2026/02/28 by Morteza Zarei, Mohammad Hossein Zarei
Physics and Astronomy · #quant-ph #cond-mat.stat-mech
11 pages, 7 figures, Accepted for publication in Physical Review A
arxiv created 2026/08/06 · arxiv updated 2026/08/07
We use a quantum formalism for the partition function of the classical XY model to identify a resilience phase transition in the zero-syndrome postselected sector of a noisy toric-rotor code. To this end, we consider a logical state of toric-rotor code under phase-shift noise described by a von Mises probability distribution. We then show that the fidelity of the noisy state with respect to the initial logical state is proportional to the partition function of the XY model, such that a Kosterlitz-Thouless phase transition at a critical temperature Tc corresponds to a resilience phase transition at a critical width σc. To characterize this transition, we map the spin stiffness of the XY model to a topological order parameter 0≤ λ≤ 1, which quantifies the intrinsic resilience of the code to decoherence within the zero-syndrome subspace. We show that the initial logical state exhibits partial resilience to noise for widths less than σc ≈ 0.89, where λ satisfies 0< λ<1 and drops discontinuously to zero at σc. We further discuss the implications of our results for postselected quantum error correction in the toric-rotor code in higher dimensions. Our work shows that the quantum formalism for partition functions provides a mathematically rigorous framework for studying noisy continuous-variable quantum codes.