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Title: Majorana Fermion Surface Code for Universal Quantum Computation

Abstract

In this study, we introduce an exactly solvable model of interacting Majorana fermions realizing Z2 topological order with a Z2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid-state systems, including topological insulators, nanowires, or two-dimensional electron gases, proximitized by s-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.

Authors:
; ;
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1228798
Alternate Identifier(s):
OSTI ID: 1240141
Grant/Contract Number:  
SC0010526
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 5 Journal Issue: 4; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; condensed matter physics; quantum information; superconductivity

Citation Formats

Vijay, Sagar, Hsieh, Timothy H., and Fu, Liang. Majorana Fermion Surface Code for Universal Quantum Computation. United States: N. p., 2015. Web. https://doi.org/10.1103/PhysRevX.5.041038.
Vijay, Sagar, Hsieh, Timothy H., & Fu, Liang. Majorana Fermion Surface Code for Universal Quantum Computation. United States. https://doi.org/10.1103/PhysRevX.5.041038
Vijay, Sagar, Hsieh, Timothy H., and Fu, Liang. Thu . "Majorana Fermion Surface Code for Universal Quantum Computation". United States. https://doi.org/10.1103/PhysRevX.5.041038.
@article{osti_1228798,
title = {Majorana Fermion Surface Code for Universal Quantum Computation},
author = {Vijay, Sagar and Hsieh, Timothy H. and Fu, Liang},
abstractNote = {In this study, we introduce an exactly solvable model of interacting Majorana fermions realizing Z2 topological order with a Z2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid-state systems, including topological insulators, nanowires, or two-dimensional electron gases, proximitized by s-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.},
doi = {10.1103/PhysRevX.5.041038},
journal = {Physical Review. X},
number = 4,
volume = 5,
place = {United States},
year = {2015},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevX.5.041038

Citation Metrics:
Cited by: 28 works
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