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QI: Fachverband Quanteninformation
QI 7: Quantum Error Correction
QI 7.5: Vortrag
Montag, 18. März 2024, 16:00–16:15, HFT-TA 441
Accurate optimal quantum error correction thresholds from coherent information — •Luis Colmenarez1,2, Ze-min Huang3, Sebastian Diehl4, and Markus Mueller1,2 — 1Institute for Quantum Information, RWTH Aachen University, Aachen, Germany — 2Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Juelich, Juelich, Germany — 3Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Illinois, USA — 4Institute for Theoretical Physics, University of Cologne, Cologne, Germany
In general, obtaining optimal thresholds of quantum error correcting codes (QEC) implies simulating QEC using complicated and, often, sub-optimal decoding strategies. In a few cases, optimal decoding can be framed as a phase transition in disordered classical spin models. In both situations, accurate estimation of thresholds demands intensive computational resources. In this work we use the coherent information of noisy mixed states, to accurately estimate 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, and then extend the coherent information based methodology for phenomenological and circuit level noise. For all examples we obtain optimal error thresholds from small instances of the codes with 1% difference compared to known values. We establish the coherent information as a reliable competitive practical tool for the calculation of optimal thresholds under realistic noise models.
Keywords: Quantum error correction; Optimal thresholds; Coherent information; Circuit level noise; Numerical calculation