Application Of Quantum Simulation And Quantum Algorithm In The Superconducting Quantum System

Quantum computing has attracted the attention of researcher in recent years,since it can not only be used in studying fundamental quantum mechanics,but also has great potential power in solving specific problems.Superconducting quantum computing has become one of the most promising candidate to realize the quantum computing because of the stability in manipulation and scalability.Josephson junction is the ba-sic component in the circuit of superconducting qubit.As the development of Circuit Quantum Electrodynamics,using the microwave resonator coupled with the supercon-ducting qubit become a popular readout scheme.This scheme can both increase the decoherence time and improve the signal-to-noise ratio of the measurement,which play an important role in most experiment.As the great difficulty to realize the uni-versal quantum computing,the main directions at present in superconducting quantum computing include quantum error correction schemes,quantum simulation,quantum annealing and so on.Also,some researchers have proposed to firstly use the quantum system to solve specific problems,which can achieved the goal of' quantum suprema-cy'.This thesis mainly study the measurement and manipulation of superconducting qubit and apply the superconducting qubit to realize certain quantum simulation and quantum algorithm.The first two chapters of the thesis is an introduction of the theory in supercon-ducting quantum computing.Firstly,I introduce the basic concepts of the quantum computing and the possible application of quantum computing,including some quan-tum algorithms and quantum simulation.Then move to the superconducting quantum computing.The basic component in superconducting quantum circuit is Josephson juc-tion and LC oscillator.There are three types of superconducting qubit:charge qubit,flux qubit and phase qubit.In this thesis,the experiment is conduct on the transmon qubit which is a improved version of charge qubit.The end of this part is the Circuit Quantum Electrodynamics in the system of superconducting qubit coupled with res-onator.It includes the theory of Cavity Quantum Electrodynamics and the introduction of some experimentally used microwave resonators.The next part is about the manipulation and measurement of superconducting qubit.The experimental setup can be divided into two part.One part is the low temper-ature setup in a dilution refrigerator and the other is the room temperature setup.Then I introduce the characterization of a superconducting qubit.The characterization ex-periment includes the spectroscopy measurement,Rabi oscillation,energy relaxation,Ramsey interference,spin-echo,quantum state tomography and so on.In the chapter 4 and chapter 5,I demonstrate the application of superconducting qubit,including quantum simulation and quantum algorithm.In the quantum simu-lation experiment,by using bichromatic driving,we can engineer the desired effec-tive Hamiltonian to simulate the semi-classical Rabi model.This method provides an easy way to study the dynamics of the general semi-classical Rabi model in the strong driving regime.In the quantum algorithm part,I demonstrate the experimentally re-alization of quantum permutation parity determination algorithm in a superconducting qutrit,which realize a two to one speed-up towards classical case.