Universal topological quantum computation with strongly correlated Majorana edge modes
Abstract
Abstract Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In reference Hu and Kane (2018 Phys. Rev. Lett. 120 066801), it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibonacci anyon τ and a thermal operator anyon ɛ in the tricritical Ising model. The deconfinement of τ and ɛ via the interaction between the fermion modes yields the anyon collisions and gives the braiding of either τ or ɛ . With these braidings, the complete members of a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for one-qubit as well as controlled-NOT (CNOT) gate for two-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit where the CNOT gate turns out to be a probabilistic gate and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, wemore »
- Authors:
- Publication Date:
- Research Org.:
- Boston College, Chestnut Hill, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); NNSF of China
- OSTI Identifier:
- 1861165
- Alternate Identifier(s):
- OSTI ID: 1979334
- Grant/Contract Number:
- FG02-99ER45747; 12174067; 11474061; 11804223
- Resource Type:
- Published Article
- Journal Name:
- New Journal of Physics
- Additional Journal Information:
- Journal Name: New Journal of Physics Journal Volume: 24 Journal Issue: 4; Journal ID: ISSN 1367-2630
- Publisher:
- IOP Publishing
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; universal topological quantum computation; strongly correlated Majorana edge modes; braiding of anyons; thin films of the chiral topological superconductor
Citation Formats
Zhan, Ye-Min, Chen, Yu-Ge, Chen, Bin, Wang, Ziqiang, Yu, Yue, and Luo, Xi. Universal topological quantum computation with strongly correlated Majorana edge modes. United Kingdom: N. p., 2022.
Web. doi:10.1088/1367-2630/ac5f87.
Zhan, Ye-Min, Chen, Yu-Ge, Chen, Bin, Wang, Ziqiang, Yu, Yue, & Luo, Xi. Universal topological quantum computation with strongly correlated Majorana edge modes. United Kingdom. https://doi.org/10.1088/1367-2630/ac5f87
Zhan, Ye-Min, Chen, Yu-Ge, Chen, Bin, Wang, Ziqiang, Yu, Yue, and Luo, Xi. Tue .
"Universal topological quantum computation with strongly correlated Majorana edge modes". United Kingdom. https://doi.org/10.1088/1367-2630/ac5f87.
@article{osti_1861165,
title = {Universal topological quantum computation with strongly correlated Majorana edge modes},
author = {Zhan, Ye-Min and Chen, Yu-Ge and Chen, Bin and Wang, Ziqiang and Yu, Yue and Luo, Xi},
abstractNote = {Abstract Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In reference Hu and Kane (2018 Phys. Rev. Lett. 120 066801), it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibonacci anyon τ and a thermal operator anyon ɛ in the tricritical Ising model. The deconfinement of τ and ɛ via the interaction between the fermion modes yields the anyon collisions and gives the braiding of either τ or ɛ . With these braidings, the complete members of a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for one-qubit as well as controlled-NOT (CNOT) gate for two-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit where the CNOT gate turns out to be a probabilistic gate and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, we show the application to Shor’s integer factorization algorithm.},
doi = {10.1088/1367-2630/ac5f87},
journal = {New Journal of Physics},
number = 4,
volume = 24,
place = {United Kingdom},
year = {Tue Apr 05 00:00:00 EDT 2022},
month = {Tue Apr 05 00:00:00 EDT 2022}
}
https://doi.org/10.1088/1367-2630/ac5f87
Works referenced in this record:
Quantum computational advantage using photons
journal, December 2020
- Zhong, Han-Sen; Wang, Hui; Deng, Yu-Hao
- Science, Vol. 370, Issue 6523
Quantum Information Processing Using Quantum Dot Spins and Cavity QED
journal, November 1999
- Imamog¯lu, A.; Awschalom, D. D.; Burkard, G.
