1 / 26

Mark Tame QTeQ - Quantum Technology at Queen’s Queen’s University, Belfast qteq

Measurement-based quantum protocols with minimal resources. Mark Tame QTeQ - Quantum Technology at Queen’s Queen’s University, Belfast www.qteq.info. Introduction to MB one-way quantum computation Protocols/algorithms on small cluster states Summary and Outlook. Introduction.

tracen
Download Presentation

Mark Tame QTeQ - Quantum Technology at Queen’s Queen’s University, Belfast qteq

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Measurement-based quantum protocols with minimal resources Mark Tame QTeQ - Quantum Technology at Queen’s Queen’s University, Belfast www.qteq.info

  2. Introduction to MB one-way quantum computation • Protocols/algorithms on small cluster states • Summary and Outlook

  3. Introduction. - R. Raussendorf & H.-J. Briegel, PRL 2001- Raussendorf, Browne & Briegel, PRA 2003just type “one-way” or “cluster state” on the arXiv. Universal resource for one-way QC -Van den Nest, Miyake, Dür, Briegel PRL 97, 150504 (2006)

  4. Introduction. 1) Preparation of |+> Sac: |0> |0> --> |0> |0> |0> |1> --> |0> |1> |1> |0> --> |1> |0> |1> |1> --> - |1> |1> | y > = |+> |+> |+> |+> 2) Application of CZ ’s | y > = 1/4(|+> |+> |+> |+> + |+> |-> |+> |-> + |-> |+> |-> |+> - |-> |-> |-> |-> )

  5. Introduction. - Raussendorf, Browne & Briegel, J. Mod. Opt. 2002

  6. Introduction. (i) | y > = ( a|0> |+> + b|1> |-> ) (ii) | y > = ( a g |0> |0> + a d |0> |1>+ b g |0> |1> - b d |0> |1> ) (iii)

  7. Introduction. 1) Preparation of |+> Local/Global noise: • Pauli error • General error • Loss 2) Application of CZ ’s • controlled phase gate error • controlled unitary gate error • Loss from non-deterministic gates 3) Measurement process • error in measurement of qubits • propagates into the remaining cluster 4) Environment effects during time evolution – Decoherence • Pauli error • General error • Loss

  8. Introduction. State-of-the-art: - C.-Y. Lu et al., Nature Physics (2007) - O. Mandel et al., Nature (2003)

  9. Protocols. Some small cluster configurations

  10. Grover’s Algorithm: Protocols. Deutsch’s Algorithm: M. S. Tame et al., PRL (2007) P. Walther et al., Nature (2005) Decoherence-free subspace processing: R. Prevedel et al., Nature (2006) M. S. Tame et al., NJP (in press, 2007) R. Prevedel et al., (submitted, 2007) Quantum Games: M. Paternostro, M. S. Tame, M. S. Kim, NJP (2005) R. Prevedel et al., NJP (in press, 2007)

  11. N. Kiesel et al., PRL (2005) Protocols. A.-N. Zhang et al., PRA (R) (2005) - C.-Y. Lu et al., Nature Physics (2007) P. Walther et al., Nature (2005); R. Prevedel et al., Nature (2006); M. S. Tame et al., PRL (2007)

  12. Protocols. Grover’s Algorithm: and active feed-forward! L .K. Grover, Phys. Rev. Lett. 79, 325 (1997). R. Prevedel et al., Nature (2006) P. Walther et al., Nature (2005)

  13. Protocols. Deutsch’s Algorithm: Fair coin: D. Deutsch, Proc. Roy. Soc. Lond. A 400, 97 (1985). D. Deutsch and R. Jozsa, Proc. R. Soc. Lond. A 439, 553 (1992). R. Cleve et al., Proc. R. Soc. Lond. A 454, 399 (1998). M. S. Tame et al., PRL (2007). Unfair coin:

