Hardware

1
Flexible Representation of Quantum Images its
Computational Complexity Analysis
Le Quang Phuc phuclq_at_hrt.dis.titech.ac.jp
Quantum Image Compression Reduce computational
resource (basic operations)
Classical Image Compression Reduce computational
resource (memory) JPEG
What we need Image Representation
Qubit Lattices Venegas-Andraca, 2003
QIC
Proposed
Real Ket Latorre, 2005
A same color group
Do not provide Preparation procedures Image
Processing Operators
Polynomial Preparation Theorem
Build Boolean Terms
Hardware Quantum Computer Faster
64 rotations
Build Boolean Expression
Feynman, 1982 Shor, 1994
old
QIC
Minimize Boolean Expression
(Reduce 75)
new
Output minimized Boolean Expression
Colors Positions
Colors
Positions
FRQI
4 rotations
End
N No. of positions K - Constant
Proposed

• Image Processing Operators on Quantum Images
• - Invertible (expressed in unitary form)
• Some classical operators are not invertible
  Lomont,2003

Complexity of the preparation process?
Turn it on
FRQI
Quantum Image Processing Operators
Proposed
Colors
U
Type I
Positions
Type II
Preparation
Image processing operators
Type III
Polynomial Preparation Theorem
can be done efficiently by P using polynomial
number of single qubit controlled-2 qubit
gates
Proposed
Controlled Rotation gates
Hadamard gates
Retrieving Quantum Images Measurements ?
Probability Distribution Probability Distribution
? estimate Theta(i) Theta(i) ? Image
Storing Quantum Images Gray Image ? Theta(i)
(Angles encoding colors) Theta(i) ? Controlleded
Rotations Hadamard Controlled Rotations ?
Quantum State
FRQI
Flexible Representation of Quantum Images
QIC

• Polynomial Preparation
• Invertible Image Processing Operators
• 3 Types

Polynomial Preparation Theorem
Image Processing Operators
Simple line detection on binary image using the
operator in type III with quantum Fourier
transform
Type III
QIC
Quantum Image Compression
6.67 31.62

• Reduce basic gates used in preparation
• 6.67 31.62