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. doi: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}
}
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https://doi.org/10.1103/PhysRevX.5.041038
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