Teleportation-based quantum information processing with Majorana zero modes

Vijay, Sagar; Fu, Liang

doi:10.1103/PhysRevB.94.235446

Title: Teleportation-based quantum information processing with Majorana zero modes

Journal Article · Thu Dec 29 00:00:00 EST 2016 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.94.235446· OSTI ID:1424929

Vijay, Sagar ^[1]; Fu, Liang ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics; Kavli Institute for Theoretical Physics, Santa Barbara, CA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

In this work, we present a measurement-based scheme for performing braiding operations on Majorana zero modes in mesoscopic superconductor islands and for detecting their non-Abelian statistics without moving or hybridizing them. In our scheme for “braiding without braiding”, the topological qubit encoded in any pair of well-separated Majorana zero modes is read out from the transmission phase shift in electron teleportation through the island in the Coulomb-blockade regime. Finally, we propose experimental setups to measure the teleportation phase shift via conductance in an electron interferometer or persistent current in a closed loop.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

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

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0010526

OSTI ID:: 1424929

Alternate ID(s):: OSTI ID: 1338093

Journal Information:: Physical Review B, Vol. 94, Issue 23; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 100 works

Citation information provided by
Web of Science

References (52)

Fractionalization in Josephson junction arrays hinged by quantum spin Hall edges Xu, Cenke; Fu, Liang Physical Review B, Vol. 81, Issue 13 https://doi.org/10.1103/PhysRevB.81.134435	journal	April 2010
Physical implementation of a Majorana fermion surface code for fault-tolerant quantum computation Vijay, Sagar; Fu, Liang Physica Scripta, Vol. T168 https://doi.org/10.1088/0031-8949/T168/1/014002	journal	January 2016
Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires Halperin, Bertrand I.; Oreg, Yuval; Stern, Ady Physical Review B, Vol. 85, Issue 14 https://doi.org/10.1103/PhysRevB.85.144501	journal	April 2012
Non-Abelian Statistics of Half-Quantum Vortices in $p$ -Wave Superconductors Ivanov, D. A. Physical Review Letters, Vol. 86, Issue 2 https://doi.org/10.1103/PhysRevLett.86.268	journal	January 2001
Conductance of a proximitized nanowire in the Coulomb blockade regime van Heck, B.; Lutchyn, R. M.; Glazman, L. I. Physical Review B, Vol. 93, Issue 23 https://doi.org/10.1103/PhysRevB.93.235431	journal	June 2016
Electron Teleportation via Majorana Bound States in a Mesoscopic Superconductor Fu, Liang Physical Review Letters, Vol. 104, Issue 5 https://doi.org/10.1103/PhysRevLett.104.056402	journal	February 2010
Globally symmetric topological phase: from anyonic symmetry to twist defect Teo, Jeffrey C. Y. Journal of Physics: Condensed Matter, Vol. 28, Issue 14 https://doi.org/10.1088/0953-8984/28/14/143001	journal	March 2016
Towards Realistic Implementations of a Majorana Surface Code Landau, L. A.; Plugge, S.; Sela, E. Physical Review Letters, Vol. 116, Issue 5 https://doi.org/10.1103/PhysRevLett.116.050501	journal	February 2016
Coulomb-assisted braiding of Majorana fermions in a Josephson junction array van Heck, B.; Akhmerov, A. R.; Hassler, F. New Journal of Physics, Vol. 14, Issue 3 https://doi.org/10.1088/1367-2630/14/3/035019	journal	March 2012
Majorana Fermion Surface Code for Universal Quantum Computation Vijay, Sagar; Hsieh, Timothy H.; Fu, Liang Physical Review X, Vol. 5, Issue 4 https://doi.org/10.1103/PhysRevX.5.041038	journal	December 2015
Measurement-Only Topological Quantum Computation Bonderson, Parsa; Freedman, Michael; Nayak, Chetan Physical Review Letters, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevLett.101.010501	journal	June 2008
