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

1. Fault-tolerant one-way quantum computation using minimal resources - Decoherence-free subspaces (DFS) Mark Tame QTeQ - Quantum Technology at Queen’s Queen’s University, Belfast

2. 2/14 Noise in the one-way model for quantum computation Preparation of |+> Local/Global noise: • Pauli error • General error • Loss Application of CZ ’s • controlled phase gate error • controlled unitary gate error • Loss from non-deterministic gates Measurement process • error in measurement of qubits • propagates into the remaining cluster • Environment effects during • time evolution – Decoherence • Pauli error • General error • Loss

3. 3/14 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:

4. 4/14 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 add 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-tolerence using less resources?

5. 5/14 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 et al., PRL 97, 150504 (2006)

6. 6/14 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

7. 7/14 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)

8. 8/14 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)

9. 9/14 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)

10. 10/14 Performance of Decoherence-free subspace one-way model - Theoretical (I)

11. 11/14 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.

12. 12/14 Summary and Outlook 1) Investigating the error threshold performance 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) and the natural fault-tolerance of cluster states? 2) Most resourceful method for the 3-qubit code M. S. Tame et al., work in progress (2007)

13. 13/14 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

14. 14/14 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

20. Gt=0.5 Gt=0.15 Gt=5 Gt=1