- Physical Review Letters, Vol. 83, Issue 20
Controlled-NOT gate for multiparticle qubits and topological quantum computation based on parity measurements
journal, January 2008
- Zilberberg, Oded; Braunecker, Bernd; Loss, Daniel
- Physical Review A, Vol. 77, Issue 1
Superconducting quantum bits
journal, June 2008
- Clarke, John; Wilhelm, Frank K.
- Nature, Vol. 453, Issue 7198
On the theory of identical particles
journal, January 1977
- Leinaas, J. M.; Myrheim, J.
- Il Nuovo Cimento B Series 11, Vol. 37, Issue 1
Quantized Conductance of Majorana Zero Mode in the Vortex of the Topological Superconductor (Li 0.84 Fe 0.16 )OHFeSe
journal, April 2019
- Chen, C.; Liu, Q.; Zhang, T. Z.
- Chinese Physics Letters, Vol. 36, Issue 5
Multipartite Entanglement Among Single Spins in Diamond
journal, June 2008
- Neumann, P.; Mizuochi, N.; Rempp, F.
- Science, Vol. 320, Issue 5881
Room temperature manipulation of long lifetime spins in metallic-like carbon nanospheres
journal, July 2016
- Náfrádi, Bálint; Choucair, Mohammad; Dinse, Klaus-Peter
- Nature Communications, Vol. 7, Issue 1
Atomic line defects and zero-energy end states in monolayer Fe(Te,Se) high-temperature superconductors
journal, March 2020
- Chen, Cheng; Jiang, Kun; Zhang, Yi
- Nature Physics, Vol. 16, Issue 5
Observation of Spin Injection at a Ferromagnet-Semiconductor Interface
journal, July 1999
- Hammar, P. R.; Bennett, B. R.; Yang, M. J.
- Physical Review Letters, Vol. 83, Issue 1
Charge Detection Enables Free-Electron Quantum Computation
journal, July 2004
- Beenakker, C. W. J.; DiVincenzo, D. P.; Emary, C.
- Physical Review Letters, Vol. 93, Issue 2
Quantum Mechanics of Fractional-Spin Particles
journal, October 1982
- Wilczek, Frank
- Physical Review Letters, Vol. 49, Issue 14
Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure
journal, July 2017
- He, Qing Lin; Pan, Lei; Stern, Alexander L.
- Science, Vol. 357, Issue 6348
Multiple topological states in iron-based superconductors
journal, September 2018
- Zhang, Peng; Wang, Zhijun; Wu, Xianxin
- Nature Physics, Vol. 15, Issue 1
The quest and hope of Majorana zero modes in topological superconductor for fault-tolerant quantum computing: An introductory overview
conference, January 2021
- Ayukaryana, Nur R.; Fauzi, Mohammad H.; Hasdeo, Eddwi H.
- PROCEEDINGS OF THE 4TH INTERNATIONAL SEMINAR ON METALLURGY AND MATERIALS (ISMM2020): Accelerating Research and Innovation on Metallurgy and Materials for Inclusive and Sustainable Industry, AIP Conference Proceedings
Spin-Polarized Current in Noncollinear Antiferromagnets
journal, November 2017
- Železný, Jakub; Zhang, Yang; Felser, Claudia
- Physical Review Letters, Vol. 119, Issue 18
Fast Multiqubit Gates by Adiabatic Evolution in Interacting Excited-State Manifolds of Rydberg Atoms and Superconducting Circuits
journal, June 2020
- Khazali, Mohammadsadegh; Mølmer, Klaus
- Physical Review X, Vol. 10, Issue 2
Non-Abelian statistics and topological quantum information processing in 1D wire networks
journal, February 2011
- Alicea, Jason; Oreg, Yuval; Refael, Gil
- Nature Physics, Vol. 7, Issue 5
Fractional statistics in anyon collisions
journal, April 2020
- Bartolomei, H.; Kumar, M.; Bisognin, R.
- Science, Vol. 368, Issue 6487
Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer
journal, July 1985
- Deutsch, D.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 400, Issue 1818
The octonions
journal, December 2001
- Baez, John C.
