Regensburg 2019 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 62: Glasses and Glass transition (joint session DY/CPP)
DY 62.5: Vortrag
Freitag, 5. April 2019, 11:00–11:15, H19
Decoding of the Toric Code: A High Temperature Series Analysis — •Benedikt Placke1, Nikolas Breuckmann2, and Ananda Roy1,3 — 1JARA Institute for Quantum Information, RWTH Aachen University — 2Department of Physics and Astronomy, University College London — 3Insitut de Physique Théorique, CEA Saclay
The decoding of several topological quantum codes (TQC) can be mapped onto statistical physics models (SPM). This mapping relates the successful decoding of the error syndrome of the TQC to a certain phase of the respective SPM. The error-correction performance of several TQC-s have been analyzed using Monte Carlo (MC) simulations of the corresponding SPM. We, on the other hand, use high-temperature series expansion (HTSE) to analyze the decoding performance of the toric code. In contrast to zero temperature simulations, which estimate the threshold of the minimum-weight perfect-matching decoder, our method naturally provides an estimate of that of the maximum-likelihood decoder. First, we analyze the full phase diagram of the 2D random-bond Ising model by computing HTSE to a higher order than previously performed. From our analysis, we estimate the accuracy threshold of the toric code in absence of measurement imperfections. We compare our result to those obtained by MC simulations and network model analysis. Then, we perform HTSE of the zero-field free-energy and the Wilson loop order parameter in the 3D Ising gauge theory in the presence of quenched disorder. The latter model describes the decoding of the toric code subject to measurement errors.