Scalable fermionic error correction in Majorana surface codes

Viyuela, Oscar; Vijay, Sagar; Fu, Liang

doi:10.1103/physrevb.99.205114

Title: Scalable fermionic error correction in Majorana surface codes

Journal Article · Fri May 10 00:00:00 EDT 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.99.205114· OSTI ID:1611438

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

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

We study the error correcting properties of Majorana surface codes (MSCs), topological quantum codes constructed out of interacting Majorana fermions, which can be used to store quantum information and perform quantum computation. Furthermore, these quantum memories suffer from purely “fermionic” errors, such as quasiparticle poisoning (QP), that have no analog in conventional platforms with bosonic qubits. In physical realizations where QP dominates, we show that errors can be corrected provided that the poisoning rate is below a threshold of ~11%. When QP is highly suppressed and fermionic bilinear (“bosonic”) errors become dominant, we find an error threshold of ~16%, which is much higher than the threshold for spin-based topological memories like the surface code or the color code. In addition, we derive lattice gauge theories to account for measurement errors. These results, together with the inherent error suppression provided by the superconducting gap in physical realizations of the MSCs, makes this a strong candidate for a robust topological quantum memory.

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

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

Grant/Contract Number:: SC0010526; SC0019275

OSTI ID:: 1611438

Alternate ID(s):: OSTI ID: 1511884

Journal Information:: Physical Review. B, Vol. 99, Issue 20; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 6 works

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References (61)

