The Study Of Quantum Algorithm And Qauntum Simulation Based On Non-unitary Evolution

Quantum computing is a kind of information processing mode,which is based on quantum mechanics,that exploits unique quantum mechanical properties mainly containing quantum superposition and quantum entanglement to realise calculation task.Quantum computer can process quantum information and the quantum super parallel property provides more powerful data processing capabilities than classical computers.Utilizing quantum computer,we can accelerate the classical algorithm,the famous Shor's factoring algorithm and Grover's searching algorithm which gains exponential speedup and square order speed-up respectively exhibit the significant advantage of quantum computing completely.The traditional quantum computing is through the unitary evolution to process information,a calculation process corresponding to a closed quantum system evolution.Compared with traditional computing mode,duality quantum computing handle information through non-unitary evolution with a certain probability in the form of a linear superposition of unitary operator.It extends the methods to construct quantum algorithms.This paper focus on the new quantum algorithms based on non-unitary evolution.The content is listed as following.· Realizing Childs' algorithm and Berry's algorithm which are non-unitary evolutionalgorithms based on linear combination of unitary operations by duality quantumcomputing.The completely and standard quantum circuit is given,which providethe experiment scheme to prove the algorithm.· Proposing a duality quantum algorithm for simulating Hamiltonian evolution of anopen quantum system.Open quantum system inevitable coupled with the environ-ment can be described by the evolution of density matrix and the environment effectcan be expressed by Kraus operators.By constructing non-unitary Kraus opera-tors and approximation of truncated Tylor series,the duality quantum computingalgorithm described open quantum system is realized.Compared with traditionalunitary algorithm,the complexity is decreased and efficiency is improved.· Designing and performing experimental schemes to realise three quantum channelsin nuclear magnetic resonance platform.Furthermore,proposing the algorithm ofuniversal quantum channels in arbitrary dimension and performing it on IBM cloud quantum computer in two dimension case.