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  • Letter
  • Open Access

Accurate optimal quantum error correction thresholds from coherent information

Luis Colmenarez1,2,*, Ze-Min Huang3,4, Sebastian Diehl4, and Markus Müller1,2

  • *Contact author: colmenarez@physik.rwth-aachen.de
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Phys. Rev. Research 6, L042014 – Published 15 October, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042014

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 practical tool for the calculation of optimal thresholds of state-of-the-art QEC codes under realistic noise models.

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Phys. Rev. Research 6, L042014– Published 15 October, 2024
  • Received 18 December 2023
  • Accepted 25 August 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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