Research On Remote Preparation Of An Arbitrary Two-Qubit State And Optimal Control Of Quantum Logical Gates

The research about the quantum world is the theme of the 21 th century.In recent decades,with the ultimate goal is to achieve quantum computer and long-distance absolutely secure quantum communication,quantum information have gained the attention of many researchers in related fields all over the world,and achieved rapid development and great success.In the field of quantum communication,quantum teleportation(QT)and remote state preparation(RST)have been widely studied as the important quantum communication protocols.The purpose of both protocols is to prepare the initial state from sender to receiver by using the quantum entanglement channel and classical communication.In QT,the information of initial state is unknown for the sender,but in RST,the sender is completely aware of the information of initial state.Then Joint-RSP protocol emerges,in which the senders can share the information of the quantum state.At the same time,the quantum communication process is inevitably affected by the surrounding environment,so it is important to study the influence of quantum noise during quantum communication.In the field of quantum computation,quantum computing has the great advantage of parallelism,which can solve the problems in the field of classical computing.The key element of quantum computing is quantum bits,and the quantum computer composed of quantum bits is essentially different from the classical computer composed of classical bits.Quantum computers mainly rely on the realization of quantum logic operations and quantum algorithms to achieve the purpose of controlling the evolution of quantum systems.In recent years,it has become an important issue to study different physical systems in which quantum information carriers can perform quantum computation.The polar molecular system is regarded as one of the effective physical systems for implementation quantum computing with permanent electric dipole moment,Strong dipole-dipole interaction and diverse energy structures,for example,electronic states,vibrational states and long-life rotational states.The main ideas of this thesis are: Based on two types of quantum communication RSP schemes,we design the quantum logic circuit via the basic quantum logical gates and discuss the influence of quantum noise on RSP;Based on two quantum optimization control methods,in specific molecular systems,we optimize single-and two-qubit logic gates with external control pulses.The main study of this thesis include the following aspects:1.Study on deterministic joint remote preparation of an arbitrary two-qubit state in noisy environments.Based on four Einstein-PodolskyRosen(EPR)states,we study the deterministic joint remote preparation of an arbitrary two-qubit state.We construct the corresponding quantum logic circuit for the deterministic JRSP protocol and the four EPR channels in the presence of several noises including bit-flip noise,dephasing noise,isotropic noise,as well as zero-and high-temperature environments.We analyze the average fidelity of out-put state and initial state for the deterministic JRSP under the influence of all the studied noises acting on the four EPR states.Our results show that the average fidelities have different evolution as function of time subjected to different noisy environments.For the limit of long time,the influence of the dephasing noise and the zero-temperature environment on the average fidelity is relatively small,while that of the isotropic noise and the high-temperature environment is relatively large.2.Study on deterministic remote state preparation of an arbitrary two qubit states in dissipative environments.We propose a deterministic remote state preparation protocol of an arbitrary two qubit states through two EPR states and two auxiliary bits and design the quantum logic circuit of the scheme.In this scheme,two EPR pairs and two classic bits can be saved.Then we consider the evolution of average fidelity of out-put state and initial state in dissipative environment.Our results show that the average fidelity gradually approaches a constant value as function of time in Markov environment,but the average fidelity is gradually changing to a fixed value with a certain degree of recovery in the non-Markov environment.In addition,it is found that,if the time is long enough,and the non-markovity and the parameter of detuning satisfy acertain value at the same time,the average fidelity can be kept close to the ideal value 1.3.Study on the single-qubit gates optimization in molecular rotational system.We analyze that the Multi-Constraint(MC)quantum optimal control theory is applied to optimize single-qubit gates in the molecular rotational system,and the fidelities are obtained as 0.9999 in both resonant and non-resonant cases.For the CO rotational system,it is found that the pulse intensity in the resonance case is smaller than that in the non-resonant case,but the phase is better maintained in the latter.In addition,we discuss the influence on the optimized pulse by the two constraints: pulse zero-area and constantfluence.In the structure of Hamiltonian based on Pauli operations,the test of ultra-fast pulse optimization is performed.It is found that the number of iterations in resonant case is less than that in the non-resonant case to reach the ideal value for the same pulse duration.4.Study on the two-qubit gates optimization in molecular pendular system.By applying Multi-Target(MT)and MC quantum optimal control theory,we optimize two-qubit logic gate in SrO pendular system.The results show that,in the case of resonance,the fidelity of optimization for two-qubit CNOT gate is around 0.97 in the MT optimal control theory,however,in the MC optimal control theory,both the fidelities for CNOT and SWAP can reach0.999,and the convergence speed is significantly faster than the former.MC optimal control theory is based on iteratively solving the unitary operator,and then it will act on any initial quantum state to obtain the ideal final state.In addition,we study the optimization of CNOT quantum logic gate by modifying MC theory in the non-resonant optimization.The optimization in non-resonant case requires stronger pulse strength than that in the resonance case.In addition,the optimized Code time in MC theory is ten to several tens of orders faster than the MT theory.The schemes of remote state preparation,the improvement of quantum optimization algorithm and some obtained results in this thesis are beneficial to deepen understanding of the transmission and loss of information in quantumcommunication protocols and the process of quantum logic gate optimization,and has certain guiding significance for the development of related experiments.