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Measurement-based quantum protocols with minimal resources. Mark Tame QTeQ - Quantum Technology at Queen’s Queen’s University, Belfast www.qteq.info. Introduction to MB one-way quantum computation Protocols/algorithms on small cluster states Summary and Outlook. Introduction.

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Measurement-based quantum protocols with minimal resources

Mark Tame

QTeQ - Quantum Technology at Queen’s

Queen’s University, Belfast

www.qteq.info


  • Introduction to MB one-way quantum computation

  • Protocols/algorithms on small cluster states

  • Summary and Outlook


Introduction.

- R. Raussendorf & H.-J. Briegel, PRL 2001- Raussendorf, Browne & Briegel, PRA 2003just type “one-way” or “cluster state” on the arXiv.

Universal resource for one-way QC

-Van den Nest, Miyake, Dür, Briegel

PRL 97, 150504 (2006)


Introduction.

1) Preparation of |+>

Sac: |0> |0> --> |0> |0>

|0> |1> --> |0> |1>

|1> |0> --> |1> |0>

|1> |1> --> - |1> |1>

| y > = |+> |+> |+> |+>

2) Application of CZ ’s

| y > = 1/4(|+> |+> |+> |+> + |+> |-> |+> |->

+ |-> |+> |-> |+> - |-> |-> |-> |-> )


Introduction.

- Raussendorf, Browne & Briegel, J. Mod. Opt. 2002


Introduction.

(i)

| y > = ( a|0> |+> + b|1> |-> )

(ii)

| y > = ( a g |0> |0> + a d |0> |1>+ b g |0> |1> - b d |0> |1> )

(iii)


Introduction.

1) Preparation of |+>

Local/Global noise:

  • Pauli error

  • General error

  • Loss

2) Application of CZ ’s

  • controlled phase gate error

  • controlled unitary gate error

  • Loss from non-deterministic gates

3) Measurement process

  • error in measurement of qubits

  • propagates into the remaining cluster

4) Environment effects during

time evolution – Decoherence

  • Pauli error

  • General error

  • Loss


Introduction.

State-of-the-art:

- C.-Y. Lu et al., Nature Physics (2007)

- O. Mandel et al., Nature (2003)


Protocols.

Some small cluster configurations


Grover’s Algorithm:

Protocols.

Deutsch’s Algorithm:

M. S. Tame et al., PRL (2007)

P. Walther et al., Nature (2005)

Decoherence-free

subspace processing:

R. Prevedel et al., Nature (2006)

M. S. Tame et al.,

NJP (in press, 2007)

R. Prevedel et al.,

(submitted, 2007)

Quantum Games:

M. Paternostro, M. S. Tame, M. S. Kim, NJP (2005)

R. Prevedel et al., NJP (in press, 2007)


N. Kiesel et al., PRL (2005)

Protocols.

A.-N. Zhang et al., PRA (R) (2005)

- C.-Y. Lu et al., Nature Physics (2007)

P. Walther et al., Nature (2005);

R. Prevedel et al., Nature (2006); M. S. Tame et al., PRL (2007)


Protocols.

Grover’s Algorithm:

and active feed-forward!

L .K. Grover, Phys. Rev. Lett. 79, 325 (1997).

R. Prevedel et al., Nature (2006)

P. Walther et al., Nature (2005)


Protocols.

Deutsch’s Algorithm:

Fair coin:

D. Deutsch, Proc. Roy. Soc. Lond. A 400, 97 (1985).

D. Deutsch and R. Jozsa, Proc. R. Soc. Lond. A 439, 553 (1992).

R. Cleve et al., Proc. R. Soc. Lond. A 454, 399 (1998).

M. S. Tame et al., PRL (2007).

Unfair coin:


Protocols.

Deutsch’s Algorithm:

M. S. Tame et al., PRL (2007)


Protocols.

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:


Protocols.

G. M. Palma et al., Proc. Roy. Soc. London A 452, 567-584 (1996)

Basic 1-bit teleportation unit: 4 physical qubits


Protocols.

Probe states:

H

H

QPT techniques:

H

H

M. S. Tame, M. Paternostro, M. S. Kim

NJP (in press, 2007)


Protocols.

Gt=0.5

Gt=0.15

Gt=1

Gt=5

M. S. Tame, M. Paternostro, M. S. Kim

NJP (in press, 2007)


Protocols.

Linear optical setup

DFS encoded

R. Prevedel, M. S. Tame, A. Stefanov,

M. Paternostro, M. S. Kim and A. Zeilinger

(submitted, 2007)

Information transfer protocol: 4 physical qubits

See also:

Kwiat et al., Science 290, 498-501 (2000)

for single qubit DFS encoding.


Protocols.

Protection from all collective errors

M. S. Tame, M. Paternostro, M. S. Kim

NJP (in press, 2007)


Summary.

Grover’s

Algorithm

Active

Feed-forward

Quantum Games

DFS Protocol

Deutsch’s Algorithm


Polarisation-momentum

entangled cluster states

Outlook.

G. Vallone et al., PRL (2007)

Continuous Variable cluster states

X. Su et al., PRL (2007)

M. S. Tame et al., PRA (2005)

Gross and Eisert., PRL (2007)

K. Chen et al., Arxiv (2007)

Van den Nest, Miyake, Dür, Briegel

PRL 97, 150504 (2006)

and more…

M. S. Tame et al.,

(work in progress, 2007)


Thanks for listening

Special thanks to Collaborators

: Mauro Paternostro and Myungshik Kim

Queen’s, UK

: Robert Prevedel,

André Stefanov, Pascal Böhi,

Anton Zeilinger

: Vlatko Vedral

Vienna, Austria

Leeds, UK

QUINFO @

: Chris Hadley,

Sougato Bose

: Massimo Palma

London, UK

Palermo, Italy


Protocols.

Quantum Games:

J. Eisert, M. Wilkens, M. Lewenstein, PRL (1999)

M. Paternostro, M. S. Tame, M. S. Kim, NJP (2005)

R. Prevedel et al., NJP (in press, 2007)

Rational reasoning causes each player to pick

this strategy.

Dominant Strategy: A strategy that does at least as well

as any competing strategy against any

possible moves by the other players.


Pareto Optimal: The set of strategies from

which no player can obtain a higher

pay-off, without reducing the pay-off of another.

Protocols.

Quantum Games:

J. Eisert, M. Wilkens, M. Lewenstein, PRL (1999)

M. Paternostro, M. S. Tame, M. S. Kim, NJP (2005)

R. Prevedel et al., NJP (in press, 2007)

Find by elimination

Nash Equilibrium: The set of strategies where no player can benefit by changing

their strategy, while the other players keep their strategy

unchanged.


Protocols.

Quantum Games:

J. Eisert, M. Wilkens, M. Lewenstein, PRL (1999)

M. Paternostro, M. S. Tame, M. S. Kim, NJP (2005)

R. Prevedel et al., NJP (in press, 2007)

Pareto Optimal / Nash Equilibrium

(3,3) Payoff


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