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Tensor networks and quantum error correction.

Andrew J Ferris1, David Poulin2

  • 1ICFO-Institut de Ciencies Fotoniques, Parc Mediterrani de la Tecnologia, 08860 Barcelona, Spain and Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse, 1, 85748 Garching, Germany and Département de Physique, Université de Sherbrooke, Québec J1K 2R1, Canada.

Physical Review Letters
|August 2, 2014
PubMed
Summary
This summary is machine-generated.

We found connections between quantum error correction (QEC) and tensor network (TN) methods. This research introduces new quantum codes and decoding algorithms by leveraging the equivalence between QEC decoding and TN contraction.

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Area of Science:

  • Quantum Information Science
  • Quantum Many-Body Physics
  • Quantum Computing

Background:

  • Quantum error correction (QEC) is crucial for fault-tolerant quantum computation.
  • Tensor network (TN) methods are powerful tools for studying quantum many-body systems.
  • Existing QEC codes like quantum polar codes have limitations.

Purpose of the Study:

  • To establish novel relationships between QEC and TN methods.
  • To develop a new framework for quantum code design and decoding.
  • To generalize and enhance existing quantum coding techniques.

Main Methods:

  • Identifying correspondences between QEC codes and TN structures.
  • Demonstrating the formal equivalence of QEC decoding and TN contraction.
  • Developing generalized quantum codes based on TN principles.

Main Results:

  • Established several key relations between QEC and TN methodologies.
  • Showcased a formal equivalence between decoding quantum error correction codes and contracting tensor networks.
  • Proposed a new family of quantum codes and associated decoding algorithms.

Conclusions:

  • The equivalence between QEC decoding and TN contraction provides a powerful new perspective.
  • The proposed quantum codes and decoding algorithms offer improvements over existing methods.
  • This work bridges quantum error correction and tensor network approaches for advancing quantum computing.