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Natural three-qubit interactions in one-way quantum computing

Natural three-qubit interactions in one-way quantum computing. HOT TOPIC presentation at the EPSRC Network on " Transport,Dissipation and Control in Quantum Devices ". HP Laboratories, Bristol. Tuesday 27th September 2005. Mark Tame Queen’s Quantum Technology Group

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Natural three-qubit interactions in one-way quantum computing

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  1. Natural three-qubit interactions in one-way quantum computing HOT TOPIC presentation at the EPSRC Network on "Transport,Dissipation and Control in Quantum Devices". HP Laboratories, Bristol. Tuesday 27th September 2005 Mark Tame Queen’s Quantum Technology Group Queen’s University Belfast m.tame@qub.ac.uk

  2. Natural three-qubit interactions in one-way quantum computing Mauro Paternostro (Queen’s) The collaborators: Vlatko Vedral (Leeds) (Queen’s) Myungshik Kim

  3. Natural three-qubit interactions in one-way quantum computing Overview of talk: • Overview of one-way model • Scaling problems with noise (Motivation) • One-way computing with three-qubit interactions • Physical realization • Future work and references

  4. Natural three-qubit interactions in one-way quantum computing 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!

  5. p a p b Natural three-qubit interactions in one-way quantum computing 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,M. S. Kim, quant-ph/0509066.

  6. Natural three-qubit interactions in one-way quantum computing Noisy 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 Q: Can the search algorithm be generalized to larger registers in an “economical” way?

  7. Natural three-qubit interactions in one-way quantum computing The Model: A “bowtie” lattice structure

  8. Natural three-qubit interactions in one-way quantum computing The Model: A Toffoli gate Enlargement of 3-spin triangle

  9. Natural three-qubit interactions in one-way quantum computing 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 three-qubit interactions in one-way quantum computing Physical Realization: -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 three-qubit interactions in one-way quantum computing Physical Realization: + = lattice lattice Bowties! S. Peil et al., PRA 67, 051603 (2003).

  12. Natural three-qubit interactions in one-way quantum computing Future Work: • Problem of single atom addressing - partially solved by “blurred” removal, see Tame et al., quant-ph/0507173 for more details. • Propagating the logical qubits in/out in the same direction (trilinear) after the 3 qubit interaction and is this even necessary? • More fundamental: • Is there a different 3-qubit entanglement structure that can be engineered using Heff to allow for a stabilizer approach or something similar? • How does this scheme scale compared to the original one-way model for QC for generalized versions of various algorithms?

  13. Natural three-qubit interactions in one-way quantum computing 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. S. Tame, M. Paternostro, M. S. Kim & V. Vedral, quant-ph/0412156- A. Barenco et al., PRA 52 3457 (1995)- T. Calarco et al., J. Mod. Opt. 47, 2137 (2000)- 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)- S. Peil et al., PRA 67, 051603 (2003) • - M. S. Tame et al., quant-ph/0507173

  14. . . . . . . . . . . . Natural three-qubit interactions in one-way quantum computing Consider a simple generalization to 3 qubits: The main problem is the necessity of performing a Toffoli gate for the tagging-inversion steps: not naturally performed by the one-way model Stabilizer approach A. Barenco et al., PRA 52 3457 (1995) Raussendorf, Browne & Briegel, PRA 2003 For large cluster states, the stabilizer approach becomes a more valuable tool for circuit/QC design than simple concatenation In any case, large qubit registers are required: and as we have seen, these are quite prone to realistic noise and errors

  15. Natural three-qubit interactions in one-way quantum computing Imperfect Entanglement: M. S. Tame et al., quant-ph/0507173

  16. Natural three-qubit interactions in one-way quantum computing Blurred Removal: M. S. Tame et al., quant-ph/0507173 State of central qubit is irrelevant Raman Transition

  17. Natural three-qubit interactions in one-way quantum computing Hyperfine states: T. Calarco et al., J. Mod. Opt. 47, 2137 (2000). Dms=0,+/-1 (linear, circularly polarized)

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