Research On Preparation Of Pseudo-pure States In Nuclear Magnetic Resonance Systems

With the rapid development of quantum mechanics and information technology,quantum computing which is a new computing model has caused important changes in our world.Based on the characteristic trait of quantum entanglement,the computing capability of quantum computing could far exceed that of classical computers on some specific problems.Among the numerous candidate schemes to realize quantum computation,the nuclear magnetic resonance(NMR)system has many advantages.Lots of quantum algorithms and simulations have already been completed on this platform.Considering that NMR quantum computation belongs to ensemble quantum computation,it adopts the method of pseudo-pure states in the process of quantum state preparation.The existing schemes for preparing pseudo-pure states include temporal averaging,spatial averaging,logical labeling and the cat-state method.However,these methods all have inevitable disadvantages,such as time consumption caused by an exponential number of experiments,signal attenuation caused by the frequent use of gradient fields,and waste of qubit resources caused by a lot of ancillary qubits.Therefore,more efficiently to prepare pseudo-pure states with high fidelity is the key to complete the NMR quantum computing experiments.The thesis focuses on the research about the preparation of pseudo-pure states in NMR system.The relevant research works can be summarized as follows: Chapter 1provides a briefly introduction to the development course and basic principles of quantum computing.Chapter 2 focuses on the realization of NMR quantum computing and some related technologies.Then a summary of the existing pseudo-pure state preparation schemes and their characteristics is given in Chapter 3.The main achievements of this thesis are in Chapter 4.We propose a new algorithm for preparing the pseudo-pure states called the one-step method and we use only one experimental round,one ancillary qubit,and one gradient field regardless of the size of the quantum system,which results in our scheme obtaining a better overall performance compared to previous methods.At the same time,we present a general quantum circuit corresponding to this method.Through the exponential simulation scheme and the polynomial simulation scheme,we give the specific complexity of the quantum circuit respectively.The results show that the circuit complexity of this method can be described as polynomial complexity,even though the number of system qubits is sufficiently large.Then we compare this method with the other schemes and summarize corresponding advantages in terms of the number of experimental acquisitions,the form of the obtained pseudo-pure states,the restriction of the molecular structure,and the signal intensity of NMR experiment.As a proof-ofprinciple demonstration,we experimentally implement the scheme in a four-qubit NMR system.The experimental results obtained by quantum state tomography are completely consistent with the theoretical results.And the pseudo-pure states in the two corresponding subspaces both have high fidelity.Finally,we simulate the robustness of the scheme in a noisy environment.Simulation results show that the scheme is still very robust under certain noisy environment.