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

Fault-tolerant One-way quantum computation using minimal resources. Mark Tame QTeQ - Quantum Technology at Queen’s Queen’s University, Belfast. 2/21. The one-way model for quantum computation – Brief introduction. 1) Preparation of |+>. S ac : |0> |0> --> |0> |0>

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

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  1. Fault-tolerantOne-way quantum computation using minimal resources Mark Tame QTeQ - Quantum Technology at Queen’s Queen’s University, Belfast

  2. 2/21 The one-way model for quantum computation – Brief 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(|+> |+> |+> |+> + |+> |-> |+> |-> + |-> |+> |-> |+> - |-> |-> |-> |-> ) - R. Raussendorf & H.-J. Briegel, PRL 2001- Raussendorf, Browne & Briegel, PRA 2003just type “one-way” or “cluster state” on the archive.

  3. 3/21 The one-way model for quantum computation – Brief introduction 3) Measurement process ?

  4. 4/21 The one-way model for quantum computation – Brief introduction 3) Measurement process | Q1> = ( a|0> + b|1>) (i) | y > = ( a|0> |+> + b|1> |-> )

  5. 5/21 The one-way model for quantum computation – Brief introduction | Q1> = ( a|0> + b|1>) 3) Measurement process | Q2> = ( g|0> + d|1>) (ii) | y > = ( a g |0> |0> + a d |0> |1>+ b g |0> |1> - b d |0> |1> )

  6. 6/21 The one-way model for quantum computation – Brief introduction 3) Measurement process (iii)

  7. 7/21 The one-way model for quantum computation – Brief introduction 3) Measurement process

  8. 8/21 The one-way model for quantum computation – Brief introduction Grover’s Algorithm Algorithms: P. Walther et al., PRL (2005) Deutsch’s Algorithm M. S. Tame et al., PRL (2007) Quantum Games M. Paternostro et al., NJP (2005)

  9. 9/21 Noise in the one-way model for quantum computation Preparation of |+> Local/Global noise: • Pauli error • General error • Loss Application of CZ ’s Stage 1 • controlled phase gate error • controlled unitary gate error • Loss from non-deterministic gates Measurement process Stage 2 • error in measurement of qubits • propagates into the remaining cluster • Environment effects during • time evolution – Decoherence • Pauli error • General error • Loss

  10. 10/21 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:

  11. 11/21 Problems with Fault-tolerant schemes in the one-way model • Large resource overheads: • - A minimum of 7 qubits for an encoded qubit (STEANE code) • Complicated structure for the encoded qubit: • - Underlying graph to encode qubit is complex • Error syndrome extraction techniques lead to additional overheads • “One-buffered”, “two-at-a-time” and “fully-parallel” approaches • complicate the model: • - They modify the measurement patterns and entangling steps • Off-line preparation of ancilla qubits can also be a cumbersome • process: • - setup dependent Q: Is there a way to achieve fault-tolerance using less resources?

  12. 12/21 Minimal-resource Fault-tolerance in the one-way model Local Collective noise 4-qubit collective noise 2-qubit collective noise 3-qubit collective noise Universal resource for one-way QC -Van den Nest, Miyake, Dür, Briegel PRL 97, 150504 (2006)

  13. 13/21 Decoherence-free subspace one-way model - Simple protection from collective noise G. M. Palma et al., Proc. Roy. Soc. London A 452, 567-584 (1996) Basic 1-bit teleportation unit: 4 physical qubits

  14. 14/21 Decoherence-free subspace one-way model - Protection from all types of collective noise (I) Theory: Kempe et al., PRA 63 042307 (2001) Experiment: Bourenanne et al., PRL 92 107901 (2004)

  15. 15/21 Decoherence-free subspace one-way model - Protection from all types of collective noise (II) Basic 1-bit teleportation unit: 6 physical qubits Knill, Laflamme and Viola PRL 84, 2525 (2000) (Decoherence-free subsystems)

  16. 16/21 Performance of Decoherence-free subspace one-way model - Theoretical (I) Probe states: H H QPT techniques: H H M. S. Tame, M. Paternostro, M. S. Kim -submitted (2007)

  17. 17/21 Performance of Decoherence-free subspace one-way model - Theoretical (I)

  18. 18/21 Performance of Decoherence-free subspace one-way model - Experimental (II) Linear optical setup Standard R. Prevedel, M. S. Tame, A. Stefanov, M. Paternostro, M. S. Kim and A. Zeilinger -submitted (2007) DFS encoded Information transfer protocol: 4 physical qubits See also: Kwiat et al., Science 290, 498-501 (2000) for single qubit DFS encoding.

  19. 19/21 Outlook 1) Investigating the performance of the fault-tolerance, for asymmetries in the collective approximation How does the performance of the 2- and 3-qubit Codes with asymmetries compare to standard cluster state Quantum Error Correcting Codes (QECC). 2) Most resourceful method for the 3-qubit code M. S. Tame et al., work in progress (2007)

  20. 20/21 Special thanks to Collaborators : Mauro Paternostro and Myungshik Kim Queen’s, UK : Robert Prevedel, André Stefanov, Pascal Böhi, Anton Zeilinger Vienna, Austria : Vlatko Vedral Leeds, UK QUINFO @ : Chris Hadley, Sougato Bose London, UK : Massimo Palma Palermo, Italy

  21. 21/21 References -M. S. Tame, M. Paternostro, M. S. Kim -submitted (2007) DFS one-way QC -R. Prevedel, M. S. Tame, A. Stefanov, M. Paternostro, M. S. Kim and A. Zeilinger -submitted (2007) -Hein et al.,Proceedings of the International School of Physics "Enrico Fermi" on "Quantum Computers, Algorithms and Chaos", Varenna, Italy, July, 2005; also at quant-ph/0602096 Introduction to graph states and one-way QC using cluster states -Raussendorf, Browne and Briegel, PRA 68, 022312 (2003). -Dawson, Haselgrove and Nielsen, PRL 96, 020501 (2006) PRA 73, 052306 (2006) Fault-tolerant one-way QC using QECC -Lidar and Birgitta Whaley, "Irreversible Quantum Dynamics", F. Benatti and R. Floreanini (Eds.), pp. 83-120 (Springer Lecture Notes in Physics vol. 622, Berlin, 2003); also at quant-ph/0301032 Introduction to DFS *Thanks for your attention*

  22. Gt=0.5 Gt=0.15 Gt=5 Gt=1

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