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Overview:

Extending the One-Way Model for Quantum Computation Mark Tame Queen’s Quantum Technology Group Queen’s University Belfast. Overview:. Short Introduction to Standard One-way QC Motivation for extensions/modifications 1) Graph State One-way QC 2) Natural 3-Qubit Interactions One-way QC

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Overview:

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  1. Extending the One-Way Model for Quantum ComputationMark TameQueen’s Quantum Technology GroupQueen’s University Belfast

  2. Overview: • Short Introduction to Standard One-way QC • Motivation for extensions/modifications • 1) Graph State One-way QC • 2) Natural 3-Qubit Interactions One-way QC • 3) Qudit One-way QC • Summary and Outlook…

  3. Short Introduction to Standard One-way QC : A brief overview of: One-way quantum computing very brief ! 2) 1) 3) • M.S. Tame, M. Paternostro, M.S. Kim & V. Vedral, PRA 72, 012319 (2005).-Danos et al. quant-ph/0411071 - R. Raussendorf & H.-J. Briegel, PRL 2001- Raussendorf, Browne & Briegel, PRA 2003just type “one-way” or “cluster state” on the archive!

  4. p a p b Short Introduction to Standard One-way QC : 2-qubit Search Algorithm: - P. Walther et al., Nature 434, 196 (2005) | + > | + > Box cluster (just 4 qubits & measurements) Also Quantum Games can be played on small clusters like this: M. Paternostro, M. S. Tame andM. S. Kim, New J. Phys. 7 226 (2005)

  5. Motivation: Decoherence/noise in cluster states: Stabilizer approach(redundancies) Individual dephasing channels Unitary noise (eg. controlled collisions of atoms): M.S. Tame, M. Paternostro, M.S. Kim & V. Vedral, quant-ph/0412156, PRA 72, 012319 (2005) Concatenation approach For other work on decoherence and cluster states, see: W. Dur and H. J. Briegel, Phys. Rev. Lett. 92, 180403 (2004) M. A. Nielsen and C. M. Dawson, quant-ph/0405134 (2004)

  6. Graph State One-way QC : Cutting down on the number of physical qubits… S. C. Benjamin, J. Eisert, T. M. Stace., New J. Phys. 7, 194 (2005) Trading qubit resource for entanglement resource But this has no natural system for its realization... Engineered entanglement creates protocol specific graph state

  7. Natural 3-Qubit Interactions One-way QC: What about changing the entanglement structure? A “bowtie” lattice structure M. S. Tame et al., PRA 73, 022309 (2006)

  8. Natural 3-Qubit Interactions One-way QC: The Model: A Toffoli gate Enlargement of 3-spin triangle

  9. Natural 3-Qubit Interactions One-way QC: Physical Realization: T. Calarco et al., J. Mod. Opt. 47, 2137 (2000). Hexagonal lattice (transverse trapping field confines to x-y plane) Assume loading of one atom per lattice site (Mott insulator MI)

  10. Natural 3-Qubit Interactions One-way QC: Physical Realization: D. Jaksch et al., Phys Rev Lett. 81, 3108 (1998). -2 species Bose-Hubbard Hamiltonian -Confine indexing to unit triangular cell - J. K. Pachos and M. B. Plenio, PRL 93, 056402 (2004)- J. K. Pachos and E. Rico, PRA 70, 053620 (2004)- J. K. Pachos et al., Opt. Spectrosc. 99, 355 (2005)

  11. Natural 3-Qubit Interactions One-way QC: Physical Realization: + = lattice lattice Bowties! S. Peil et al., PRA 67, 051603 (2003).

  12. Natural 3-Qubit Interactions One-wayQC: Problems? • Problem of single atom addressing - partially solved by “blurred” removal, see Tame et al., PRA 73, 022309 (2006) for more details. State of central qubit is irrelevant There are other nice schemes that may be utilised: eg. J. Joo et al. Quant-ph/0601100 Raman Transition

  13. Qudit One-way QC : Original paper: D. L. Zhou et al., PRA 68, 062303 (2003). There are some nice reviews with better explanation: W. Hall, quant-ph/0512130. S. Clarke, J. Phys. A: Math. Gen. 39 2701 (2006)

  14. Qudit One-way QC : M. S. Tame et al., in preparation (2006).

  15. Qudit One-way QC : Ion traps: A. B. Klimov et al., PRA 67, 062313 (2003) Photonic modes: Cavity QED: N. K. Langford et al., PRL 93, 053601 (2004) S. B. Zheng, PRA 68, 035801 (2003)

  16. Qudit One-way QC : M. S. Tame et al., in preparation (2006). Qubit: Qutrit: 4 5 6 7 8 quatrit , quinit, qusenit, quseptit, quoctit, quonit, qudecit,………, qusexagesit…… 9 10 60

  17. Qudit One-way QC : @ Gt @ Gt M. S. Tame et al., in preparation (2006).

  18. Qudit One-way QC :

  19. Summary and Outlook… 1) Graph State One-way QC 2) Natural 3-Qubit Interactions One-way QC 3) Qudit One-way QC • Group measurements (M. S. Tame et al., PRA 73, 022309 (2006); J. Joo et al. quant-ph/0601100) • Error Correction (R. Raussendorf et al. quant-ph/0510135)

  20. References: M.S. Tame, M. Paternostro, M.S. Kim & V. Vedral, PRA 72, 012319 (2005).Danos et al. quant-ph/0411071 R. Raussendorf & H.-J. Briegel, PRL 2001 Raussendorf, Browne & Briegel, PRA 2003 P. Walther et al., Nature 434, 196 (2005) M. Paternostro, M. S. Tame andM. S. Kim, New J. Phys. 7 226 (2005) M.S. Tame, M. Paternostro, M.S. Kim & V. Vedral, quant-ph/0412156. S. Peil et al., PRA 67, 051603 (2003). J. Joo et al. quant-ph/0601100 W. Dur and H. J. Briegel, Phys. Rev. Lett. 92, 180403 (2004) M. A. Nielsen and C. M. Dawson, quant-ph/0405134 (2004) D. L. Zhou et al., PRA 68, 062303 (2003).W. Hall, quant-ph/0512130. S. Clarke, J. Phys. A: Math. Gen. 39 2701 (2006) S. C. Benjamin, J. Eisert, T. M. Stace., New J. Phys. 7, 194 (2005) M. S. Tame et al., PRA 73, 022309 (2006) M. S. Tame et al., in preparation (2006). T. Calarco et al., J. Mod. Opt. 47, 2137 (2000). A. B. Klimov et al., PRA 67, 062313 (2003) J. K. Pachos and M. B. Plenio, PRL 93, 056402 (2004)J. K. Pachos and E. Rico, PRA 70, 053620 (2004)J. K. Pachos et al., Opt. Spectrosc. 99, 355 (2005) N. K. Langford et al., PRL 93, 053601 (2004) S. B. Zheng, PRA 68, 035801 (2003) D. Jaksch et al., Phys Rev Lett. 81, 3108 (1998).

  21. Level Structure of alkali metal atoms, eg Rb: Dms=0,+/-1 (linear, circularly polarized) T. Calarco et al., J. Mod. Opt. 47, 2137 (2000).

  22. Natural 3-Qubit Interactions One-wayQC: Imperfect Entanglement: M. S. Tame et al., PRA 73, 022309 (2006)

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