The Research Of The Geometric Quantum Computing Scheme Based On Decoherence Free Subspace

The quantum computer has the ability to massively parallel computing,for the sake of that the quantum bit with the superposition state.Compared with the classical computer,the quantum computer has a huge advantage faced with some specific problems which include the problem of the factorization of large number.Therefore,quantum computation is one of the hot spots.In order to ensure than the information in the quantum computation remain the same,the evolution of the coding state of the quantum physical system must be unitary evolution.The evolution of the quantum state of an isolated system is unitary.In the fact,the quantum system will inevitably interact with the environment,so,the unitary evolution of the encoding mode will be destroyed and the information on the quantum state will change.the process is named by the coherent process.The cancellation effect of quantum system is the biggest obstacle to realizing quantum computation.In order to maintain the coherence of the coding state,the scientists introduced the quantum error correction codes.However,the quantum error correcting codes introduce redundancy,and the evolution of the coding state becomes more complicated and indirectly increases the chance of error.Therefore,the quantum system itself should b-e capable of fault tolerance,which is the point of this paper.The main contents of this paper can be summarized as follows:Firstly,the article introduces the nature of Berry phase in detail.The size of Berry's phase is completely determined by the geometrical properties of the curved surface of the closed path,which has nothing to do with the speed of the evolution of quantum states.Therefore,geometric quantum computation is not sensitive to some random fluctuation of the environment,which has certain inherent fault tolerance.Then the properties of the coherent subspace and the characteristics of the quantum physical system are introduced.Secondly,in the paper,we could find a two-dimensional decoherence free subspace in four-qubit system.Meanwhile,the geometric quantum bit could be constructed in this decoherence free.The coherence effect of quantum states is minimized in theory.