  14. Protocols. Deutsch’s Algorithm: M. S. Tame et al., PRL (2007)

  15. Protocols. Work on Fault-tolerance in the one-way model: -Raussendorf, PhD Thesis (2003) (http://edoc.ub.unimuenchen.de/archive/00001367) -Nielsen and Dawson, PRA 71, 042323 (2005) -Aliferis and Leung, PRA 73, 032308 (2006) Proved that an Error Threshold existed, which could be determined by mapping noise in the cluster state to noise in a corresponding circuit model. -Dawson, Haselgrove and Nielsen, PRL 96, 020501 (2006). -Dawson, Haselgrove and Nielsen, PRL 96, 020501 (2006) PRA 73, 052306 (2006) Error correcting schemes and associated error threshold values for optical setups STEANE 7 qubit and GOLAY 23 qubit codes -Ralph, Hayes and Gilchrist PRL, 95, 100501 (2005) -Varnava, Browne and Rudolph PRL 97, 120501 (2006) Loss tolerant schemes for linear optics setups -Silva et al., quant-ph/0611273 (2006). Fault-tolerant using topological error correction and surface codes -Raussendorf, Harrington and Goyal, Ann. Phys. 321, 2242 (2006) -Raussendorf and Harrington, quant-ph/0610082 (2006) -Silva et al., quant-ph/0611273 (2006) -Fujii and Yamamoto, quant-ph/0611160 (2006) Most Recently:

  16. Protocols. G. M. Palma et al., Proc. Roy. Soc. London A 452, 567-584 (1996) Basic 1-bit teleportation unit: 4 physical qubits

  17. Protocols. Probe states: H H QPT techniques: H H M. S. Tame, M. Paternostro, M. S. Kim NJP (in press, 2007)

  18. Protocols. Gt=0.5 Gt=0.15 Gt=1 Gt=5 M. S. Tame, M. Paternostro, M. S. Kim NJP (in press, 2007)

  19. Protocols. Linear optical setup DFS encoded R. Prevedel, M. S. Tame, A. Stefanov, M. Paternostro, M. S. Kim and A. Zeilinger (submitted, 2007) Information transfer protocol: 4 physical qubits See also: Kwiat et al., Science 290, 498-501 (2000) for single qubit DFS encoding.

  20. Protocols. Protection from all collective errors M. S. Tame, M. Paternostro, M. S. Kim NJP (in press, 2007)

  21. Summary. Grover’s Algorithm Active Feed-forward Quantum Games DFS Protocol Deutsch’s Algorithm

  22. Polarisation-momentum entangled cluster states Outlook. G. Vallone et al., PRL (2007) Continuous Variable cluster states X. Su et al., PRL (2007) M. S. Tame et al., PRA (2005) Gross and Eisert., PRL (2007) K. Chen et al., Arxiv (2007) Van den Nest, Miyake, Dür, Briegel PRL 97, 150504 (2006) and more… M. S. Tame et al., (work in progress, 2007)

  23. Thanks for listening Special thanks to Collaborators : Mauro Paternostro and Myungshik Kim Queen’s, UK : Robert Prevedel, André Stefanov, Pascal Böhi, Anton Zeilinger : Vlatko Vedral Vienna, Austria Leeds, UK QUINFO @ : Chris Hadley, Sougato Bose : Massimo Palma London, UK Palermo, Italy

  24. Protocols. Quantum Games: J. Eisert, M. Wilkens, M. Lewenstein, PRL (1999) M. Paternostro, M. S. Tame, M. S. Kim, NJP (2005) R. Prevedel et al., NJP (in press, 2007) Rational reasoning causes each player to pick this strategy. Dominant Strategy: A strategy that does at least as well as any competing strategy against any possible moves by the other players.

  25. Pareto Optimal: The set of strategies from which no player can obtain a higher pay-off, without reducing the pay-off of another. Protocols. Quantum Games: J. Eisert, M. Wilkens, M. Lewenstein, PRL (1999) M. Paternostro, M. S. Tame, M. S. Kim, NJP (2005) R. Prevedel et al., NJP (in press, 2007) Find by elimination Nash Equilibrium: The set of strategies where no player can benefit by changing their strategy, while the other players keep their strategy unchanged.

  26. Protocols. Quantum Games: J. Eisert, M. Wilkens, M. Lewenstein, PRL (1999) M. Paternostro, M. S. Tame, M. S. Kim, NJP (2005) R. Prevedel et al., NJP (in press, 2007) Pareto Optimal / Nash Equilibrium (3,3) Payoff

More Related