Abstract
In quantum computation non classical features such as superposition states and entanglement are used to solve problems in new ways, impossible on classical digital computers.We illustrate by Deutsch algorithm how a quantum computer can use superposition states to outperform any classical computer. We comment on the view of a quantum computer as a massive parallel computer and recall Amdahl’s law for a classical parallel computer. We argue that the view on quantum computation as a massive parallel computation disregards the presence of entanglement in a general quantum computation and the non classical way in which parallel results are combined to obtain the final output.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amdahl, G.M.: 1967, Validity of the Single-Processor Approach to Achieving Large-Scale Computing Capabilities. AFIPS Conference Proceedings, Spring Joint Computing Conference (Atlantic City, N.J., Apr. 18–20). Reston, VA: AFIPS Press, 30, 483–485.
Arvind (2001) ArticleTitleQuantum Entanglement and Quantum Computational Algorithms Pramana Jr. of Physics 56 357–365
Arvind and N. Mukunda: 2000, A Two-qubit Algorithm Involving Quantum Entanglement. e-print: quant-ph/0006069.
A. Barenco D. Deutsch A. Ekert R. Jozsa (1995) ArticleTitleConditional Quantum Dynamics and Logic Gates Phys. Rev. Lett 74 4083–4086 Occurrence Handle1:CAS:528:DyaK2MXls1anu7g%3D Occurrence Handle10058408
Bernstein, E. and U. Vazirani: 1993, Quantum Complexity Theory. Proc. 25th ACM Symp. on Theory of Computating, 11-20.
M.J. Bremner C.M. Dawson J.L. Dodd A. Gilchrist A.W. Harrow D. Mortimer M.A. Nielsen T.J. Osborne (2002) ArticleTitleA Practical Scheme for Quantum Computation with Any Two-qubit Entangling Gate Phys. Rev. Lett 89 247902 Occurrence Handle12484981
A.R. Calderbank P.W. Shor (1996) ArticleTitleGood Quantum Error-Correcting Codes Exist Phys. Rev. A 54 IssueID2 1098–1106 Occurrence Handle1:CAS:528:DyaK28XltVeiu7c%3D Occurrence Handle9913578
D. Deutsch (1985) ArticleTitleQuantum Theory, the Church-Turing Principle, and the Universal Quantum Computer Proc. Roy. Soc. London A400 97
D. Deutsch (1986) Three Connections between Everett’s Interpretation and Experiment R. Penrose C.J. Isham (Eds) Quantum Concepts in Space and Time Clarendon Press Oxford 215–225
D. Deutsch R. Jozsa (1992) ArticleTitleRapid Solutions of Problems by Quantum Computation Proc. Roy. Soc. Lond A439 553–558
D. Dieks (1982) ArticleTitleCommunication by EPR Devices Phys. Lett A92 271
D.P. DiVincenzo (1995) ArticleTitleTwo-bit Gates are Universal for Quantum Computation Phys. Rev A51 1015–1022
Dodd, J.L., M.A. Nielsen, M.J. Bremner and R.T. Thew: 2001, Universal Quantum Computation and Simulation Using Any Entangling Hamiltonian and Local Unitaries. e-print: quant-ph/0106064.
R. Feynman (1982) ArticleTitleSimulating Physics with Computers Int. J. Theor. Phys 21 467–488 Occurrence HandleMR658311
R. Feynman (1986) ArticleTitleQuantum Mechanical Computers Found. Phys 16 507
Grover, L.K.: 1996, A Fast Quantum Mechanical Algorithm for Database Search. Proceedings of the 28th Annual ACM Symposium on Computing, 212.
Jozsa, R. and N. Linden: 2002, On the Role of Entanglement in Quantum Computational Speed-up. e-print: quant-ph/0201143.
M.A. Nielsen I.L. Chuang (2000) Quantum Computation and Quantum Information University Press Cambridge
R.L. Rivest A. Shamir L.M. Adleman (1978) ArticleTitleA Method for Obtaining Digital Signatures and Public-Key Cryptosystems Communications of the ACM 21 2 120–126
P.W. Shor (1994) Algorithms for quantum Computation, Discrete Logarithms and Factoring Proc. 35th Annual symposium on Foundations of Computer Science. IEEE Computer Society Press Los Alamitos, CA 124
D. Simon (1994) ArticleTitleOn the Power of Quantum Computation. In FOCS’94,116-123 Journal version available at SIAM J Comp., 1997 26 IssueID5 1474–1483
L.M.K. Vandersypen M. Steffen G. Breyta C.S. Yannoni M.H. Sherwood I.L. Chuang (2001) ArticleTitleExperimental Realization of Shor’s Quantum Factoring Algorithm Using Nuclear Magnetic Resonance Nature 414 883–887 Occurrence Handle1:CAS:528:DC%2BD38XhtlOitg%3D%3D Occurrence Handle11780055
W.K. Wootters W.H. Zurek (1982) ArticleTitleA Single Quantum Cannot be Cloned Nature 299 982–983
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
D’hooghe, B., Pykacz, J. Quantum Mechanics and Computation. Found Sci 9, 387–404 (2004). https://doi.org/10.1007/s10699-005-4827-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10699-005-4827-y