Majorana Zero Mode Detected with Spin Selective Andreev Reflection in the Vortex of a Topological Superconductor Sun, Hao-Hua; Zhang, Kai-Wen; Hu, Lun-Hui Physical Review Letters, Vol. 116, Issue 25 https://doi.org/10.1103/PhysRevLett.116.257003	journal	June 2016
Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices Mourik, V.; Zuo, K.; Frolov, S. M. Science, Vol. 336, Issue 6084 https://doi.org/10.1126/science.1222360	journal	April 2012
Search for Majorana Fermions in Superconductors Beenakker, C. W. J. Annual Review of Condensed Matter Physics, Vol. 4, Issue 1 https://doi.org/10.1146/annurev-conmatphys-030212-184337	journal	April 2013
Milestones Toward Majorana-Based Quantum Computing Aasen, David; Hell, Michael; Mishmash, Ryan V. Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031016	journal	August 2016
Quantum computation by measurement and quantum memory Nielsen, Michael A. Physics Letters A, Vol. 308, Issue 2-3 https://doi.org/10.1016/S0375-9601(02)01803-0	journal	February 2003
New directions in the pursuit of Majorana fermions in solid state systems Alicea, Jason Reports on Progress in Physics, Vol. 75, Issue 7 https://doi.org/10.1088/0034-4885/75/7/076501	journal	June 2012
Roadmap to Majorana surface codes Plugge, S.; Landau, L. A.; Sela, E. Physical Review B, Vol. 94, Issue 17 https://doi.org/10.1103/PhysRevB.94.174514	journal	November 2016
Unpaired Majorana fermions in quantum wires Kitaev, A. Yu Physics-Uspekhi, Vol. 44, Issue 10S https://doi.org/10.1070/1063-7869/44/10S/S29	journal	October 2001
Majorana Braiding with Thermal Noise Pedrocchi, Fabio L.; DiVincenzo, David P. Physical Review Letters, Vol. 115, Issue 12 https://doi.org/10.1103/PhysRevLett.115.120402	journal	September 2015
Majorana Single-Charge Transistor Hützen, R.; Zazunov, A.; Braunecker, B. Physical Review Letters, Vol. 109, Issue 16 https://doi.org/10.1103/PhysRevLett.109.166403	journal	October 2012
Experimental Detection of a Majorana Mode in the core of a Magnetic Vortex inside a Topological Insulator-Superconductor ${Bi}_{2} {Te}_{3} / {NbSe}_{2}$ Heterostructure Xu, Jin-Peng; Wang, Mei-Xiao; Liu, Zhi Long Physical Review Letters, Vol. 114, Issue 1 https://doi.org/10.1103/PhysRevLett.114.017001	journal	January 2015
Controlling non-Abelian statistics of Majorana fermions in semiconductor nanowires Sau, Jay D.; Clarke, David J.; Tewari, Sumanta Physical Review B, Vol. 84, Issue 9 https://doi.org/10.1103/PhysRevB.84.094505	journal	September 2011
Exponential protection of zero modes in Majorana islands Albrecht, S. M.; Higginbotham, A. P.; Madsen, M. Nature, Vol. 531, Issue 7593 https://doi.org/10.1038/nature17162	journal	March 2016
Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect Read, N.; Green, Dmitry Physical Review B, Vol. 61, Issue 15 https://doi.org/10.1103/PhysRevB.61.10267	journal	April 2000
Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator Fu, Liang; Kane, C. L. Physical Review Letters, Vol. 100, Issue 9 https://doi.org/10.1103/PhysRevLett.100.096407	journal	March 2008
Generic New Platform for Topological Quantum Computation Using Semiconductor Heterostructures Sau, Jay D.; Lutchyn, Roman M.; Tewari, Sumanta Physical Review Letters, Vol. 104, Issue 4 https://doi.org/10.1103/PhysRevLett.104.040502	journal	January 2010
Multichannel Generalization of Kitaev’s Majorana End States and a Practical Route to Realize Them in Thin Films Potter, Andrew C.; Lee, Patrick A. Physical Review Letters, Vol. 105, Issue 22 https://doi.org/10.1103/PhysRevLett.105.227003	journal	November 2010
Non-Abelian statistics and topological quantum information processing in 1D wire networks Alicea, Jason; Oreg, Yuval; Refael, Gil Nature Physics, Vol. 7, Issue 5 https://doi.org/10.1038/nphys1915	journal	February 2011
Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor Nadj-Perge, S.; Drozdov, I. K.; Li, J. Science, Vol. 346, Issue 6209 https://doi.org/10.1126/science.1259327	journal	October 2014
Shortcuts to non-Abelian braiding Karzig, Torsten; Pientka, Falko; Refael, Gil Physical Review B, Vol. 91, Issue 20 https://doi.org/10.1103/PhysRevB.91.201102	journal	May 2015
Programmable Quantum Gate Arrays Nielsen, M. A.; Chuang, Isaac L. Physical Review Letters, Vol. 79, Issue 2 https://doi.org/10.1103/PhysRevLett.79.321	journal	July 1997
Nonlocal adiabatic response of a localized system to local manipulations Khemani, Vedika; Nandkishore, Rahul; Sondhi, S. L. Nature Physics, Vol. 11, Issue 7 https://doi.org/10.1038/nphys3344	journal	June 2015
Monte Carlo studies of the self-correcting properties of the Majorana quantum error correction code under braiding Pedrocchi, Fabio L.; Bonesteel, N. E.; DiVincenzo, David P. Physical Review B, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevB.92.115441	journal	September 2015
Nonabelions in the fractional quantum hall effect Moore, Gregory; Read, Nicholas Nuclear Physics B, Vol. 360, Issue 2-3 https://doi.org/10.1016/0550-3213(91)90407-O	journal	August 1991
Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator Fu, L.; Kane, C. L. Topologica, Vol. 2, Issue 1 https://doi.org/10.3731/topologica.2.013	journal	January 2009
Superconducting proximity effect and Majorana fermions at the surface of a topological insulator Fu, Liang; Kane, C. L. arXiv https://doi.org/10.48550/arxiv.0707.1692	text	January 2007
Non-Abelian Anyons and Topological Quantum Computation Nayak, Chetan; Simon, Steven H.; Stern, Ady arXiv https://doi.org/10.48550/arxiv.0707.1889	text	January 2007
Measurement-Only Topological Quantum Computation Bonderson, Parsa; Freedman, Michael; Nayak, Chetan arXiv https://doi.org/10.48550/arxiv.0802.0279	text	January 2008
Electron Teleportation via Majorana Bound States in a Mesoscopic Superconductor Fu, Liang arXiv https://doi.org/10.48550/arxiv.0909.5172	text	January 2009
Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films Potter, Andrew C.; Lee, Patrick A. arXiv https://doi.org/10.48550/arxiv.1007.4569	text	January 2010
Search for Majorana fermions in superconductors Beenakker, C. W. J. arXiv https://doi.org/10.48550/arxiv.1112.1950	text	January 2011
Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires Halperin, Bertrand I.; Oreg, Yuval; Stern, Ady arXiv https://doi.org/10.48550/arxiv.1112.5333	text	January 2011
Majorana single-charge transistor Hützen, R.; Zazunov, A.; Braunecker, B. arXiv https://doi.org/10.48550/arxiv.1206.3912	text	January 2012
Non-local Adiabatic Response of a Localized System to Local Manipulations Khemani, Vedika; Nandkishore, Rahul; Sondhi, S. L. arXiv https://doi.org/10.48550/arxiv.1411.2616	text	January 2014
Majorana Fermion Surface Code for Universal Quantum Computation Vijay, Sagar; Hsieh, Timothy H.; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1504.01724	text	January 2015
Towards realistic implementations of a Majorana surface code Landau, L. A.; Plugge, S.; Sela, E. arXiv https://doi.org/10.48550/arxiv.1509.05345	text	January 2015
Globally symmetric topological phase: from anyonic symmetry to twist defect Teo, Jeffrey C. Y. arXiv https://doi.org/10.48550/arxiv.1511.00912	text	January 2015
Milestones toward Majorana-based quantum computing Aasen, David; Hell, Michael; Mishmash, Ryan V. arXiv https://doi.org/10.48550/arxiv.1511.05153	text	January 2015
Roadmap to Majorana surface codes Plugge, S.; Landau, L. A.; Sela, E. arXiv https://doi.org/10.48550/arxiv.1606.08408	text	January 2016
Non-abelian statistics of half-quantum vortices in p-wave superconductors Ivanov, D. A. arXiv https://doi.org/10.48550/arxiv.cond-mat/0005069	text	January 2000
Programmable quantum gate arrays Nielsen, M. A.; Chuang, Isaac L. arXiv https://doi.org/10.48550/arxiv.quant-ph/9703032	text	January 1997

