Hardware Quantum Computer Faster

1. U P Shifting Color (Rotation) Quantum State U P Hardware Quantum Computer Image State Hardware Quantum Computer Initialized state Changing Color at some positions (Controlled-Rotation) P P P Fourier Transform (Quantum Fourier Transform) U U 2 1 3 6 5 4 Flexible Representation of Quantum Images Polynomial Preparation Theorem Conclusions Quantum Image Compression Experiments on Quantum Images Quantum Image Processing Operators Flexible Representation of Quantum Images& its Computational Complexity Analysis Le Quang Phuc phuclq@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 classicaloperators 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 • Storing Quantum Images • Gray Image  Theta(i) (Angles encoding colors) • Theta(i)  Controlleded Rotations • Hadamard & Controlled Rotations  Quantum State • Retrieving Quantum Images • Measurements  Probability Distribution • Probability Distribution  estimate Theta(i) • Theta(i)  Image 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%