Statistical mechanical models and topological color codes Bombin, H.; Martin-Delgado, M. A. Physical Review A, Vol. 77, Issue 4 https://doi.org/10.1103/PhysRevA.77.042322	journal	April 2008
Quantum computing with Majorana fermion codes Litinski, Daniel; von Oppen, Felix Physical Review B, Vol. 97, Issue 20 https://doi.org/10.1103/PhysRevB.97.205404	journal	May 2018
Tricolored lattice gauge theory with randomness: fault tolerance in topological color codes Andrist, Ruben S.; Katzgraber, Helmut G.; Bombin, H. New Journal of Physics, Vol. 13, Issue 8 https://doi.org/10.1088/1367-2630/13/8/083006	journal	August 2011
Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures Lutchyn, Roman M.; Sau, Jay D.; Das Sarma, S. Physical Review Letters, Vol. 105, Issue 7 https://doi.org/10.1103/PhysRevLett.105.077001	journal	August 2010
Topological quantum memory Dennis, Eric; Kitaev, Alexei; Landahl, Andrew Journal of Mathematical Physics, Vol. 43, Issue 9 https://doi.org/10.1063/1.1499754	journal	September 2002
Error tolerance of topological codes with independent bit-flip and measurement errors Andrist, Ruben S.; Katzgraber, Helmut G.; Bombin, H. Physical Review A, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevA.94.012318	journal	July 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
Reliable quantum computers Preskill, John Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 454, Issue 1969 https://doi.org/10.1098/rspa.1998.0167	journal	January 1998
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
Class of quantum error-correcting codes saturating the quantum Hamming bound Gottesman, Daniel Physical Review A, Vol. 54, Issue 3 https://doi.org/10.1103/PhysRevA.54.1862	journal	September 1996
Superconducting quantum circuits at the surface code threshold for fault tolerance Barends, R.; Kelly, J.; Megrant, A. Nature, Vol. 508, Issue 7497 https://doi.org/10.1038/nature13171	journal	April 2014
Helical Liquids and Majorana Bound States in Quantum Wires Oreg, Yuval; Refael, Gil; von Oppen, Felix Physical Review Letters, Vol. 105, Issue 17 https://doi.org/10.1103/PhysRevLett.105.177002	journal	October 2010
Majorana fermion codes Bravyi, Sergey; Terhal, Barbara M.; Leemhuis, Bernhard New Journal of Physics, Vol. 12, Issue 8 https://doi.org/10.1088/1367-2630/12/8/083039	journal	August 2010
Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor Nadj-Perge, S.; Drozdov, I. K.; Bernevig, B. A. Physical Review B, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevB.88.020407	journal	July 2013
Topological Quantum Distillation Bombin, H.; Martin-Delgado, M. A. Physical Review Letters, Vol. 97, Issue 18 https://doi.org/10.1103/PhysRevLett.97.180501	journal	October 2006
Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems Li, Ying Physical Review Letters, Vol. 117, Issue 12 https://doi.org/10.1103/PhysRevLett.117.120403	journal	September 2016
End States and Subgap Structure in Proximity-Coupled Chains of Magnetic Adatoms Ruby, Michael; Pientka, Falko; Peng, Yang Physical Review Letters, Vol. 115, Issue 19 https://doi.org/10.1103/PhysRevLett.115.197204	journal	November 2015
Simulating topological tensor networks with Majorana qubits Wille, C.; Egger, R.; Eisert, J. Physical Review B, Vol. 99, Issue 11 https://doi.org/10.1103/PhysRevB.99.115117	journal	March 2019
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
Probing atomic structure and Majorana wavefunctions in mono-atomic Fe chains on superconducting Pb surface Pawlak, Rémy; Kisiel, Marcin; Klinovaja, Jelena npj Quantum Information, Vol. 2, Issue 1 https://doi.org/10.1038/npjqi.2016.35	journal	November 2016
Error Threshold for Color Codes and Random Three-Body Ising Models Katzgraber, Helmut G.; Bombin, H.; Martin-Delgado, M. A. Physical Review Letters, Vol. 103, Issue 9 https://doi.org/10.1103/PhysRevLett.103.090501	journal	August 2009
Majorana bound state in a coupled quantum-dot hybrid-nanowire system Deng, M. T.; Vaitiekėnas, S.; Hansen, E. B. Science, Vol. 354, Issue 6319 https://doi.org/10.1126/science.aaf3961	journal	December 2016
Topological superconducting phase in helical Shiba chains Pientka, Falko; Glazman, Leonid I.; von Oppen, Felix Physical Review B, Vol. 88, Issue 15 https://doi.org/10.1103/PhysRevB.88.155420	journal	October 2013
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
Combining Topological Hardware and Topological Software: Color-Code Quantum Computing with Topological Superconductor Networks Litinski, Daniel; Kesselring, Markus S.; Eisert, Jens Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevX.7.031048	journal	September 2017
Magnetic-field-dependent quasiparticle dynamics of nanowire single-Cooper-pair transistors van Veen, Jasper; Proutski, Alex; Karzig, Torsten Physical Review B, Vol. 98, Issue 17 https://doi.org/10.1103/PhysRevB.98.174502	journal	November 2018
Topological Computation without Braiding Bombin, H.; Martin-Delgado, M. A. Physical Review Letters, Vol. 98, Issue 16 https://doi.org/10.1103/PhysRevLett.98.160502	journal	April 2007
Majorana qubit decoherence by quasiparticle poisoning Rainis, Diego; Loss, Daniel Physical Review B, Vol. 85, Issue 17 https://doi.org/10.1103/PhysRevB.85.174533	journal	May 2012
Fault-tolerant fermionic quantum computation based on color code Li, Ying Physical Review A, Vol. 98, Issue 1 https://doi.org/10.1103/PhysRevA.98.012336	journal	July 2018
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
Internal Energy, Specific Heat and Correlation Function of the Bond-Random Ising Model Nishimori, H. Progress of Theoretical Physics, Vol. 66, Issue 4 https://doi.org/10.1143/PTP.66.1169	journal	October 1981
