Abstract
We present a scalable quantum algorithm to solve binary consensus in a system of n crash-prone quantum processes. The algorithm works in \({\mathcal O}(\text{polylog }n)\) time sending \({\mathcal O}(n \text{ polylog } n)\) qubits against the adaptive adversary. The time performance of this algorithm is asymptotically better than a lower bound \(\Omega(\sqrt{n/\log n})\) on time of classical randomized algorithms against adaptive adversaries. Known classical randomized algorithms having each process send \({\mathcal O}(\text{polylog } n)\) messages work only for oblivious adversaries. Our quantum algorithm has a better time performance than deterministic solutions, which have to work in Ω(t) time for t < n failures.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aharonov, D., Ben-Or, M.: Fault-tolerant quantum computation with constant error rate. SIAM Journal on Computing 38(4), 1207–1282 (2008)
Bar-Joseph, Z., Ben-Or, M.: A tight lower bound for randomized synchronous consensus. In: Proceedings of the 17th ACM Symposium on Principles of Distributed Computing (PODC), pp. 193–199 (1998)
Ben-Or, M., Hassidim, A.: Fast quantum Byzantine agreement. In: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC), pp. 481–485 (2005)
Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Physical Review Letters 69(20), 2881–2884 (1992)
Broadbent, A., Tapp, A.: Can quantum mechanics help distributed computing? SIGACT News 39(3), 67–76 (2008)
Buhrman, H., Röhrig, H.: Distributed quantum computing. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 1–20. Springer, Heidelberg (2003)
Chlebus, B.S., Kowalski, D.R.: Time and communication efficient consensus for crash failures. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 314–328. Springer, Heidelberg (2006)
Chlebus, B.S., Kowalski, D.R.: Locally scalable randomized consensus for synchronous crash failures. In: Proceedings of the 21st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 290–299 (2009)
Chlebus, B.S., Kowalski, D.R., Strojnowski, M.: Fast scalable deterministic consensus for crash failures. In: Proceedings of the 28th ACM Symposium on Principles of Distributed Computing (PODC), pp. 111–120 (2009)
Chor, B., Merritt, M., Shmoys, D.B.: Simple constant-time consensus protocols in realistic failure models. Journal of the ACM 36(3), 591–614 (1989)
Cleve, R., Buhrman, H.: Substituting quantum entanglement for communication. Physical Review A 56(2), 1201–1204 (1997)
Cleve, R., van Dam, W., Nielsen, M., Tapp, A.: Quantum entanglement and the communication complexity of the inner product function. In: Williams, C.P. (ed.) QCQC 1998. LNCS, vol. 1509, pp. 61–74. Springer, Heidelberg (1999)
de Wolf, R.: Quantum communication and complexity. Theoretical Computer Science 287(1), 337–353 (2002)
Denchev, V.S., Pandurangan, G.: Distributed quantum computing: a new frontier in distributed systems or science fiction? SIGACT News 39(3), 77–95 (2008)
Dolev, D., Reischuk, R.: Bounds on information exchange for Byzantine agreement. Journal of the ACM 32(1), 191–204 (1985)
Gavoille, C., Kosowski, A., Markiewicz, M.: What can be observed locally? Round-based models for quantum distributed computing. In: Keidar, I. (ed.) DISC 2009. LNCS, vol. 5805, pp. 243–257. Springer, Heidelberg (2009)
Gilbert, S., Kowalski, D.R.: Distributed agreement with optimal communication complexity. In: Proceedings of the 21st ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 965–977 (2010)
Hadzilacos, V., Halpern, J.Y.: Message-optimal protocols for Byzantine agreement. Mathematical Systems Theory 26(1), 41–102 (1993)
Holevo, A.S.: Bounds for the quantity of information transmitted by a quantum communication channel. Problems of Information Transmission 9(3), 177–183 (1973)
Holtby, D., Kapron, B.M., King, V.: Lower bound for scalable Byzantine agreement. Distributed Computing 21(4), 239–248 (2008)
King, V., Saia, J.: From almost everywhere to everywhere: Byzantine agreement with \(\tilde{O}(n^{3/2})\) bits. In: Keidar, I. (ed.) DISC 2009. LNCS, vol. 5805, pp. 464–478. Springer, Heidelberg (2009)
King, V., Saia, J., Sanwalani, V., Vee, E.: Towards secure and scalable computation in peer-to-peer networks. In: Proceedings of the 47th IEEE Symposium on Foundations of Computer Science (FOCS), pp. 87–98 (2006)
Kobayashi, H., Matsumoto, K., Tani, S.: Fast exact quantum leader election on anonymous rings. In: Proceedings of the 8th Asian Conference on Quantum Information Science (AQIS), pp. 157–158 (2008)
Linial, N.: Distributive graph algorithms - global solutions from local data. In: Proceedings of the 28th Symposium on Foundations of Computer Science (FOCS), pp. 331–335 (1987)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Ta-Shma, A.: Classical versus quantum communication complexity. SIGACT News 30(3), 25–34 (1999)
Ta-Shma, A., Umans, C., Zuckerman, D.: Lossless condensers, unbalanced expanders, and extractors. Combinatorica 27(2), 213–240 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chlebus, B.S., Kowalski, D.R., Strojnowski, M. (2010). Scalable Quantum Consensus for Crash Failures. In: Lynch, N.A., Shvartsman, A.A. (eds) Distributed Computing. DISC 2010. Lecture Notes in Computer Science, vol 6343. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15763-9_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-15763-9_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15762-2
Online ISBN: 978-3-642-15763-9
eBook Packages: Computer ScienceComputer Science (R0)