- Bulletin of the American Mathematical Society, Vol. 39, Issue 02
Controlled exchange interaction between pairs of neutral atoms in an optical lattice
journal, July 2007
- Anderlini, Marco; Lee, Patricia J.; Brown, Benjamin L.
- Nature, Vol. 448, Issue 7152
Parity independence of the zero-bias conductance peak in a nanowire based topological superconductor-quantum dot hybrid device
journal, December 2014
- Deng, M. T.; Yu, C. L.; Huang, G. Y.
- Scientific Reports, Vol. 4, Issue 1
Theory of tunneling conductance of anomalous Rashba metal/superconductor junctions
journal, October 2015
- Fukumoto, Toshiyuki; Taguchi, Katsuhisa; Kobayashi, Shingo
- Physical Review B, Vol. 92, Issue 14
Absence of evidence for chiral Majorana modes in quantum anomalous Hall-superconductor devices
journal, January 2020
- Kayyalha, Morteza; Xiao, Di; Zhang, Ruoxi
- Science, Vol. 367, Issue 6473
Quantized Majorana conductance
journal, March 2018
- Zhang, Hao; Liu, Chun-Xiao; Gazibegovic, Sasa
- Nature, Vol. 556, Issue 7699
Toward tailoring Majorana bound states in artificially constructed magnetic atom chains on elemental superconductors
journal, May 2018
- Kim, Howon; Palacio-Morales, Alexandra; Posske, Thore
- Science Advances, Vol. 4, Issue 5
Universal quantum computation with the fractional quantum Hall state
journal, April 2006
- Bravyi, Sergey
- Physical Review A, Vol. 73, Issue 4
Fibonacci Topological Superconductor
journal, February 2018
- Hu, Yichen; Kane, C. L.
- Physical Review Letters, Vol. 120, Issue 6
Deterministic Creation and Braiding of Chiral Edge Vortices
journal, April 2019
- Beenakker, C. W. J.; Baireuther, P.; Herasymenko, Y.
- Physical Review Letters, Vol. 122, Issue 14
Stabilization of point-defect spin qubits by quantum wells
journal, December 2019
- Ivády, Viktor; Davidsson, Joel; Delegan, Nazar
- Nature Communications, Vol. 10, Issue 1
Atomic-scale spin-polarization maps using functionalized superconducting probes
journal, January 2021
- Schneider, Lucas; Beck, Philip; Wiebe, Jens
- Science Advances, Vol. 7, Issue 4
Multiple-particle interference and quantum error correction
journal, November 1996
- Steane, Andrew
- Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 452, Issue 1954, p. 2551-2577
Half-integer level shift of vortex bound states in an iron-based superconductor
journal, August 2019
- Kong, Lingyuan; Zhu, Shiyu; Papaj, Michał
- Nature Physics, Vol. 15, Issue 11
Anomalous Zero-Bias Conductance Peak in a Nb–InSb Nanowire–Nb Hybrid Device
journal, February 2012
- Deng, M. T.; Yu, C. L.; Huang, G. Y.
- Nano Letters, Vol. 12, Issue 12
Spin-resolved Andreev levels and parity crossings in hybrid superconductor–semiconductor nanostructures
journal, December 2013
- Lee, Eduardo J. H.; Jiang, Xiaocheng; Houzet, Manuel
- Nature Nanotechnology, Vol. 9, Issue 1
Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance
journal, September 2019
- Pustogow, A.; Luo, Yongkang; Chronister, A.
- Nature, Vol. 574, Issue 7776
Magnetic-Field-Tuned Aharonov-Bohm Oscillations and Evidence for Non-Abelian Anyons at
journal, October 2013
- Willett, R. L.; Nayak, C.; Shtengel, K.
