Lattice Surgery with a Twist: Simplifying Clifford Gates of Surface Codes

Daniel Litinski and Felix von Oppen

Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We present a planar surface-code-based scheme for fault-tolerant quantum computation which eliminates the time overhead of single-qubit Clifford gates, and implements long-range multi-target CNOT gates with a time overhead that scales only logarithmically with the control-target separation. This is done by replacing hardware operations for single-qubit Clifford gates with a classical tracking protocol. Inter-qubit communication is added via a modified lattice surgery protocol that employs twist defects of the surface code. The long-range multi-target CNOT gates facilitate magic state distillation, which renders our scheme fault-tolerant and universal.

► BibTeX data

► References

[1] J. Preskill, Reliable quantum computers, Proc. Roy. Soc. Lond. A 454, 385 (1998).
https:/​/​doi.org/​10.1098/​rspa.1998.0167

[2] A. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303, 2 (2003).
https:/​/​doi.org/​10.1016/​S0003-4916(02)00018-0

[3] B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87, 307 (2015).
https:/​/​doi.org/​10.1103/​RevModPhys.87.307

[4] M. H. Devoret and R. J. Schoelkopf, Superconducting circuits for quantum information: An outlook, Science 339, 1169 (2013).
https:/​/​doi.org/​10.1126/​science.1231930

[5] D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A 57, 120 (1998).
https:/​/​doi.org/​10.1103/​PhysRevA.57.120

[6] R. M. Lutchyn, E. P. A. M. Bakkers, L. P. Kouwenhoven, P. Krogstrup, C. M. Marcus, and Y. Oreg, Realizing Majorana zero modes in superconductor-semiconductor heterostructures, arXiv:1707.04899 (2017).
arXiv:1707.04899

[7] D. Gottesman, Stabilizer codes and quantum error correction, Ph.D. thesis, California Institute of Technology (1997).
arXiv:quant-ph/9705052

[8] S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv:quant-ph/​9811052 (1998).
arXiv:quant-ph/9811052

[9] E. T. Campbell, B. M. Terhal, and C. Vuillot, Roads towards fault-tolerant universal quantum computation, Nature 549, 172 (2017).
https:/​/​doi.org/​10.1038/​nature23460

[10] D. S. Wang, A. G. Fowler, A. M. Stephens, and L. C. L. Hollenberg, Threshold error rates for the toric and planar codes, Quantum Info. Comput. 10, 456 (2010).
http:/​/​dl.acm.org/​citation.cfm?id=2011362.2011368

[11] R. S. Andrist, H. G. Katzgraber, H. Bombin, and M. A. Martin-Delgado, Error tolerance of topological codes with independent bit-flip and measurement errors, Phys. Rev. A 94, 012318 (2016).
https:/​/​doi.org/​10.1103/​PhysRevA.94.012318

[12] H. Bombin and M. A. Martin-Delgado, Topological quantum distillation, Phys. Rev. Lett. 97, 180501 (2006).
https:/​/​doi.org/​10.1103/​PhysRevLett.97.180501

[13] A. J. Landahl, J. T. Anderson, and P. R. Rice, Fault-tolerant quantum computing with color codes, arXiv:1108.5738 (2011).
arXiv:1108.5738

[14] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.86.032324

[15] H. Bombin, Topological order with a twist: Ising anyons from an abelian model, Phys. Rev. Lett. 105, 030403 (2010).
https:/​/​doi.org/​10.1103/​PhysRevLett.105.030403

[16] B. J. Brown, K. Laubscher, M. S. Kesselring, and J. R. Wootton, Poking holes and cutting corners to achieve Clifford gates with the surface code, Phys. Rev. X 7, 021029 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.021029

[17] M. B. Hastings and A. Geller, Reduced space-time and time costs using dislocation codes and arbitrary ancillas, Quantum Info. Comput. 15, 962 (2015).
http:/​/​dl.acm.org/​citation.cfm?id=2871350.2871356

[18] D. Gottesman, The Heisenberg representation of quantum computers, Proc. XXII Int. Coll. Group. Th. Meth. Phys. 1, 32 (1999).
arXiv:quant-ph/9807006

[19] C. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter, Surface code quantum computing by lattice surgery, New J. Phys. 14, 123011 (2012).
https:/​/​doi.org/​10.1088/​1367-2630/​14/​12/​123011

[20] S. Bravyi and A. Kitaev, Universal quantum computation with ideal Clifford gates and noisy ancillas, Phys. Rev. A 71, 022316 (2005).
https:/​/​doi.org/​10.1103/​PhysRevA.71.022316

[21] T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flensberg, S. Plugge, Y. Oreg, C. M. Marcus, and M. H. Freedman, Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes, Phys. Rev. B 95, 235305 (2017).
https:/​/​doi.org/​10.1103/​PhysRevB.95.235305

[22] D. Litinski, M. S. Kesselring, J. Eisert, and F. von Oppen, Combining topological hardware and topological software: Color-code quantum computing with topological superconductor networks, Phys. Rev. X 7, 031048 (2017).
https:/​/​doi.org/​10.1103/​PhysRevX.7.031048

