Experimental Quantum Computation And Quantum Simulation Based On Nuclear Magnetic Resonance Technology

Quantum computing as an interdisciplinary research has attracted extensive atten-tions and research in recent years.It is based on the principles of quantum mechanics which is totally different from classical computation and has some unique properties including quantum entanglement and quantum state superposition.The ultimate goal of quantum computing research is to build a general computer based on quantum me-chanics,which can demonstrate the novel,unique and fast quantum properties.We are now in the Noisy Intermediate-Scale Quantum(NISQ)era.Nuclear Magnetic Res-onance(NMR)is one of the earliest and fastest quantum systems which is used for quantum computing.In the late 1990s,NMR began to be applied in the field of quan-tum computing.In NMR,spin-1/2 nuclei in a chemical molecule are used as qubits.Radio-frequency pulses can realize arbitrary single-qubit rotations on spins.Two-qubit quantum gates can be realized via the interaction between different nuclei.As a con-trolled quantum system based on nuclear spins,NMR has wide applications in quantum algorithm,quantum simulations and developments of quantum control techniques.This thesis focuses on characterizing and verifying the quantum system,and the ground state properties of a quantum system.The contents are as follows:1.The first chapter is the review of the background of quantum computing.Start-ing from the definition of qubit,the basic concepts of quantum computing are illustrated.Then several numerical methods used to simulate quantum circuits on classical computers are briefly introduced.2.The second chapter mainly introduces how NMR,a mature and widely used sys-tem in biology and medicine,is used in quantum computing experiments.Some commonly used pulse manipulation techniques are also reviewed in this part.3.Chapter 3 studies how to identify and verify an unknown quantum system.On the one hand,we use the quantum quench proposal to measure the scalar coupling constants in a 3-spin chain.This method only requires polynomial experimental measurement and computational complexity,while the traditional quantum pro-cess tomography need exponential resource consumption.On the other hand,The question"is it possible for a purely-classical client to verify the output of a quantum prover?”,that is,how to verify whether a black box has quantum prop-erty.The question has been extensively explored for more than ten years.We propose a quantum cryptography verification scheme for quantum cloud services,and conduct comparative experiments on IBM cloud server and NMR platform.4.Chapter 4 focuses on one of the important practical applications of quantum com-puter,called quantum simulation.We use the nuclear spins to simulate the physics of spin-boson systems,and study the properties of the ground state of the Dicke model.The experiment shows the quantum superradiant phase tran-sition of the ground state beyond the no-go theorem induced by anti-squeezing.And the ground state phase diagram modulated by the anti-squeezing effect is obtained.5.Chapter 5 is my conclusion and perspective.