a Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China; b College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China
Abstract Vector quantization (VQ) is an important data compression method. The key of the encoding of VQ is to find the closest vector among N vectors for a feature vector. Many classical linear search algorithms take $O(N)$ steps of distance computing between two vectors. The quantum VQ iteration and corresponding quantum VQ encoding algorithm that takes $O(\sqrt N )$ steps are presented in this paper. The unitary operation of distance computing can be performed on a number of vectors simultaneously because the quantum state exists in a superposition of states. The quantum VQ iteration comprises three oracles, by contrast many quantum algorithms have only one oracle, such as Shor's factorization algorithm and Grover's algorithm. Entanglement state is generated and used, by contrast the state in Grover's algorithm is not an entanglement state. The quantum VQ iteration is a rotation over subspace, by contrast the Grover iteration is a rotation over global space. The quantum VQ iteration extends the Grover iteration to the more complex search that requires more oracles. The method of the quantum VQ iteration is universal.
Received: 10 May 2005
Revised: 15 September 2005
Accepted manuscript online:
PACS:
03.67.Lx
(Quantum computation architectures and implementations)
(Entanglement measures, witnesses, and other characterizations)
Fund: Project supported by the National Fundamental Research Program of China (Grant No 2001CB309300), the Innovation Funds of the Chinese Academy of Sciences and the Fundamental Research of Sichuan Normal University (Grant No 037003).
Cite this article:
Pang Chao-Yang (庞朝阳), Zhou Zheng-Wei (周正威), Chen Ping-Xing (陈平形), Guo Guang-Can (郭光灿) Design of quantum VQ iteration and quantum VQ encoding algorithm taking $O(\sqrt N )$ steps for data compression 2006 Chinese Physics 15 618
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