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Fault-Tolerant Operations for Universal Blind Quantum Computation

Published:03 August 2015Publication History
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Abstract

Blind quantum computation is an appealing use of quantum information technology because it can conceal both the client's data and the algorithm itself from the server. However, problems need to be solved in the practical use of blind quantum computation and fault-tolerance is a major challenge. Broadbent et al. proposed running error correction over blind quantum computation, and Morimae and Fujii proposed using fault-tolerant entangled qubits as the resource for blind quantum computation. Both approaches impose severe demands on the teleportation channel, the former requiring unrealistic data rates and the latter near-perfect fidelity. To extend the application range of blind quantum computation, we suggest that Alice send input qubits encoded with error correction code instead of single input qubits. Two fault-tolerant protocols are presented and we showed the trade-off of the computational overhead using the ten-bit quantum carry-lookahead adder as an example. Though these two fault-tolerant protocols require the client to have more quantum computing ability than using approaches from prior work, they provide better fault-tolerance when the client and the server are connected by realistic quantum repeater networks.

References

  1. Dorit Aharonov, Michael Ben-Or, and Elad Eban. 2008. Interactive proofs for quantum computations. http://arxiv.org/abs/0810.5375.Google ScholarGoogle Scholar
  2. Pablo Arrighi and Louis Salvail. 2006. Blind quantum computation. Int. J. Quantum Info. 4, 5, 883--898. DOI:http://dx.doi.org/10.1142/S0219749906002171Google ScholarGoogle ScholarCross RefCross Ref
  3. Dave Bacon and Wim van Dam. 2010. Recent progress in quantum algorithms. Commun. ACM 53, 2, 84--93. DOI:http://dx.doi.org/10.1145/1646353.1646375 Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Stefanie Barz, Elham Kashefi, Anne Broadbent, Joseph F. Fitzsimons, Anton Zeilinger, and Philip Walther. 2012. Demonstration of blind quantum computing. Science 335, 6066, 303--308. DOI:http://dx.doi.org/10.1126/science.1214707Google ScholarGoogle Scholar
  5. David Beckman, Amalavoyal N. Chari, Srikrishna Devabhaktuni, and John Preskill. 1996. Efficient networks for quantum factoring. Phys. Rev. A 54, 2, 1034--1063. DOI:http://dx.doi.org/10.1103/PhysRevA.54.1034Google ScholarGoogle ScholarCross RefCross Ref
  6. Anne Broadbent, Joseph Fitzsimons, and Elham Kashefi. 2009. Universal blind quantum computation. In Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (FOCS '09). IEEE, 517--526. DOI:http://dx.doi.org/10.1109/FOCS.2009.36 Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Nai-Hui Chia, Chia-Hung Chien, Wei-Ho Chung, and Sy-Yen Kuo. 2012. Quantum blind computation with teleportation-based computation. In Proceedings of the 9th International Conference on Information Technology: New Generations (ITNG'12). IEEE, 769--774. DOI:http://dx.doi.org/10.1109/ITNG.2012.149 Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Andrew M. Childs. 2005. Secure assisted quantum computation. Quantum Info. Computation 5, 6, 456--466. http://dl.acm.org/citation.cfm?id=2011674 Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Vincent Danos and Elham Kashefi. 2006. Determinism in the one-way model. Phys. Rev. A 74, 5, Article 052310. DOI:http://dx.doi.org/10.1103/PhysRevA.74.052310Google ScholarGoogle ScholarCross RefCross Ref
