaction order sets the onset cost of steady-state quantum magic
Abstract
Maintaining quantum magic under continuous noise requires coherent control and a supply of purity. We determine the cost of local stabilizer replacement resets sustaining any positive stationary magic in autonomous qubit networks with depolarization rate γ, interactions on at most k sites, and Hamiltonian strength J per site. An exact global stabilizer decomposition and a matching finite construction give the optimal onset scaling γ(γ/J)1/(k−1), uniformly over network size and noisy ancillas. For two-body interactions, the leading maximal-reset-rate coefficient is 1/(2√2) for every fixed finite size N≥2, allowing mixed reset targets and heterogeneous rates. The same coefficient holds uniformly over growing networks with pure Pauli targets and equal reset rates. The converse combines hafnian stabilizer geometry with a positive random-order forest expansion.
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BibTeX
@misc{xu2026interaction,
title = {{Interaction order sets the onset cost of steady-state quantum magic}},
author = {Mingdi Xu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02095},
eprint = {2611.02095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02095},
}
RIS
TY - UNPB
TI - Interaction order sets the onset cost of steady-state quantum magic
AU - Mingdi Xu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02095
UR - https://arxiv.org/abs/2611.02095
AB - Maintaining quantum magic under continuous noise requires coherent control and a supply of purity. We determine the cost of local stabilizer replacement resets sustaining any positive stationary magic in autonomous qubit networks with depolarization rate γ, interactions on at most k sites, and Hamiltonian strength J per site. An exact global stabilizer decomposition and a matching finite construction give the optimal onset scaling γ(γ/J)^1/(k−1), uniformly over network size and noisy ancillas. For two-body interactions, the leading maximal-reset-rate coefficient is 1/(2√2) for every fixed finite size N≥2, allowing mixed reset targets and heterogeneous rates. The same coefficient holds uniformly over growing networks with pure Pauli targets and equal reset rates. The converse combines hafnian stabilizer geometry with a positive random-order forest expansion.
ER -