Cited By (27)

Supercurrent and Multiple Andreev Reflections in InSb Nanosheet SNS Junctions Zhi, Jinhua; Kang, Ning; Li, Sen physica status solidi (b), Vol. 256, Issue 6 https://doi.org/10.1002/pssb.201800538	journal	January 2019
Epitaxy of advanced nanowire quantum devices Gazibegovic, Sasa; Car, Diana; Zhang, Hao Nature, Vol. 548, Issue 7668 https://doi.org/10.1038/nature23468	journal	August 2017
Parity transitions in the superconducting ground state of hybrid InSb–Al Coulomb islands Shen, Jie; Heedt, Sebastian; Borsoi, Francesco Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-07279-7	journal	November 2018
Next steps of quantum transport in Majorana nanowire devices Zhang, Hao; Liu, Dong E.; Wimmer, Michael Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-13133-1	journal	November 2019
Measurement-only quantum computation with Floquet Majorana corner modes Bomantara, Raditya Weda; Gong, Jiangbin Physical Review B, Vol. 101, Issue 8 https://doi.org/10.1103/physrevb.101.085401	journal	February 2020
Majorana qubits in a topological insulator nanoribbon architecture Manousakis, J.; Altland, A.; Bagrets, D. Physical Review B, Vol. 95, Issue 16 https://doi.org/10.1103/physrevb.95.165424	journal	April 2017
Proximity-induced low-energy renormalization in hybrid semiconductor-superconductor Majorana structures Stanescu, Tudor D.; Das Sarma, Sankar Physical Review B, Vol. 96, Issue 1 https://doi.org/10.1103/physrevb.96.014510	journal	July 2017
Measurement and control of a Coulomb-blockaded parafermion box Snizhko, Kyrylo; Egger, Reinhold; Gefen, Yuval Physical Review B, Vol. 97, Issue 8 https://doi.org/10.1103/physrevb.97.081405	journal	February 2018
Distinguishing Majorana bound states from localized Andreev bound states by interferometry Hell, Michael; Flensberg, Karsten; Leijnse, Martin Physical Review B, Vol. 97, Issue 16 https://doi.org/10.1103/physrevb.97.161401	journal	April 2018
Quantum transport in coupled Majorana box systems Gau, Matthias; Plugge, Stephan; Egger, Reinhold Physical Review B, Vol. 97, Issue 18 https://doi.org/10.1103/physrevb.97.184506	journal	May 2018
Lifetime of Majorana qubits in Rashba nanowires with nonuniform chemical potential Aseev, Pavel P.; Klinovaja, Jelena; Loss, Daniel Physical Review B, Vol. 98, Issue 15 https://doi.org/10.1103/physrevb.98.155414	journal	October 2018
Majorana finite-frequency nonequilibrium quantum noise Smirnov, Sergey Physical Review B, Vol. 99, Issue 16 https://doi.org/10.1103/physrevb.99.165427	journal	April 2019
Deterministic Creation and Braiding of Chiral Edge Vortices Beenakker, C. W. J.; Baireuther, P.; Herasymenko, Y. Physical Review Letters, Vol. 122, Issue 14 https://doi.org/10.1103/physrevlett.122.146803	journal	April 2019
Quantum computation by teleportation and symmetry Wang, Dong-Sheng International Journal of Modern Physics B, Vol. 33, Issue 15 https://doi.org/10.1142/s0217979219300044	journal	June 2019
