量子算法及其在图像处理中的应用

Quantum Algorithm and Its Application to Image Processing

量子计算与量子信息是涉及物理学、计算机科学、数学以及信息科学等多个学科的新兴综合性交叉研究领域,是量子力学理论和经典计算理论完美结合的产物.由于其强大的计算能力及广阔的应用前景,使得其在国际学术界以及政府科研机构中引起巨大的兴趣.在量子计算的研究中,计算性能的优越性主要体现在算法的有效性上.目前为止,被公认的最具代表性的量子算法有Shor的大数质因子分解算法以及G rover提出的数据库搜索量子算法.集合运算是科学技术很多领域的基础,如数据库操作、信号处理、图像压缩等等都可最终归结为对集合的操作.但是对于包含了高维无序向量的集合,要对其进行有效快速的集合运算,在经典电子计算机上是困难的.因此,需要新的原理和新的算法来有效操作集合.量子图像处理(QIP)就是利用量子计算机来处理图像信息从而希望获得比电子计算机更好的处理效果.量子图像处理研究才刚刚起步,在不久的将来可能会成为一个受关注的研究热点.对目前的量子算法研究进展、量子集合运算、量子图像处理以及量子Hopfield神经网络研究作一个综述性论述.

Quantum computation and quantum information is a new research field and interdiscipline of physics, mathematics, computer and information sciences. It is a wonderful combination of the theory of quantum mechanics and classical computation. It has been concerned by many national governments and research groups. Algorithm is the kernel of classical computation as well known, and this situation is the same to quantum computation. Currently, the most representative algorithms are only two. One is Shor＇ s algorithm. The other is Grover＇ s algorithm. The fast computation of set operation is very important, and it is the base of many aspects of sciences and techniques, such as database operation, image processing, signal processing. But, for the set with high-dimension unsorted vectors, the classical electronic computer can do nothing for the requirement of fast computation. Therefore, the new computation principle and new algorithm will be needed for set operations. Quantum image processing is a progress that uses quantum computer to process image and wants to get a better result than that of the electronic computer. It is a new born topic, which will be a hot research topic in the future. This paper presents a comprehensive statementabout quantum algorithm, quantum set operation, quantum image processing and quantum Hopfield neural network.