Construction method of quantum fault-tolerant encoded gates of stabilizer code based on teleportation

Yan-yan WANG; Ying LIU; Sheng-mei ZHAO

doi:10.3969/j.issn.1007-5461. 2013.06.017

[1] Deutsch D. Quantum computational networks ［C］. Proceedings of the Royal Society A, 1989, 425: 73-90.

[2] Shor P W. Fault-tolerant quantum computation ［C］. Proceedings of the 37th Symposium on Fundamentals of Computer Science, Los Alamitos, 1996, 56-65.

[3] Preskill J. Reliable quantum computers ［C］. Proceedings of the Royal Society A, 1998, 454: 385-410.

[4] Knill E. Quantum computing with very noisy devices ［J］. Nature, 2004, 434: 39-44.

[5] Gottesman D. An introduction to quantum error correction and fault-tolerant quantum computation ［C］. Proceedings of Symposia in Applied Mathematics, 2010, 68: 24-70.

[6] Li Y, Barrett S D, Stace T M, et al. Fault-tolerant quantum computation with nondeterministic gates ［J］. Phys. Rev. Lett., 2010, 105: 250502.

[7] Fujii K, et al. Fault-tolerant topological one-way quantum computation with probabilistic two-qubit gates ［J］. Phys. Rev. Lett., 2010, 105: 250503.

[8] Chow J M, Gambetta J M, Corcoles A D, et al. Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits ［J］. Phys. Rev. Lett., 2012, 109: 060501.

[10] Li Chengzu, Chen Pingxing, et al. Research on Quantum Computer (Rudin)-Correcting and Fault-Tolerant Computation ［M］. Beijing: Science Press, 2011: 467-471.

[13] Bravyi S, Kitaev A. Universal quantum computation with ideal Clifford gates and noisy ancillas ［J］. Phys. Rev. A, 2005, 71: 022316.

[14] Eastin B, Knill E. Restriction on transversal encoded quantum gate sets ［J］. Phys. Rev. Lett., 2009, 102: 110502.

[15] Zeng B, Cross A, Chuang I L. Transversality versus universality for additive quantum codes ［J］. IEEE Trans. Inform. Theory, 2011, 57: 6272-6284.

[16] Gottesman D. A theory of fault-tolerant quantum computation ［J］. Physical Review A, 1998, 57: 127-137.

[18] Gottesman D, Chuang I L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations ［J］. Nature, 1999, 402: 390-393.

[19] Gottesman D, Chuang I L. Quantum teleportation is a universal computational primitive ［J］. Phys. Rev. Lett., 1999, 101: 240501.

[20] Zhou X L, Debbie W L, Chuang I L. Methodology for quantum logic gate construction ［J］. Phys. Rev. A, 2000, 62: 052316.

[21] Stean A M, Ibinson B. Fault-tolerant logical gate networks for CSS codes ［J］. Phys. Rev. A, 2005, 62: 052316.

[22] Goebel A, Wagenknecht C, Zhang Q, et al. Teleportation-based controlled-not gate for fault-tolerant quantum computation ［OL］. 2010, http://arxiv.org/abs/0809.3583.

[23] Steane A M. Overhead and noise threshold of fault-tolerant quantum error correction ［J］. Phys. Rev. A, 2003, 68: 042322.

[24] Paetznick A, Reichardt B W. Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code ［OL］. 2011, http://arxiv.org/abs/1106.2190v1.