Family of non-Abelian Kitaev models on a lattice: Topological condensation and confinement Bombin, H.; Martin-Delgado, M. A. Physical Review B, Vol. 78, Issue 11 https://doi.org/10.1103/PhysRevB.78.115421	journal	September 2008
Good quantum error-correcting codes exist Calderbank, A. R.; Shor, Peter W. Physical Review A, Vol. 54, Issue 2 https://doi.org/10.1103/PhysRevA.54.1098	journal	August 1996
Strong Resilience of Topological Codes to Depolarization Bombin, H.; Andrist, Ruben S.; Ohzeki, Masayuki Physical Review X, Vol. 2, Issue 2 https://doi.org/10.1103/PhysRevX.2.021004	journal	April 2012
Demonstration of a quantum error detection code using a square lattice of four superconducting qubits Córcoles, A. D.; Magesan, Easwar; Srinivasan, Srikanth J. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms7979	journal	April 2015
Quantum Phase Transitions of the Majorana Toric Code in the Presence of Finite Cooper-Pair Tunneling Roy, Ananda; Terhal, Barbara M.; Hassler, Fabian Physical Review Letters, Vol. 119, Issue 18 https://doi.org/10.1103/PhysRevLett.119.180508	journal	November 2017
Fermionic measurement-based quantum computation Chiu, Yu-Ju; Chen, Xie; Chuang, Isaac L. Physical Review A, Vol. 87, Issue 1 https://doi.org/10.1103/PhysRevA.87.012305	journal	January 2013
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
Phase structure of the random-plaquette gauge model: accuracy threshold for a toric quantum memory Ohno, Takuya; Arakawa, Gaku; Ichinose, Ikuo Nuclear Physics B, Vol. 697, Issue 3 https://doi.org/10.1016/j.nuclphysb.2004.07.003	journal	October 2004
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
Quantum computations: algorithms and error correction Kitaev, A. Yu Russian Mathematical Surveys, Vol. 52, Issue 6 https://doi.org/10.1070/RM1997v052n06ABEH002155	journal	December 1997
Topological Superconductivity and Majorana Fermions in RKKY Systems Klinovaja, Jelena; Stano, Peter; Yazdani, Ali Physical Review Letters, Vol. 111, Issue 18 https://doi.org/10.1103/PhysRevLett.111.186805	journal	November 2013
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
Quantum error correction for quantum memories Terhal, Barbara M. Reviews of Modern Physics, Vol. 87, Issue 2 https://doi.org/10.1103/RevModPhys.87.307	journal	April 2015
Non-Abelian anyons and topological quantum computation Nayak, Chetan; Simon, Steven H.; Stern, Ady Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.1083	journal	September 2008
Multicritical point of Ising spin glasses on triangular and honeycomb lattices de Queiroz, S. L. A. Physical Review B, Vol. 73, Issue 6 https://doi.org/10.1103/PhysRevB.73.064410	journal	February 2006
Fault-tolerant quantum computation by anyons Kitaev, A. Yu. Annals of Physics, Vol. 303, Issue 1 https://doi.org/10.1016/S0003-4916(02)00018-0	journal	January 2003
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
Transport Signatures of Quasiparticle Poisoning in a Majorana Island Albrecht, S. M.; Hansen, E. B.; Higginbotham, A. P. Physical Review Letters, Vol. 118, Issue 13 https://doi.org/10.1103/PhysRevLett.118.137701	journal	March 2017
Surface code quantum computing with error rates over 1% Wang, David S.; Fowler, Austin G.; Hollenberg, Lloyd C. L. Physical Review A, Vol. 83, Issue 2 https://doi.org/10.1103/PhysRevA.83.020302	journal	February 2011
Quantum computations on a topologically encoded qubit Nigg, D.; Muller, M.; Martinez, E. A. Science, Vol. 345, Issue 6194 https://doi.org/10.1126/science.1253742	journal	June 2014
The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles Rokhinson, Leonid P.; Liu, Xinyu; Furdyna, Jacek K. Nature Physics, Vol. 8, Issue 11 https://doi.org/10.1038/nphys2429	journal	September 2012
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
Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction Fu, Liang; Kane, C. L. Physical Review B, Vol. 79, Issue 16 https://doi.org/10.1103/PhysRevB.79.161408	journal	April 2009
Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions Das, Anindya; Ronen, Yuval; Most, Yonatan Nature Physics, Vol. 8, Issue 12 https://doi.org/10.1038/nphys2479	journal	November 2012
Effects of spin-dependent quasiparticle renormalization in Fe, Co, and Ni photoemission spectra:An experimental and theoretical study Sánchez-Barriga, J.; Braun, J.; Minár, J. Physical Review B, Vol. 85, Issue 20 https://doi.org/10.1103/PhysRevB.85.205109	journal	May 2012
Exact topological quantum order in $D = 3$ and beyond: Branyons and brane-net condensates Bombin, H.; Martin-Delgado, M. A. Physical Review B, Vol. 75, Issue 7 https://doi.org/10.1103/PhysRevB.75.075103	journal	February 2007
Interplay between Classical Magnetic Moments and Superconductivity in Quantum One-Dimensional Conductors: Toward a Self-Sustained Topological Majorana Phase Braunecker, Bernd; Simon, Pascal Physical Review Letters, Vol. 111, Issue 14 https://doi.org/10.1103/PhysRevLett.111.147202	journal	October 2013
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
Exact results and critical properties of the Ising model with competing interactions Nishimori, H. Journal of Physics C: Solid State Physics, Vol. 13, Issue 21 https://doi.org/10.1088/0022-3719/13/21/012	journal	July 1980
Superconductor-nanowire devices from tunneling to the multichannel regime: Zero-bias oscillations and magnetoconductance crossover Churchill, H. O. H.; Fatemi, V.; Grove-Rasmussen, K. Physical Review B, Vol. 87, Issue 24 https://doi.org/10.1103/PhysRevB.87.241401	journal	June 2013

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