mark tame qteq - quantum technology at queen’s queen’s university, belfast fault-tolerant...
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Mark TameMark Tame
QTeQ - Quantum Technology at Queen’sQTeQ - Quantum Technology at Queen’s
Queen’s University, BelfastQueen’s University, Belfast
Fault-tolerant one-way quantum Fault-tolerant one-way quantum computation using minimal resources - computation using minimal resources -
Decoherence-free subspaces (DFS)Decoherence-free subspaces (DFS)
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2/14Noise 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
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3/14Work 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) 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 schemesfor linear optics setups
-Raussendorf, Harrington and Goyal, Ann. Phys. 321, 2242 (2006)-Raussendorf and Harrington, quant-ph/0610082 (2006)
Fault-tolerant using topological error correction and surface codes
-Silva et al., quant-ph/0611273 (2006)-Fujii and Yamamoto, quant-ph/0611160 (2006)
Most Recently:
-Dawson, Haselgrove and Nielsen, PRL 96, 020501 (2006).
-Silva et al., quant-ph/0611273 (2006).
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4/14Problems 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?
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5/14Minimal-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)
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6/14Decoherence-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
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7/14Decoherence-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)
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8/14Decoherence-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
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9/14Performance 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
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10/14Performance of Decoherence-free subspace one-way model
- Theoretical (I)
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11/14Performance 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, 498-501 (2000)for single qubit DFS encoding.
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12/14Summary 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
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13/14Special 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
QUINFO @
London, UK
: Chris Hadley, Sougato Bose
Palermo, Italy
: Massimo Palma
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14/14References
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/0602096
-Raussendorf, Browne and Briegel, PRA 68, 022312 (2003).
-Dawson, Haselgrove and Nielsen, PRL 96, 020501 (2006) PRA 73, 052306 (2006)
-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 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)
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t=0.15 t=0.5
t=1 t=5