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

[3] 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).

[4] 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).

[5] 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).

[6] 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).

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

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

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

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

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

[12] 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).

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

[14] 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).

The above citations are from Crossref's cited-by service (last updated 2019-07-15 10:09:42) and SAO/NASA ADS (last updated 2019-07-15 10:09:43). The list may be incomplete as not all publishers provide suitable and complete citation data.