  10. Simon J. Devitt, Kae Nemoto, and William J. Munro. 2011. Quantum error correction for beginners. http://arxiv.org/abs/0905.2794.Google ScholarGoogle Scholar
  11. Thomas G. Draper, Samuel A. Kutin, Eric M. Rains, and Krysta M. Svore. 2006. A logarithmic-depth quantum carry-lookahead adder. Quantum Info. Computation 6, 4, 351--369. http://dl.acm.org/citation.cfm?id=2012090. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Vedran Dunjko, Elham Kashefi, and Anthony Leverrier. 2012. Blind quantum computing with weak coherent pulses. Phys. Rev. Lett. 108, 20, Article 200502. DOI:http://dx.doi.org/10.1103/PhysRevLett.108.200502Google ScholarGoogle ScholarCross RefCross Ref
  13. W. Dür, H.-J. Briegel, J. I. Cirac, and P. Zoller. 1999. Quantum repeaters based on entanglement purification. Phys. Rev. A 59, 169--181. DOI:http://dx.doi.org/10.1103/PhysRevA.59.169Google ScholarGoogle ScholarCross RefCross Ref
  14. Craig Gentry. 2009a. A fully homomorphic encryption scheme. Ph.D. Dissertation Stanford University. crypto.stanford.edu/craig. Google ScholarGoogle Scholar
  15. Craig Gentry. 2009b. Fully homomorphic encryption using ideal lattices. In Proceedings of the 41st Annual ACM Symposium on Theory of Computing (STOC'09). ACM, 169--178. DOI:http://dx.doi.org/10.1145/1536414.1536440 Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Nicolas Gisin and Rob Thew. 2007. Quantum communication. Nature Photonics 1, 165--171. DOI:http://dx.doi.org/10.1038/nphoton.2007.22Google ScholarGoogle ScholarCross RefCross Ref
  17. Daniel Gottesman. 1997. Stabilizer codes and quantum error correction. Ph.D. Dissertation, California Institute of Technology. http://arxiv.org/abs/1302.3428.Google ScholarGoogle Scholar
  18. Daniel Gottesman. 2009. An introduction to quantum error correction and fault-tolerant quantum computation. http://arxiv.org/abs/0904.2557Google ScholarGoogle Scholar
  19. N. Cody Jones, Rodney Van Meter, Austin G. Fowler, Peter L. McMahon, Jungsang Kim, Thaddeus D. Ladd, and Yoshihisa Yamamoto. 2012a. Layered architecture for quantum computing. Phys. Rev. X 2, Article 8. DOI:http://dx.doi.org/10.1103/PhysRevX.2.031007Google ScholarGoogle Scholar
  20. N. Cody Jones, James D. Whitfield, Peter L. McMahon, Man-Hong Yung, Rodney Van Meter, Alan Aspuru-Guzik, and Yoshihisa Yamamoto. 2012b. Faster quantum chemistry simulation on fault-tolerant quantum computers. New J. Phys. 14, Article 115023. DOI:http://dx.doi.org/10.1088/1367-2630/14/11/115023Google ScholarGoogle Scholar
  21. Ivan Kassal, James D. Whitfield, Alejandro Perdomo-Ortiz, Man-Hong Yung, and Alan Aspuru-Guzik. 2011. Simulating chemistry using quantum computers. Annu. Rev. Phys. Chem. 62, 185--207. DOI:http://dx.doi.org/10.1146/annurev-physchem-032210-103512Google ScholarGoogle ScholarCross RefCross Ref
  22. H. J. Kimble. 2008. The quantum internet. Nature Photonics 453, 1023--1030. DOI:http://dx.doi.org/10.1038/nature07127Google ScholarGoogle ScholarCross RefCross Ref
  23. T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. OBrien. 2010. Quantum computers. Nature 464, 45--53. DOI:http://dx.doi.org/10.1038/nature08812Google ScholarGoogle ScholarCross RefCross Ref
  24. Tomoyuki Morimae and Keisuke Fujii. 2012. Blind topological measurement-based quantum computation. Nature Commun. 3, Article 1036. DOI:http://dx.doi.org/10.1038/ncomms2043Google ScholarGoogle Scholar
  25. Michele Mosca. 2008. Quantum algorithms. http://arxiv.org/abs/0808.0369Google ScholarGoogle Scholar
