Schemes for parallel quantum computation without local control of qubits

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 2, 2000, Pages 203011-203014

  Benjamin, S C ^a  

^a NONE

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EID: 0345991534     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. A.M. Steane, Rep. Prog. Phys. 61, 117 (1998).
2. A result due to P. Shor; for an analysis see, e.g., A. Ekert and R. Joza, Rev. Mod. Phys. 68, 733 (1996).
3. L. Grover, Phys. Rev. Lett. 79, 325 (1997).
4. S. C. Benjamin and N. F. Johnson, Phys. Rev. A 60, 4334 (1999).
5. J.A. Jones, and M. Mosca, J. Chem. Phys. 109, 1648 (1998).
6. A.M. Steane, Appl. Phys. B: Lasers Opt. 64, 623 (1997).
7. B.E. Kane, Nature (London) 393, 133 (1998).
8. R. Vrijen et al., e-print quant-ph/9905096.
9. S. Lloyd, Science 261, 1569 (1993).
10. Seth Lloyd (unpublished).
11. Using two alternating types guarantees that while a cell is physically subjected to an update rule, its neighbors, on whom the rule is defined, are static.
12. D. Aharonov and M. Ben-Or, in Proceedings of the 29th ACM Symposium on the Theory of Computation (ACM Press, New York, 1997).
13. For additional figures, including a compact form of the useful Control-Control-U gate, please see web page www.qubit.org/ research/Nano/1DCA/Figs.html
14. S. C. Benjamin (unpublished).
15. This computation may be entirely classical. A suitable universal classical gate can be obtained from the CCU of Ref. [13] by choosing U to be a simple inversion (i.e., a NOT).
16. There must be patterns of CUs that cannot be produced using a sequence of less than O(N) updates, given that the number of distinct updates is limited. Otherwise, we would have a means of compressing N arbitrary bits, corresponding to the N enabled/disabled CUs, into less than O(N) symbols. The author thanks W. van Dam for this observation.
17. For an introduction to the art of addressing multiplets through shaped pulses, composite pulses, etc., see, e.g., R. Freeman, Spin Choreography (Spektrum, Oxford, 1997).