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

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

3/14 Work on Fault-tolerance in the one-way model -Raussendorf, PhD Thesis (2003) ( -Nielsen and Dawson, PRA 71, (2005) -Aliferis and Leung, PRA 73, (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, (2006) PRA 73, (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, (2005) -Varnava, Browne and Rudolph PRL 97, (2006) Loss tolerant schemes for linear optics setups -Raussendorf, Harrington and Goyal, Ann. Phys. 321, 2242 (2006) -Raussendorf and Harrington, quant-ph/ (2006) Fault-tolerant using topological error correction and surface codes -Silva et al., quant-ph/ (2006) -Fujii and Yamamoto, quant-ph/ (2006) Most Recently: -Dawson, Haselgrove and Nielsen, PRL 96, (2006). -Silva et al., quant-ph/ (2006).

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?

5/14 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, (2006)

6/14 Decoherence-free subspace one-way model - Simple protection from collective noise G. M. Palma et al., Proc. Roy. Soc. London A 452, (1996) Basic 1-bit teleportation unit: 4 physical qubits

7/14 Decoherence-free subspace one-way model - Protection from all types of collective noise (I) Theory: Kempe et al., PRA (2001) Experiment: Bourenanne et al., PRL (2004)

8/14 Decoherence-free subspace one-way model - Protection from all types of collective noise (II) Knill, Laflamme and Viola PRL 84, 2525 (2000) (Decoherence-free subsystems) Basic 1-bit teleportation unit: 6 physical qubits

9/14 Performance of Decoherence-free subspace one-way model - Theoretical (I) M. S. Tame, M. Paternostro, M. S. Kim -submitted (2007) Probe states: QPT techniques: H H H H

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

11/14 Performance of Decoherence-free subspace one-way model - Experimental (II) R. Prevedel, M. S. Tame, A. Stefanov, M. Paternostro, M. S. Kim and A. Zeilinger -submitted (2007) Standard DFS encoded Information transfer protocol: 4 physical qubits Linear optical setup See also: Kwiat et al., Science 290, (2000) for single qubit DFS encoding.

12/14 Summary and Outlook M. S. Tame et al., work in progress (2007) 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

13/14 Special thanks to Collaborators Queen’s, UK : Mauro Paternostro and Myungshik Kim Vienna, Austria : Robert Prevedel, André Stefanov, Pascal Böhi, Anton Zeilinger Leeds, UK : Vlatko Vedral London, UK : Chris Hadley, Sougato Bose Palermo, Italy : Massimo Palma

14/14 References DFS one-way QC -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/ Raussendorf, Browne and Briegel, PRA 68, (2003). -Dawson, Haselgrove and Nielsen, PRL 96, (2006) PRA 73, (2006) -Lidar and Birgitta Whaley, "Irreversible Quantum Dynamics", F. Benatti and R. Floreanini (Eds.), pp (Springer Lecture Notes in Physics vol. 622, Berlin, 2003); also at quant-ph/ Introduction to graph states and one-way QC using cluster states Fault-tolerant one-way QC using QECC Introduction to DFS -M. S. Tame, M. Paternostro, M. S. Kim -submitted (2007) -R. Prevedel, M. S. Tame, A. Stefanov, M. Paternostro, M. S. Kim and A. Zeilinger -submitted (2007)

 t=0.15  t=0.5  t=1  t=5