- Physical Review Letters, Vol. 111, Issue 18
Majorana Zero Mode Detected with Spin Selective Andreev Reflection in the Vortex of a Topological Superconductor
journal, June 2016
- Sun, Hao-Hua; Zhang, Kai-Wen; Hu, Lun-Hui
- Physical Review Letters, Vol. 116, Issue 25
Evidence for dispersing 1D Majorana channels in an iron-based superconductor
journal, January 2020
- Wang, Zhenyu; Rodriguez, Jorge Olivares; Jiao, Lin
- Science, Vol. 367, Issue 6473
Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices
journal, April 2012
- Mourik, V.; Zuo, K.; Frolov, S. M.
- Science, Vol. 336, Issue 6084
Seven-sphere and the exceptional N = 7 and N = 8 superconformal algebras
journal, May 1996
- Günaydin, Murat; Ketov, Sergei V.
- Nuclear Physics B, Vol. 467, Issue 1-2
Quantum computer hardware based on rare-earth-ion-doped inorganic crystals
journal, January 2002
- Ohlsson, Nicklas; Krishna Mohan, R.; Kröll, Stefan
- Optics Communications, Vol. 201, Issue 1-3
Topological quantum computation based on chiral Majorana fermions
journal, October 2018
- Lian, Biao; Sun, Xiao-Qi; Vaezi, Abolhassan
- Proceedings of the National Academy of Sciences, Vol. 115, Issue 43
Failure of protection of Majorana based qubits against decoherence
journal, March 2012
- Budich, Jan Carl; Walter, Stefan; Trauzettel, Björn
- Physical Review B, Vol. 85, Issue 12
Non-Abelian anyons and topological quantum computation
journal, September 2008
- Nayak, Chetan; Simon, Steven H.; Stern, Ady
- Reviews of Modern Physics, Vol. 80, Issue 3
Quantum gold rush: the private funding pouring into quantum start-ups
journal, October 2019
- Gibney, Elizabeth
- Nature, Vol. 574, Issue 7776
Spin-triplet superconductivity in Sr2RuO4 identified by 17O Knight shift
journal, December 1998
- Ishida, K.; Mukuda, H.; Kitaoka, Y.
- Nature, Vol. 396, Issue 6712
Bath-induced decoherence in finite-size Majorana wires at non-zero temperature
journal, January 2022
- Breckwoldt, Niels; Posske, Thore; Thorwart, Michael
- New Journal of Physics, Vol. 24, Issue 1
Atomic-scale interface engineering of Majorana edge modes in a 2D magnet-superconductor hybrid system
journal, July 2019
- Palacio-Morales, Alexandra; Mascot, Eric; Cocklin, Sagen
- Science Advances, Vol. 5, Issue 7
Superstrings and manifolds of exceptional holonomy
journal, September 1995
- Shatashvili, S. L.; Vafa, C.
- Selecta Mathematica, Vol. 1, Issue 2
Majorana zero modes and topological quantum computation
journal, October 2015
- Sarma, Sankar Das; Freedman, Michael; Nayak, Chetan
- npj Quantum Information, Vol. 1, Issue 1
Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor
journal, October 2014
- Nadj-Perge, S.; Drozdov, I. K.; Li, J.
- Science, Vol. 346, Issue 6209
2n-quasihole states realize 2n−1-dimensional spinor braiding statistics in paired quantum Hall states
journal, November 1996
- Nayak, Chetan; Wilczek, Frank
- Nuclear Physics B, Vol. 479, Issue 3
Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions
journal, November 2012
- Das, Anindya; Ronen, Yuval; Most, Yonatan
- Nature Physics, Vol. 8, Issue 12
Scalable Majorana vortex modes in iron-based superconductors
journal, February 2020
- Chiu, Ching-Kai; Machida, T.; Huang, Yingyi
- Science Advances, Vol. 6, Issue 9
Superconductor-nanowire devices from tunneling to the multichannel regime: Zero-bias oscillations and magnetoconductance crossover
journal, June 2013
- Churchill, H. O. H.; Fatemi, V.; Grove-Rasmussen, K.
- Physical Review B, Vol. 87, Issue 24