循环群状态空间中的量子搜索过程
Quantum search processes in the cyclic group state spaces
摘要：
标准量子搜索算法难以解决非结构化量子搜索问题的主要原因是，与其他已知量子操作相关联的oracle幺正操作对标记态的振幅放大效率较低。为了绕过标准量子搜索算法的平方加速比限制，有必要开发其他类型的量子搜索算法。本文详细介绍了一种解决循环群状态空间中量子搜索问题的量子动力学方法。将n比特量子系统的希尔伯特空间中量子态的二元动力学表示推广到循环群状态空间中量子态的多基动力学表示.因此，循环群状态空间中的任何量子态都可以用一组与循环群的对称性和结构密切相关的动力学参数来描述。因此，量子搜索问题可以通过确定完全描述搜索问题的未知标记状态的动力学参数集来解决，而不是通过直接测量标记状态来解决，这是标准量子搜索算法中的必要步骤。希尔伯特空间中的非结构量子搜索问题不可避免地受到群的对称性和结构的影响。本文的主要尝试是利用群的对称性质和结构来解决群状态空间中的量子搜索问题。在通用量子计算机上，利用循环群的对称性和结构，将量子搜索过程从循环群状态空间简化到这些循环群状态子空间.
英文摘要：
The hardness to solve an unstructured quantum search problem by a standard quantum search algorithm mainly originates from the low efficiency to amplify the amplitude of the marked state by the oracle unitary operation associated with other known quantum operations. In order to bypass the square speedup limitation of a standard quantum search algorithm it is necessary to develop other type of quantum search algorithms. It is described in detail in the paper for a quantum dynamical method to solve the quantum search problems in the cyclic group state space. The binary dynamical representation for a quantum state in the Hilbert space of the n-qubit quantum system is generalized to the multi-base dynamical representation for a quantum state in the cyclic group state space. Thus, any quantum state in the cyclic group state space may be described completely in terms of a set of dynamical parameters that are closely related to the symmetric property and structure of the cyclic group. The quantum search problem therefore could be solved by determining the set of dynamical parameters that describe completely the unknown marked state of the search problem instead by directly measuring the marked state which is a necessary step in the standard quantum search algorithm. An unstructured quantum search problem in the Hilbert space is inevitably affected greatly by the symmetric property and structure of a group. The main attempt of the paper is to make use of the symmetric properties and structures of groups to help solving the quantum search problems in the group state spaces. It is shown how the quantum search process could be reduced from the cyclic group state space to these cyclic group state subspaces with the help of the symmetric property and structure of the cyclic group on a universal quantum computer.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