  26. Michael A. Nielsen and Isaac L. Chuang. 2010. Quantum Computation and Quantum Information (10th anniversary Ed.). Cambridge University Press, Cambridge, UK.Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Robert Raussendorf and Hans J. Briegel. 2001. A one-way quantum computer. Phys. Rev. Lett. 86, 22, 5188--5191. DOI:http://dx.doi.org/10.1103/PhysRevLett.86.5188Google ScholarGoogle ScholarCross RefCross Ref
  28. Robert Raussendorf, Daniel E. Browne, and Hans J. Briegel. 2003. Measurement-based quantum computation on cluster states. Phys. Rev. A 68, 2, Article 022312. DOI:http://dx.doi.org/10.1103/PhysRevA.68.022312Google ScholarGoogle ScholarCross RefCross Ref
  29. Robert Raussendorf and Jim Harrington. 2007. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, Article 190504 (May 2007), 4 pages. DOI:http://dx.doi.org/10.1103/PhysRevLett.98.190504Google ScholarGoogle Scholar
  30. Robert Raussendorf, Jim Harrington, and Kovid Goyal. 2007. Topological fault-tolerance in cluster state quantum computation. New J. Phys. 9, Article 199. DOI:http://dx.doi.org/10.1088/1367-2630/9/6/199Google ScholarGoogle Scholar
  31. Vivek V. Shende and Igor L. Markov. 2009. On the CNOT-cost of TOFFOLI gates. Quantum Inf. Computation 9, 5, 461--486. http://dl.acm.org/citation.cfm?id=2011799 Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Peter W. Shor. 1997. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 5, 1484--1509. DOI:http://dx.doi.org/10.1137/S0097539795293172 Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Andrew M. Steane. 1996. Multiple-particle interference and quantum error correction. Proc. R. Soc. London, Ser. A 452, 1954, 2551--2577. DOI:http://dx.doi.org/10.1098/rspa.1996.0136Google ScholarGoogle Scholar
  34. Takahiro Sueki, Takeshi Koshiba, and Tomoyuki Morimae. 2013. Ancilla-driven universal blind quantum computation. Phys. Rev. A 87, 6, Article 060301. DOI:http://dx.doi.org/10.1103/PhysRevA.87.060301Google ScholarGoogle ScholarCross RefCross Ref
  35. Barbara M. Terhal. 2013. Quantum error correction for quantum memories. http://arxiv.org/abs/1302.3428Google ScholarGoogle Scholar
  36. Rodney Van Meter. 2012. Quantum networking and internetworking. IEEE Network 26, 4, 59--64. DOI:http://dx.doi.org/10.1109/MNET.2012.6246754Google ScholarGoogle ScholarCross RefCross Ref
  37. Rodney Van Meter and Kohei M. Itoh. 2005. Fast quantum modular exponentiation. Phys. Rev. A 71, 5, 052320.Google ScholarGoogle Scholar
  38. Rodney Van Meter, Thaddeus D. Ladd, Austin G. Fowler, and Yoshihisa Yamamoto. 2010. Distributed quantum computation architecture using semiconductor nanophotonics. Int. J. Quantum Info. 8, 295--323. DOI:http://dx.doi.org/10.1142/S0219749910006435Google ScholarGoogle ScholarCross RefCross Ref
  39. Rodney Van Meter and Joe Touch. 2013. Designing Quantum Repeater Networks. IEEE Commun. 64--71.Google ScholarGoogle Scholar
  40. Vlatko Vedral, Adriano Barenco, and Artur Ekert. 1996. Quantum networks for elementary arithmetic operations. Phys. Rev. A 54, 1, 147--153. DOI:http://dx.doi.org/10.1103/PhysRevA.54.147Google ScholarGoogle ScholarCross RefCross Ref

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        cover image ACM Journal on Emerging Technologies in Computing Systems
        ACM Journal on Emerging Technologies in Computing Systems  Volume 12, Issue 1
        July 2015
        210 pages
        ISSN:1550-4832
        EISSN:1550-4840
        DOI:10.1145/2810396
        Issue’s Table of Contents

        Copyright © 2015 ACM

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        Publication History

        • Published: 3 August 2015
        • Accepted: 1 October 2014
        • Revised: 1 January 2014
        • Received: 1 June 2013
        Published in jetc Volume 12, Issue 1

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