Mark TameMark Tame
QTeQQTeQ - Quantum Technology at Queen’s - Quantum Technology at Queen’s
Queen’s University, BelfastQueen’s University, Belfast
Fault-tolerantFault-tolerant One-way quantum One-way quantum computation using minimal resourcescomputation using minimal resources
2/21The one-way model for quantum computation – Brief introduction
1) Preparation of |+>
2) Application of CZ ’s| > = |+> |+> |+> |+>
| > = 1/4(|+> |+> |+> |+> + |+> |-> |+> |-> + |-> |+> |-> |+> - |-> |-> |-> |-> )
Sac: |0> |0> --> |0> |0> |0> |1> --> |0> |1> |1> |0> --> |1> |0> |1> |1> --> - |1> |1>
- R. Raussendorf & H.-J. Briegel, PRL 2001- Raussendorf, Browne & Briegel, PRA 2003
just type “one-way” or “cluster state” on the archive.
3/21The one-way model for quantum computation – Brief introduction
3) Measurement process
?
4/21The one-way model for quantum computation – Brief introduction
3) Measurement process
(i)
| > = ( |0> |+> + |1> |-> )
| Q1> = ( |0> + |1>)
5/21The one-way model for quantum computation – Brief introduction
3) Measurement process
(ii)
| > = ( |0> |0> + |0> |1>+ |0> |1> - |0> |1> )
| Q1> = ( |0> + |1>)
| Q2> = ( |0> + |1>)
6/21The one-way model for quantum computation – Brief introduction
3) Measurement process
(iii)
7/21The one-way model for quantum computation – Brief introduction
3) Measurement process
8/21The one-way model for quantum computation – Brief introduction
Algorithms:
Grover’s Algorithm
Deutsch’s Algorithm
Quantum Games
M. S. Tame et al., PRL (2007)
P. Walther et al., PRL (2005)
M. Paternostro et al., NJP (2005)
9/21Noise 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
Stage 1
Stage 2
10/21Work 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).
11/21Problems 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?
12/21Minimal-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)
13/21Decoherence-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
14/21Decoherence-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)
15/21Decoherence-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
16/21Performance 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
17/21Performance of Decoherence-free subspace one-way model
- Theoretical (I)
18/21Performance 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.
19/21Outlook
M. S. Tame et al., work in progress (2007)
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
20/21Special 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
21/21References
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)
*Thanks for your attention*
t=0.15 t=0.5
t=1 t=5