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Published July 22, 2024 | Published
Journal Article Open

Quantum Lego Expansion Pack: Enumerators from Tensor Networks

  • 1. ROR icon California Institute of Technology
  • 2. Joint Center for Quantum Information and Computer Science

Abstract

We provide the first tensor-network method for computing quantum weight enumerator polynomials in the most general form. If a quantum code has a known tensor-network construction of its encoding map, our method is far more efficient, and in some cases exponentially faster than the existing approach. As a corollary, it produces decoders and an algorithm that computes the code distance. For non-(Pauli)-stabilizer codes, this constitutes the current best algorithm for computing the code distance. For degenerate stabilizer codes, it can be substantially faster compared to the current methods. We also introduce novel weight enumerators and their applications. In particular, we show that these enumerators can be used to compute logical error rates exactly and thus construct (optimal) decoders for any independent and identically distributed single qubit or qudit error channels. The enumerators also provide a more efficient method for computing nonstabilizerness in quantum many-body states. As the power for these speedups rely on a quantum Lego decomposition of quantum codes, we further provide systematic methods for decomposing quantum codes and graph states into a modular construction for which our technique applies. As a proof of principle, we perform exact analyses of the deformed surface codes, the holographic pentagon code, and the two-dimensional Bacon-Shor code under (biased) Pauli noise and limited instances of coherent error at sizes that are inaccessible by brute force. Published by the American Physical Society 2024

Copyright and License

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.

Acknowledgement

We thank Y.D. Li, D. Miller, G. Sommers, and Y.J. Zou for helpful discussions and comments on the manuscript. C.C. acknowledges the support by the U.S. Department
of Defense and NIST through the Hartree Postdoctoral Fellowship at QuICS, the Air Force Office of Scientific Research (Grant No. FA9550-19-1-0360), and the National
Science Foundation (Grant No. PHY-1733907). M.J.G. acknowledges support from the National Science Foundation (QLCI Grant No. OMA-2120757). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center. Certain commercial equipment, instruments, or materials are identified in this paper in order
to specify the procedure adequately and do not reflect any endorsement by NIST.

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Additional details

Created:
August 26, 2024
Modified:
August 26, 2024