Study On The Implementation Of Fixed-point Search Algorithm In Duality Computer And The Measure Of Coherence In Bloch Representation

The main studied content of this paper consists of two parts.Firstly,in 2009,Mizel introduced a dissipative assistant system to design a non-unitary fixed-point search algorithm with damping for quantum states,which cannot be easily implemented in ordinary quantum computer.Duality computer possess the powerful ability to allow the existence of non-unitary operations,and it can be simulated on ordinary quantum computer,which is called duality quantum computing mode.In this thesis,a scheme has been proposed to implement Mizel's fixed-point search algorithm in duality computer,and this can be theoretically simulated in an ordinary quantum computer by designing a specific duality quantum computing model and a cyclic computing model.In the scheme designed in this thesis,the recursions of the success probability and the failure probability of finding the target quantum state have obtained.The results show that the probability of search failure is close to zero with the increase of the number of the duality computing cycle,so,the probability is very high when the search is successful.The average numbers of the cycle are approximately 1.5 times of the optimal iteration of the Grover search algorithm.On the other hand,a rigorous framework that measure quantum coherence based on the superposition principle of quantum states has proposed by Baumgratz et al.in 2014.How to measure quantum coherence is recently one of the hot topics in the quantum resource theory.In this framework,the definition of quantum coherence measure requires the quantum state to be fixed on a particular basis in Hilbert space,and the result is that the coherence of the same quantum state will be changed under the same measure due to the transformation of the basis.In this thesis,a measure of coherence based on the normalized modulus of the coherent vector is proposed in coherent vector representation,where the property of the coherent vector under basis transformation is considered.The measure of coherence proposed here is independent of the choice of the basis.The incoherent states and incoherent operators based on this measure can also be well defined as the classical maximal mixed states and the unitary operators respectively.Three important properties can be obtained,namely,non-negativity,convexity and invariance on the incoherent operators.