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

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.

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► 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 (beta)

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

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