Transversal Clifford gates on folded surface codes

Moussa, Jonathan E.

doi:10.1103/PhysRevA.94.042316

Title: Transversal Clifford gates on folded surface codes

Journal Article · Wed Oct 12 04:00:00 UTC 2016 · Physical Review A

DOI: https://doi.org/10.1103/PhysRevA.94.042316 · OSTI ID:1333573

Moussa, Jonathan E. ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surface codes. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construction is presented generally for qudits of any dimension. Lastly, the specific application of these codes to universal quantum computation based on qubit fusion is also discussed.

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Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1333573

Report Number(s):: SAND--2016-2005J; 619860

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 4 Vol. 94; ISSN PLRAAN; ISSN 2469-9926

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited By (5)

Error rates and resource overheads of encoded three-qubit gates Takagi, Ryuji; Yoder, Theodore J.; Chuang, Isaac L. Physical Review A, Vol. 96, Issue 4 https://doi.org/10.1103/physreva.96.042302	journal	October 2017
The surface code with a twist Yoder, Theodore J.; Kim, Isaac H. Quantum, Vol. 1 https://doi.org/10.22331/q-2017-04-25-2	journal	April 2017
The boundaries and twist defects of the color code and their applications to topological quantum computation Kesselring, Markus S.; Pastawski, Fernando; Eisert, Jens Quantum, Vol. 2 https://doi.org/10.22331/q-2018-10-19-101	journal	October 2018
Error rates and resource overheads of encoded three-qubit gates Takagi, Ryuji; Yoder, Theodore J.; Chuang, Isaac L. arXiv https://doi.org/10.48550/arxiv.1707.00012	text	January 2017
The boundaries and twist defects of the color code and their applications to topological quantum computation Kesselring, Markus S.; Pastawski, Fernando; Eisert, Jens arXiv https://doi.org/10.48550/arxiv.1806.02820	text	January 2018

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