[23] D. Litinski and F. von Oppen, Braiding by Majorana tracking and long-range CNOT gates with color codes, Phys. Rev. B 96, 205413 (2017).
https:/​/​doi.org/​10.1103/​PhysRevB.96.205413

[24] G. Duclos-Cianci and D. Poulin, Fast decoders for topological quantum codes, Phys. Rev. Lett. 104, 050504 (2010).
https:/​/​doi.org/​10.1103/​PhysRevLett.104.050504

[25] E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, Journal of Mathematical Physics 43, 4452 (2002).
https:/​/​doi.org/​10.1063/​1.1499754

[26] T. J. Yoder and I. H. Kim, The surface code with a twist, Quantum 1, 2 (2017).
https:/​/​doi.org/​10.22331/​q-2017-04-25-2

[27] Y. Tomita and K. M. Svore, Low-distance surface codes under realistic quantum noise, Phys. Rev. A 90, 062320 (2014).
https:/​/​doi.org/​10.1103/​PhysRevA.90.062320

Cited by

[1] M. Gutiérrez, M. Müller, and A. Bermúdez, "Transversality and lattice surgery: Exploring realistic routes toward coupled logical qubits with trapped-ion quantum processors", Physical Review A 99 2, 022330 (2019).

[2] Hiroto Mukai, Keiichi Sakata, Simon J Devitt, Rui Wang, Yu Zhou, Yukito Nakajima, and Jaw-Shen Tsai, "Pseudo-2D superconducting quantum computing circuit for the surface code: proposal and preliminary tests", New Journal of Physics 22 4, 043013 (2020).

[3] Markus S. Kesselring, Fernando Pastawski, Jens Eisert, and Benjamin J. Brown, "The boundaries and twist defects of the color code and their applications to topological quantum computation", Quantum 2, 101 (2018).

[4] Christophe Vuillot, Lingling Lao, Ben Criger, Carmen García Almudéver, Koen Bertels, and Barbara M Terhal, "Code deformation and lattice surgery are gauge fixing", New Journal of Physics 21 3, 033028 (2019).

[5] Ali Lavasani and Maissam Barkeshli, "Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes", Physical Review A 98 5, 052319 (2018).

[6] X. Fu, L. Lao, K. Bertels, and C.G. Almudever, "A control microarchitecture for fault-tolerant quantum computing", Microprocessors and Microsystems 70, 21 (2019).

[7] Daniel Litinski, "A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery", Quantum 3, 128 (2019).

[8] Daniel Herr, Alexandru Paler, Simon J Devitt, and Franco Nori, "Lattice surgery on the Raussendorf lattice", Quantum Science and Technology 3 3, 035011 (2018).

[9] Adam Holmes, Yongshan Ding, Ali Javadi-Abhari, Diana Franklin, Margaret Martonosi, and Frederic T. Chong, "Resource optimized quantum architectures for surface code implementations of magic-state distillation", Microprocessors and Microsystems 67, 56 (2019).

[10] Yuval Oreg and Felix von Oppen, "Majorana Zero Modes in Networks of Cooper-Pair Boxes: Topologically Ordered States and Topological Quantum Computation", Annual Review of Condensed Matter Physics 11 1, 397 (2020).

[11] Daniel Litinski, "Magic State Distillation: Not as Costly as You Think", Quantum 3, 205 (2019).

[12] Yongshan Ding, Xin-Chuan Wu, Adam Holmes, Ash Wiseth, Diana Franklin, Margaret Martonosi, and Frederic T. Chong, 2020 ACM/IEEE 47th Annual International Symposium on Computer Architecture (ISCA) 570 (2020) ISBN:978-1-7281-4661-4.

[13] Michael Vasmer and Dan E. Browne, "Three-dimensional surface codes: Transversal gates and fault-tolerant architectures", Physical Review A 100 1, 012312 (2019).

[14] Alexandre Blais, Steven M. Girvin, and William D. Oliver, "Quantum information processing and quantum optics with circuit quantum electrodynamics", Nature Physics 16 3, 247 (2020).

[15] Laura Ortiz Martín, Springer Theses 93 (2019) ISBN:978-3-030-23648-9.

[16] Daniel Litinski and Felix von Oppen, "Quantum computing with Majorana fermion codes", Physical Review B 97 20, 205404 (2018).

[17] L. Ortiz, S. Varona, O. Viyuela, and M. A. Martin-Delgado, "Localization and oscillations of Majorana fermions in a two-dimensional electron gas coupled with d -wave superconductors", Physical Review B 97 6, 064501 (2018).

[18] Austin G. Fowler and Craig Gidney, "Low overhead quantum computation using lattice surgery", arXiv:1808.06709.

[19] Daniel Litinski and Felix von Oppen, "Braiding by Majorana tracking and long-range CNOT gates with color codes", Physical Review B 96 20, 205413 (2017).

[20] J. Pablo Bonilla Ataides, David K. Tuckett, Stephen D. Bartlett, Steven T. Flammia, and Benjamin J. Brown, "The XZZX Surface Code", arXiv:2009.07851.

The above citations are from Crossref's cited-by service (last updated successfully 2020-10-28 07:43:52) and SAO/NASA ADS (last updated successfully 2020-10-28 07:43:53). The list may be incomplete as not all publishers provide suitable and complete citation data.