Loading...

PPT – Quantum Gates and Quantum Networks PowerPoint presentation | free to view - id: 256951-ZDc1Z

The Adobe Flash plugin is needed to view this content

Quantum Gates and Quantum Networks

- L.C. Kwek

NIE, NanyangTechnological University Local

Driver, QIT Lab (NUS, Singapore) Fujitsu Visiting

Professor, University of Cambridge Talk presented

at the National Taiwan University, Taipei, 14

December 2004

QIT Group (Singapore)

Artur Ekert and C.H. Oh

- Janet Anders
- Chia Teck Chee
- Chen Jingling
- Chen Lai Keat
- Choo Keng Wah
- Du Jiangfeng
- Berge Englert
- Feng Xinli
- Ajay Gopinathan
- Darwin Gosal
- Hor Wei Hann
- D. Kaszlikowski
- Christian Kurtsiefer
- L.C. Kwek
- C.H. Lai
- Wayne Lawton
- Lim Jenn Yang
- Antia Lamas Linares

- Alex Ling
- Looi Shiang Yong
- Ivan Marcikic
- Neelima Raitha
- Kuldip Singh
- Tey Meng Khoon
- Tong Dianmin
- Wang Zisheng
- Wu Chunfeng
- 5-10 undergraduate students
- www.quantumlah.org

3rd Asia Pacific Workshop On Quantum

Information Science and 1st Joint Institute of

Mathematical Sciences -NUS conference on Quantum

Information (3rd Jan 05 to 15th Jan 05)

- http//www.quantumlah.org/workshop/

- http//www.lasphys.com/workshops/lasphys05/lphys05

.htm

Coverage

- Introduction quantum logic and classical logic
- Single qubit gate
- Two-qubit gate
- Quantum circuits for quantum algorithm
- A simple quantum network
- Experiments

Computation

OUTPUT

INPUT

1

0

1

1

0

0

0

1

1

0

1

0

Physics Inside (and outside)

Classical deterministic computation

Physically allowed operations, computational steps

Intermediate configurations

Configuration complete specification of the

state of the computer and data

Final configuration (output)

Initial configuration (input)

Classical deterministic computation

110

001

101

000

Computational steps moves from one

configuration to another are performed by

elementary operations on bits

Boolean Networks

0

OR

1

AND

0

OR

1

0

0

Basic operations logic gates

Logical AND

Wire, identity

1

AND

0

0

1

1

1

1

Output 0 apart from the (1,1) input

0

1

NOT

1

0

Logical OR

0

OR

0

0

X

X

Output 1 apart from the (0,0) input

X

Fan out

Classical probabilistic computation

Possible outputs

Input

Quantum computation

Constructive or destructive interference enhance

correct outputs suppress wrong outputs GOOD SIDE

extra computational power BAD SIDE sensitive to

decoherence

Quantum computation

Initial configuration of the three qubits

Bits and Qubits

QUBIT

BIT

Quantum Boolean Networks

H

H

H

Quantum operations

H

H

H

Single qubit gates

Hadamard

H

Continuous set of phase gates

Discrete set of phase gates

Single qubit interference

H

H

Any single qubit interference

H

H

INPUT

OUTPUT

in the matrix form

Any unitary operation on a qubit

H

H

INPUT

OUTPUT

in the matrix form the most general SU(2)

operation on a single qubit

Two and more qubits

Notation

Operations on two qubits

Controlled-NOT

Controlled-U

U

U

Quantum interferometry revisited

H

H

H

H

U

REMEMBER THIS TRICK !

Phases in a new way

H

H

U

Entangled states

H

entangled

separable

Bell GHZ states

H

H

Useful decomposition of any U in SU(2)

For any U in SU(2)

Rotation by twice the angle between axis a and

b around the axis perpendicular to a and b

Recall that ?x represents rotation by ? around

axis x

Rotation by ? around some axis a

Rotation by ? around some axis b

Building controlled-U operations

B

B-1

A-1

U

A

A, A-1, B and B-1 are single qubit operations and

can be constructed from the Hadamard and phase

gates. Controlled-U can be constructed from

single qubit operations and the controlled-NOT

gates. Hence any controlled-U gate can be

constructed from the Hadamard, the

controlled-NOT and phase gates.

Toffoli Gate

H

H

Controlled-controlled NOT

Computes logical AND

Quantum adder

Quantum Networks

H

H

Quantum adder

Quantum Hadamard transform

Quantum Hadamard Transform

H

H

H

H

Quantum Hadamard Transform

H

H

H

H

H

H

H

H

Quantum Network

(No Transcript)

f

f

f

f

f

f

f

f

Application 2 Direct measure of purity if r1

r2 r Visibility Tr (r2)

f

visibility

f

f

Possible technology?

IONS TRAP Innsbruck Oxford Munich Boulders

Cavity QED ENS Paris

Linear Optics Singapore?

NMR Oxford, MIT

Josephson Junctions Delft, Karlsruhe,Catania

Experimental

- Bruker Avance DMR 400 spectrometer
- 9.4 T
- 5mm probe
- C13 sample of alanine
- Resonant frequency of alanine 100 MHz

J.F. Du, P. Zou, M. Shi, L.C. Kwek, J.W. Pan,

C.H. Oh, A. Ekert, D.K.L. Oi and M. Ericsson, An

experimental observation of geometric phases for

mixed states using interferometry, Phys. Rev.

Lett. 91, 100403 (2003) , eprint

arXivquant-ph/0305054