Accurate optimal quantum error correction thresholds from coherent information

Physical Review Research, vol. 6

Abstract

Quantum error correcting (QEC) codes protect quantum information from decoherence as long as error rates fall below critical error thresholds. In general, obtaining thresholds implies simulating the QEC procedure using, in general, suboptimal decoding strategies. In a few cases and for sufficiently simple noise models, optimal decoding of QEC codes can be framed as a phase transition in disordered classical spin models. In both situations, accurate estimation of thresholds demands intensive computational resources. Here we use the coherent information of the mixed state of noisy QEC codes to accurately estimate the associated optimal QEC thresholds already from small-distance codes at moderate computational cost. We show the effectiveness and versatility of our method by applying it first to the topological surface and color code under bit-flip and depolarizing noise. We then extend the coherent information based methodology to phenomenological and quantum circuit level noise settings. For all examples considered, we obtain highly accurate estimates of optimal error thresholds from small, low-distance instances of the codes, in close agreement with threshold values reported in the literature. Our findings establish the coherent information as a reliable competitive tool for the calculation of optimal thresholds of state-of-the-art QEC codes under realistic noise models. Published by the American Physical Society 2024

Authors 3

1. Luis Colmenárez Aachen

   RWTH Aachen University · Forschungszentrum Jülich

   Affiliation as printed

   Forschungszentrum Jülich

   RWTH Aachen University

2. Ze-Min Huang

   University of Maryland, College Park · University of Cologne · Joint Quantum Institute

   Affiliation as printed

   Joint Quantum Institute

   University of Cologne

   University of Maryland, College Park

3. Sebastian Diehl

   University of Cologne

   Affiliation as printed

   University of Cologne