Coherent error induced phase transition

2025/05/31 by Hanchen Liu, Xiao Chen, Liu, Hanchen +1 · 1 citation
Engineering · Physics and Astronomy · #Optical Polarization and Ellipsometry #Photonic and Optical Devices #Laser-Matter Interactions and Applications

paper · pdf · doi:10.48550/arxiv.2506.00650

Abstract

We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we apply a random unitary error channel and subsequently measure stabilizer checks, resulting in a syndrome-dependent post-measurement state. By examining both this syndrome state and the associated syndrome distribution, we identify a phase transition in the behavior of the logical information. In the Clifford/stabilizer setting, the change of logical stabilizer structure in a syndrome branch determines the state-level MAP Pauli-frame return probability for a chosen logical-basis input. We separately use quantum coherent information to diagnose recoverability of arbitrary encoded inputs at the channel level. Below a critical error threshold \(p_c\), the syndrome branches remain compatible with the original logical sector, enabling a high state-return probability. Above \(p_c\), the data are consistent with effective scrambling of the encoded subspace relative to the stabilizer checks, where the syndrome-resolved logical maps approach a global-Clifford-induced stabilizer instrument. This common post-threshold picture organizes both the toric-code and finite-rate random-stabilizer-code results within the same scrambling mechanism. The syndrome distribution supplies complementary local and global structural diagnostics whose scaling depends on the code family. We refer to this phenomenon as a coherent error induced phase transition. To illustrate this transition, we study two classes of quantum error-correcting codes, the toric code and finite-rate random stabilizer codes, thereby shedding light on the design and performance limits of quantum error correction under coherent errors.

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Cited by

• Learning transitions of topological surface codes

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