Physical implementation of a Majorana fermion surface code for fault-tolerant quantum computation

Vijay, Sagar; Fu, Liang

doi:10.1088/0031-8949/T168/1/014002

Title: Physical implementation of a Majorana fermion surface code for fault-tolerant quantum computation

Journal Article · Mon Jan 25 00:00:00 EST 2016 · Physica Scripta

DOI:https://doi.org/10.1088/0031-8949/T168/1/014002· OSTI ID:1557844

Vijay, Sagar ^[1]; Fu, Liang ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

We propose a physical realization of a commuting Hamiltonian of interacting Majorana fermions realizing Z ₂ topological order, using an array of Josephson-coupled topological superconductor islands. The required multi-body interaction Hamiltonian is naturally generated by a combination of charging energy induced quantum phase-slips on the superconducting islands and electron tunneling between islands. Our setup improves on a recent proposal for implementing a Majorana fermion surface code (Vijay et al 2015 Phys. Rev. X 5 041038), a 'hybrid' approach to fault-tolerant quantum computation that combines (1) the engineering of a stabilizer Hamiltonian with a topologically ordered ground state with (2) projective stabilizer measurements to implement error correction and a universal set of logical gates. Our hybrid strategy has advantages over the traditional surface code architecture in error suppression and single-step stabilizer measurements, and is widely applicable to implementing stabilizer codes for quantum computation.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0010526

OSTI ID:: 1557844

Alternate ID(s):: OSTI ID: 1235773

Journal Information:: Physica Scripta, Vol. T168; ISSN 0031-8949

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 22 works

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Cited By (10)

Majorana zero modes in superconductor–semiconductor heterostructures Lutchyn, R. M.; Bakkers, E. P. A. M.; Kouwenhoven, L. P. Nature Reviews Materials, Vol. 3, Issue 5 https://doi.org/10.1038/s41578-018-0003-1	journal	May 2018
Topological ordering in the Majorana toric code Ziesen, Alexander; Hassler, Fabian; Roy, Ananda Physical Review B, Vol. 100, Issue 10 https://doi.org/10.1103/physrevb.100.104508	journal	September 2019
Effects of Gate-Induced Electric Fields on Semiconductor Majorana Nanowires Antipov, Andrey E.; Bargerbos, Arno; Winkler, Georg W. Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/physrevx.8.031041	journal	August 2018
Modeling noise and error correction for Majorana-based quantum computing Knapp, Christina; Beverland, Michael; Pikulin, Dmitry I. Quantum, Vol. 2 https://doi.org/10.22331/q-2018-09-03-88	journal	September 2018
Low-field topological threshold in Majorana double nanowires Schrade, Constantin; Thakurathi, Manisha; Reeg, Christopher American Physical Society https://doi.org/10.5451/unibas-ep60926	text	January 2017
Universal Quantum Computation with Hybrid Spin-Majorana Qubits Hoffman, Silas; Schrade, Constantin; Klinovaja, Jelena arXiv https://doi.org/10.48550/arxiv.1602.06923	text	January 2016
Roadmap to Majorana surface codes Plugge, S.; Landau, L. A.; Sela, E. arXiv https://doi.org/10.48550/arxiv.1606.08408	text	January 2016
Braiding by Majorana Tracking and Long-Range CNOT Gates with Color Codes Litinski, Daniel; von Oppen, Felix arXiv https://doi.org/10.48550/arxiv.1708.05012	text	January 2017
Modeling noise and error correction for Majorana-based quantum computing Knapp, Christina; Beverland, Michael; Pikulin, Dmitry I. arXiv https://doi.org/10.48550/arxiv.1806.01275	text	January 2018
Topological ordering in the Majorana Toric Code Ziesen, Alexander; Hassler, Fabian; Roy, Ananda arXiv https://doi.org/10.48550/arxiv.1906.05158	text	January 2019

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