& its Computational Complexity Analysis

molassesitalianΤεχνίτη Νοημοσύνη και Ρομποτική

6 Νοε 2013 (πριν από 4 χρόνια και 1 μήνα)

64 εμφανίσεις

Hardware

Quantum Computer

Faster

What we need


Image Representation

Qubit Lattices

[Venegas
-
Andraca, 2003]

Real Ket

[Latorre, 2005]

Do not provide

Preparation procedures

&

Image Processing Operators


[Feynman, 1982]

[Shor, 1994]

Colors

Positions

i
c
K
I
N
i
i




1
1
N


No. of positions

K
-

Constant

Quantum

State


I
FRQI

I
Hardware

Quantum Computer

Initialized state

Turn it on

Hardware

Quantum Computer

Image State

0
Complexity of the preparation process?

P

can be done
efficiently

by P using
polynomial
number of single qubit & controlled
-
2 qubit

gates






Polynomial Preparation Theorem

Controlled

Rotation gates

Hadamard

gates

64
rotations

4

rotations

(Reduce
75%)

Classical Image Compression

Reduce computational resource

(
memory
) [JPEG]

Quantum Image Compression

Reduce computational resource

(
basic operations
)

Build Boolean Terms

A same color group

Image Processing Operators on Quantum Images

-

Invertible

(expressed in unitary form)

-

Some
classical

operators are
not invertible

[Lomont,2003]

P

n

0
0
Colors

Positions

U

Preparation

Image processing operators




P


U


Shifting Color

(Rotation)




P


U


Changing Color

at some positions

(Controlled
-
Rotation)




P


U



Fourier Transform


(Quantum Fourier
Transform)

Type I

Type II

Type III

Proposed

Colors

&

Positions

Flexible Representation of Quantum Images

1

Polynomial Preparation Theorem

2

Proposed

old

new

Quantum Image Compression

3

QIC

Build Boolean
Expression

Minimize Boolean
Expression

Output minimized

Boolean Expression

End

Proposed

Polynomial Preparation Theorem

QIC

Quantum Image Processing Operators

4

FRQI

Proposed

Quantum Image Processing Operators

Experiments on Quantum Images

5

Retrieving Quantum Images

Measurements


Probability Distribution

Probability Distribution


estimate Theta(i)

Theta(i)


Image


Polynomial

Preparation


Invertible

Image Processing Operators


3 Types



Reduce

basic gates used in preparation


6.67% ~ 31.62%

Flexible Representation of Quantum Images

Quantum Image Compression

Conclusions

6

FRQI

Polynomial Preparation Theorem

QIC

Image Processing Operators

QIC

6.67% ~ 31.62%

Storing Quantum Images

Gray Image


Theta(i) (Angles encoding colors)

Theta(i)


Controlleded Rotations

Hadamard & Controlled Rotations


Quantum State

Simple line detection

on binary image

using the operator in
type III


with
quantum Fourier transform




P


U


Type III

Flexible Representation of Quantum Images

& its Computational Complexity Analysis

Le Quang Phuc

phuclq@hrt.dis.titech.ac.jp