Extending the OneWay Model for Quantum Computation Mark Tame Queens Quantum Technology Group Queens

1
Extending the One-Way Model for Quantum
ComputationMark TameQueens Quantum Technology
GroupQueens University Belfast
2
Overview

• Short Introduction to Standard One-way QC
• Motivation for extensions/modifications
• 1) Graph State One-way QC
• 2) Natural 3-Qubit Interactions One-way QC
• 3) Qudit One-way QC
• Summary and Outlook

3
Short Introduction to Standard One-way QC
A brief overview of
One-way quantum computing
very brief !
2)
1)
3)

• M.S. Tame, M. Paternostro, M.S. Kim V. Vedral,
  PRA 72, 012319 (2005).-Danos et al.
  quant-ph/0411071

- R. Raussendorf H.-J. Briegel, PRL 2001-
Raussendorf, Browne Briegel, PRA 2003just type
one-way or cluster state on the archive!
4
Short Introduction to Standard One-way QC
2-qubit Search Algorithm
- P. Walther et al., Nature 434, 196 (2005)
gt
gt
Box cluster (just 4 qubits measurements)
Also Quantum Games can be played on small
clusters like this
M. Paternostro, M. S. Tame and M. S. Kim, New J.
Phys. 7 226 (2005)
5
Motivation
Decoherence/noise in cluster states
Stabilizer approach(redundancies)
Individual dephasing channels
Unitary noise (eg. controlled collisions of
atoms)
M.S. Tame, M. Paternostro, M.S. Kim V. Vedral,
quant-ph/0412156, PRA 72, 012319 (2005)
Concatenation approach
For other work on decoherence and cluster
states, see
W. Dur and H. J. Briegel, Phys. Rev. Lett. 92,
180403 (2004)
M. A. Nielsen and C. M. Dawson, quant-ph/0405134
(2004)
6
Graph State One-way QC
Cutting down on the number of physical qubits
S. C. Benjamin, J. Eisert, T. M. Stace ., New J.
Phys. 7, 194 (2005)
Trading qubit resource for entanglement resource
But this has no natural system for its
realization...
Engineered entanglement creates protocol specific
graph state
7
Natural 3-Qubit Interactions One-way QC
What about changing the entanglement structure?
A bowtie lattice structure
M. S. Tame et al., PRA 73, 022309 (2006)
8
Natural 3-Qubit Interactions One-way QC
The Model
A Toffoli gate
Enlargement of 3-spin triangle
9
Natural 3-Qubit Interactions One-way QC
Physical Realization
T. Calarco et al., J. Mod. Opt. 47, 2137 (2000).
Hexagonal lattice (transverse trapping field
confines to x-y plane)
Assume loading of one atom per lattice site
(Mott insulator MI)
10
Natural 3-Qubit Interactions One-way QC
Physical Realization
D. Jaksch et al., Phys Rev Lett. 81, 3108 (1998).
-2 species Bose-Hubbard Hamiltonian
-Confine indexing to unit triangular cell
- J. K. Pachos and M. B. Plenio, PRL 93, 056402
(2004)- J. K. Pachos and E. Rico, PRA 70, 053620
(2004)- J. K. Pachos et al., Opt. Spectrosc. 99,
355 (2005)
11
Natural 3-Qubit Interactions One-way QC
Physical Realization


lattice
lattice
Bowties!
S. Peil et al., PRA 67, 051603 (2003).
12
Natural 3-Qubit Interactions One-way QC
Problems?

• Problem of single atom addressing - partially
  solved by blurred removal, see Tame et al.,
  PRA 73, 022309 (2006) for more details.

State of central qubit is irrelevant
There are other nice schemes that may be
utilised eg. J. Joo et al. Quant-ph/0601100
Raman Transition
13
Qudit One-way QC
Original paper D. L. Zhou et al., PRA 68, 062303
(2003). There are some nice reviews with
better explanation W. Hall, quant-ph/0512130. S
. Clarke, J. Phys. A Math. Gen. 39 2701 (2006)
14
Qudit One-way QC
M. S. Tame et al., in preparation (2006).
15
Qudit One-way QC
Ion traps
A. B. Klimov et al., PRA 67, 062313 (2003)
Photonic modes
Cavity QED
N. K. Langford et al., PRL 93, 053601 (2004)
S. B. Zheng, PRA 68, 035801 (2003)
16
Qudit One-way QC
M. S. Tame et al., in preparation (2006).
Qubit
Qutrit
4 5 6 7
8
quatrit , quinit, qusenit, quseptit, quoctit,
quonit, qudecit,, qusexagesit
9 10 60
17
Qudit One-way QC
_at_ Gt
_at_ Gt
M. S. Tame et al., in preparation (2006).
18
Qudit One-way QC
19
Summary and Outlook
1) Graph State One-way QC 2) Natural 3-Qubit
Interactions One-way QC 3) Qudit One-way QC

• Group measurements (M. S. Tame et al., PRA 73,
  022309 (2006) J. Joo et al. quant-ph/0601100)
• Error Correction (R. Raussendorf et al.
  quant-ph/0510135)

20
References
M.S. Tame, M. Paternostro, M.S. Kim V. Vedral,
PRA 72, 012319 (2005).Danos et al.
quant-ph/0411071
R. Raussendorf H.-J. Briegel, PRL 2001
Raussendorf, Browne Briegel, PRA 2003
P. Walther et al., Nature 434, 196 (2005)
M. Paternostro, M. S. Tame and M. S. Kim, New J.
Phys. 7 226 (2005)
M.S. Tame, M. Paternostro, M.S. Kim V. Vedral,
quant-ph/0412156.
S. Peil et al., PRA 67, 051603 (2003).
J. Joo et al. quant-ph/0601100
W. Dur and H. J. Briegel, Phys. Rev. Lett. 92,
180403 (2004)
M. A. Nielsen and C. M. Dawson, quant-ph/0405134
(2004)
D. L. Zhou et al., PRA 68, 062303 (2003). W.
Hall, quant-ph/0512130. S. Clarke, J. Phys. A
Math. Gen. 39 2701 (2006)
S. C. Benjamin, J. Eisert, T. M. Stace ., New J.
Phys. 7, 194 (2005)
M. S. Tame et al., PRA 73, 022309 (2006)
M. S. Tame et al., in preparation (2006).
T. Calarco et al., J. Mod. Opt. 47, 2137 (2000).
A. B. Klimov et al., PRA 67, 062313 (2003)
J. K. Pachos and M. B. Plenio, PRL 93, 056402
(2004)J. K. Pachos and E. Rico, PRA 70, 053620
(2004)J. K. Pachos et al., Opt. Spectrosc. 99,
355 (2005)
N. K. Langford et al., PRL 93, 053601 (2004)
S. B. Zheng, PRA 68, 035801 (2003)
D. Jaksch et al., Phys Rev Lett. 81, 3108 (1998).
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
Level Structure of alkali metal atoms, eg Rb
Dms0,/-1 (linear, circularly polarized)
T. Calarco et al., J. Mod. Opt. 47, 2137 (2000).
29
Natural 3-Qubit Interactions One-way QC
Imperfect Entanglement
M. S. Tame et al., PRA 73, 022309 (2006)