Quantum Representation and Basic Operations of Digital Signals

This paper presented a quantum representation and some basic operations for one-dimensional finite length digital signal. For the representation, similar to the existing flexible representation of quantum audio (FRQA), two sets of qubits are used to represent the amplitudes and positions of the signal, respectively, wherein the amplitude is represented by an (n + 1)-bit signed number in twos complement, including one sign bit, m integer bits and n − m fractional bits. The basic operations include the addition, subtraction, multiplication, division, and circular convolution of two digital signals. We designed the quantum circuits that implements these basic operations, analyzed the computational complexity, and verified the correctness of these circuits by simulations on classical computers.

[1]  Changxing Pei,et al.  Faithful qubit transmission in a quantum communication network with heterogeneous channels , 2018, Quantum Inf. Process..

[2]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[3]  Abdullah M. Iliyasu,et al.  Exploring the Implementation of Steganography Protocols on Quantum Audio Signals , 2018 .

[4]  Nan Jiang,et al.  Quantum Image Location , 2016 .

[5]  Nan Jiang,et al.  LSB Based Quantum Image Steganography Algorithm , 2015, International Journal of Theoretical Physics.

[6]  Nan Jiang,et al.  Quantum image translation , 2015, Quantum Inf. Process..

[7]  Lijiang Chen,et al.  SQR: a simple quantum representation of infrared images , 2014, Quantum Information Processing.

[8]  Nan Jiang,et al.  The quantum realization of Arnold and Fibonacci image scrambling , 2014, Quantum Inf. Process..

[9]  Kaoru Hirota,et al.  A FRAMEWORK FOR REPRESENTING AND PRODUCING MOVIES ON QUANTUM COMPUTERS , 2011 .

[10]  Simona Caraiman,et al.  Image segmentation on a quantum computer , 2015, Quantum Information Processing.

[11]  Kaoru Hirota,et al.  Watermarking and authentication of quantum images based on restricted geometric transformations , 2012, Inf. Sci..

[12]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[13]  Abdullah M. Iliyasu,et al.  A Multi-Channel Representation for images on quantum computers using the RGBα color space , 2011, 2011 IEEE 7th International Symposium on Intelligent Signal Processing.

[14]  Chris Lomont.  Quantum convolution and quantum correlation algorithms are physically impossible , 2003 .

[15]  Fei Yan,et al.  A survey of quantum image representations , 2015, Quantum Information Processing.

[16]  Kaoru Hirota,et al.  A Flexible Representation and Invertible Transformations for Images on Quantum Computers , 2011 .

[17]  Chris Lomont,et al.  Quantum image processing (QuIP) , 2003, 32nd Applied Imagery Pattern Recognition Workshop, 2003. Proceedings..

[18]  Ping Fan,et al.  Quantum image Gray-code and bit-plane scrambling , 2015, Quantum Information Processing.

[19]  Sougato Bose,et al.  Storing, processing, and retrieving an image using quantum mechanics , 2003, SPIE Defense + Commercial Sensing.

[20]  Nan Jiang,et al.  Quantum image pseudocolor coding based on the density-stratified method , 2015, Quantum Inf. Process..

[21]  Ri-Gui Zhou,et al.  Quantum Image Encryption and Decryption Algorithms Based on Quantum Image Geometric Transformations , 2013 .

[22]  Kai Xu,et al.  Local feature point extraction for quantum images , 2015, Quantum Inf. Process..

[23]  Kaoru Hirota,et al.  A flexible representation of quantum images for polynomial preparation, image compression, and processing operations , 2011, Quantum Inf. Process..

[24]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[25]  Huamin Yang,et al.  Flexible representation and manipulation of audio signals on quantum computers , 2017, Theor. Comput. Sci..

[26]  Li Shan-zhi,et al.  Design of Quantum Comparator Based on Extended General Toffoli Gates with Multiple Targets , 2012 .

[27]  Kai Lu,et al.  NEQR: a novel enhanced quantum representation of digital images , 2013, Quantum Information Processing.

[28]  Jian Wang,et al.  Quantum image matching , 2016, Quantum Inf. Process..

[29]  Fei Yan,et al.  An RGB Multi-Channel Representation for Images on Quantum Computers , 2013, J. Adv. Comput. Intell. Intell. Informatics.

[30]  Fei Yan,et al.  Quantum image rotation by an arbitrary angle , 2017, Quantum Inf. Process..

[31]  Naoki Yamamoto,et al.  Entanglement-assisted quantum feedback control , 2015, Quantum Inf. Process..

[32]  Abdullah M. Iliyasu,et al.  Fast Geometric Transformations on Quantum Images , 2010 .

[33]  Rubens Viana Ramos,et al.  Quantum-chaotic cryptography , 2018, Quantum Inf. Process..

[34]  Fei Yan,et al.  Quantum image processing: A review of advances in its security technologies , 2017 .

[35]  Jian Wang,et al.  QRDA: Quantum Representation of Digital Audio , 2016 .

[36]  José Ignacio Latorre,et al.  Image compression and entanglement , 2005, ArXiv.

[37]  Bo Sun,et al.  A duple watermarking strategy for multi-channel quantum images , 2015, Quantum Inf. Process..