• Open Access

Effective Compression of Quantum Braided Circuits Aided by ZX-Calculus

Michael Hanks, Marta P. Estarellas, William J. Munro, and Kae Nemoto
Phys. Rev. X 10, 041030 – Published 11 November 2020

Abstract

Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a topological circuit, for which braided circuits represent one candidate model. Given the large overhead associated with encoded circuits, it is paramount to reduce their size in terms of computation time and qubit number through circuit compression. While these optimizations have typically been performed in the language of three-dimensional diagrams, such a representation does not allow an efficient, general, and scalable approach to reduction or verification. We propose the use of the ZX-calculus as an intermediate language for braided circuit compression, demonstrating advantage by comparing results using this approach with those previously obtained for the compression of |A and |Y state distillation circuits. We then provide a benchmark of our method against a small set of Clifford+T circuits, yielding compression percentages of 77%. Our results suggest that the overheads of braided, defect-based circuits are comparable to those of their lattice-surgery counterparts, restoring the potential of this model for surface-code quantum computation.

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  • Received 31 January 2020
  • Revised 23 May 2020
  • Accepted 1 September 2020

DOI:https://doi.org/10.1103/PhysRevX.10.041030

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Michael Hanks1,*, Marta P. Estarellas1,*,†, William J. Munro2,1, and Kae Nemoto1

  • 1National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
  • 2NTT Basic Research Laboratories & NTT Research Center for Theoretical Quantum Physics, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan

  • *These authors contributed equally to this work.
  • mpestarellas@nii.ac.jp

Popular Summary

The fast development of quantum technology has brought the field of quantum computing into an era where proof-of-principle devices have enough qubits to outpace a classical computer, but those few qubits are still quite noisy and therefore prone to error. To achieve a truly practical advantage over classical computers, quantum devices need many more physical qubits to encode a logical qubit so that errors can be corrected. To tackle this challenge, we present an efficient compression method that reduces the resources associated with arbitrary circuits designed to run in one common quantum computer architecture known as the braiding model.

For a language capable of optimizing the volume of quantum circuits as well as verifying their correctness, we propose using the “ZX-calculus,” a graphical language introduced as a way to describe mappings between qubits. This language is able to unify the different architectures of surface-code-based computation, allowing us to exploit a hybrid approach of compilation. Our method presents an advantage of a 40% compression rate with respect to previous reductions, yielding compression rates greater than 70% of the original volume. We also show that this hybrid approach surpasses the currently preferred model for compilation.

With such compression rates, we reignite the potential of the braiding architecture model and bring practical fault-tolerant computation one step closer. Our work opens a new venue of research in large-scale quantum computing found on the hybridization of surface-code-based models of compilation.

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Vol. 10, Iss. 4 — October - December 2020

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