Fundamental thresholds of realistic quantum error correction circuits from classical spin models

Quantum, vol. 6, pp. 618

Abstract

Mapping the decoding of quantum error correcting (QEC) codes to classical disordered statistical mechanics models allows one to determine critical error thresholds of QEC codes under phenomenological noise models. Here, we extend this mapping to admit realistic, multi-parameter noise models of faulty QEC circuits, derive the associated strongly correlated classical spin models, and illustrate this approach for a quantum repetition code with faulty stabilizer readout circuits. We use Monte-Carlo simulations to study the resulting phase diagram and benchmark our results against a minimum-weight perfect matching decoder. The presented method provides an avenue to assess fundamental thresholds of QEC circuits, independent of specific decoding strategies, and can thereby help guiding the development of near-term QEC hardware.

Authors 4

1. Davide Vodola

   Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · University of Bologna

   Affiliation as printed

   Dipartimento di Fisica e Astronomia ``Augusto Righi'' dell'Università di Bologna, I-40127 Bologna, Italy

   INFN, Sezione di Bologna, I-40127 Bologna, Italy

2. Manuel Rispler

   QuTech · Delft University of Technology

   Affiliation as printed

   QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

3. Seyong Kim

   Sejong University

   Affiliation as printed

   Department of Physics, Sejong University, 05006 Seoul, Republic of Korea

4. Markus Michael Müller Aachen Institute for Quantum Information

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany

   Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich, 52428 Jülich, Germany