Electrical detection of the Majorana fusion rule for chiral edge vortices in a topological superconductor Beenakker, Carlo; Grabsch, Aurélien; Herasymenko, Yaroslav SciPost Physics, Vol. 6, Issue 2 https://doi.org/10.21468/scipostphys.6.2.022	journal	January 2019
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
Proximity-induced low-energy renormalization in hybrid semiconductor-superconductor Majorana structures Stanescu, Tudor D.; Sarma, Sankar Das arXiv https://doi.org/10.48550/arxiv.1702.03976	text	January 2017
Zero-Energy Modes from Coalescing Andreev States in a Two-Dimensional Semiconductor-Superconductor Hybrid Platform Suominen, Henri J.; Kjaergaard, Morten; Hamilton, Alexander R. arXiv https://doi.org/10.48550/arxiv.1703.03699	text	January 2017
Measurement and control of a Coulomb-blockaded parafermion box Snizhko, Kyrylo; Egger, Reinhold; Gefen, Yuval arXiv https://doi.org/10.48550/arxiv.1704.03241	text	January 2017
Epitaxy of Advanced Nanowire Quantum Devices Gazibegovic, Sasa; Car, Diana; Zhang, Hao arXiv https://doi.org/10.48550/arxiv.1705.01480	text	January 2017
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
Selective Area Grown Semiconductor-Superconductor Hybrids: A Basis for Topological Networks Vaitiekėnas, S.; Whiticar, A. M.; Deng, M. T. arXiv https://doi.org/10.48550/arxiv.1802.04210	text	January 2018
Parity transitions in the superconducting ground state of hybrid InSb-Al Coulomb islands Shen, Jie; Heedt, Sebastian; Borsoi, Francesco arXiv https://doi.org/10.48550/arxiv.1804.08405	text	January 2018
Lifetime of Majorana qubits in Rashba nanowires with non-uniform chemical potential Aseev, Pavel P.; Klinovaja, Jelena; Loss, Daniel arXiv https://doi.org/10.48550/arxiv.1807.07997	text	January 2018
Simulating topological tensor networks with Majorana qubits Wille, C.; Egger, R.; Eisert, J. arXiv https://doi.org/10.48550/arxiv.1808.04529	text	January 2018
Quantum computation by teleportation and symmetry Wang, Dong-Sheng arXiv https://doi.org/10.48550/arxiv.1808.06103	text	January 2018
Radio-frequency methods for Majorana-based quantum devices: fast charge sensing and phase diagram mapping Razmadze, Davydas; Sabonis, Deividas; Malinowski, Filip K. arXiv https://doi.org/10.48550/arxiv.1902.00789	text	January 2019

Figures / Tables (6)

Similar Records

Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

Journal Article · Tue Jul 06 00:00:00 EDT 2021 · Nature Communications · OSTI ID:1424929

Kong, Lingyuan; Cao, Lu; Zhu, Shiyu; +12 more

Universal topological quantum computation with strongly correlated Majorana edge modes

Journal Article · Tue Apr 05 00:00:00 EDT 2022 · New Journal of Physics · OSTI ID:1424929

Zhan, Ye-Min; Chen, Yu-Ge; Chen, Bin; +3 more

Quantum information processing with majorana bound states in superconducting circuits

Patent · Tue Mar 17 00:00:00 EDT 2020 · OSTI ID:1424929

Schrade, Constantin; Fu, Liang

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Majorana fermions
quantum information processing
Nanowires