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

Abstract

Abstract: Quantum fault-tolerant encoded gates could reduce the inevitable coupling of the physical qubits to the noisy environment, and it has been one of the hot topics in quantum communication and quantum computation. In this paper, we propose a novel constructing quantum fault-tolerant encoded gates method based on teleportation for the general stabilizer code. We first make use of the quantum teleportation to get the teleported code and apply the imaginary encoded gate to the teleported code, then move it forward, so the difficulty to construct encoded gate could be reduced to prepare a special ancillary state. We select the encoded Hadamard gate and phase gate as examples to explain the constructing procedure, and the numerical analysis verify that the method is valid. The results show that under the teleportation method, encoded gate decreases 60*n physical quantum gates, 5 encoded block and 5 ancilla block ; encoded gate decreases 16*n physical quantum gates, 1 encoded block and 2 ancilla block when compared with the overhead in [16].

Key words: quantum physics, fault-tolerant encoded gate, stabilizer code, teleportation, overhead

CLC Number:

O413.1

WANG Yan-yan, LIU Ying, ZHAO Sheng-mei. Construction method of quantum fault-tolerant encoded gates of the stabilizer code based on teleportation[J]. J4, 2013, 30(6): 752-758.

References

[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, Tokunaga Y. 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. [9] 苏晓琴，郭光灿. 量子通信和量子计算[J]. 量子电子学报, 2004, 21(6): 06-13 Su xiaoqin, Guo guangcan. Quantum communications and quantum computation [J]. Chinese Journal of Quantum Electronics (量子电子学报), 2004, 21(6): 06-13 (in Chinese) [10] Li Chengzu, Chen Pingxing, et al. Research on quantum computer (Rudin)-correcting and fault-tolerant computation[M]. Beijing: Science Press, 2011, 467-471. [11] 吕洪君,吴天昊,彭斐，解光军. 综合法研究量子可逆逻辑电路[J].量子电子学报,2010, 27(2): 174-179 Lv Hongjun, Wu Tianhao, Peng Fei,Xie Guangjun. Research on the quantum reversible logic circuits with compound method [J]. Chinese Journal of Quantum Electronics (量子电子学报), 2010, 27(2): 174-179(in Chinese) [12] 吕洪君,郭俊旺,彭斐,吴天昊,解光军. 用基本两位量子逻辑门实现N位量子逻辑门的研究[J].量子电子学报, 2010, 27(1): 26-30 Lv Hongjun, Guo Junwang, Peng Fei, Wu Tianhao,Xie Guangjun. n-bit quantum gate accomplished by two-bit quantum gates[J]. Chinese Journal of Quantum Electronics (量子电子学报), 2010, 27(1): 26-30(in Chinese). [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. [17] 査新未. 四粒子任意态的概率隐形传态的两种方案[J]. 量子电子学报, 2008,25(2),186-190 Zha xin-wei.Two schemes of teleporting an arbitrary four-particle entangled state[J].Chinese Journal of Quantum Electronics（量子电子学报）.2008,25(2),186-190(in chinese). [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.