Quantum Computing Based On Quantum Walk

Quantum computing can efficiently solve many complex computational prob-lems,so many people studied it in recent years.Quantum walks are quantum ana-logues of the classical random walk.It can be used to design quantum algorithms.In the system of quantum walk,unitary operator plays an important role in the evolution of quantum states.The unitary operator acting on the state vector space is equivalent to the matrix.Unitary operator can also be expressed as the form of outer product in quantum mechanics.When the unitary operator is expressed as the form of outer product,the computation in the evolution of quantum system is simple.When we choose the suitable base vectors in the state vector space,unitary operator can be expressed as the form of outer product that is simple and convenient to calculate.In this paper,we give the outer product of unitary operators in the new base vectors of the state vector space,and give some applications in quantum ensemble.We also discuss the state of some open quantum system expressed by operator sum in the physical realization of quantum computation.