Simulating Ground State Of Many-body Spin Systems On Digital Quantum Simulator

Most of the features of the complex system can be understood as the collective be-havior of multiple particles,namely many-body systems.Low-energy states,especially the ground state,properties are of high importance in physics as they are responsible for phenomena such as magnetism,molecular formation,and the emergence of a new phase of matter.Meanwhile,many-body spin system,as a class of many-body systems,has been one of the key research object in both condensed matter physics and quantum in-formation.Due to the exponentially large requirement of resources,it is intractable for a classical computer to simulate the quantum behavior of many-body spin systems.The exploitation of a relatively controllable quantum system,the so-called quantum simula-tor,is the ultimate solution of emulating the behavior of the complex system of interest.The two different approaches for implementing quantum simulators are analog and dig-ital.Analog quantum simulator is not universal,in the sense that only limited types of unitary operations can be implemented.In contrast,the capability of performing any type of unitary operation is the main advantage of a digital quantum simulator.Traditionally,in an analog sense,adiabatic evolution has been proposed to slowly evolve a simple Hamiltonian,initialized in its ground state,to the Hamiltonian of inter-est such that the final state becomes the desired ground state.However,one will need to exploit the Suzuki-Trotter expansion in order to implement the adiabatic evolution in a digital quantum simulator.This demands high-quality hardware and a huge number of quantum resources which cannot be achieved in existing noisy intermediate-scale quan-tum simulators where simulators are still noisy and with a limited size.Therefore,a hy-brid variational method,called variational quantum eigensolver(VQE),has already been proposed to simplify the quantum hardware at the price of the addition of a classical op-timizer.In this thesis,I will compare the performance of both the adiabatic method and the variational method in the digital quantum simulator.Besides,I will introduce a series of research results on optimizing the variational quantum eigensolver.The main contents are:1.I first provide a quantitative comparison in terms of the required quantum re-sources in simulating ground state of many-body spin systems on digital quantum simula-tors,namely the depth of the circuit and the number of two-qubit quantum gates,between the adiabatic evolution and hybrid variational method.Our simulation results show that the required resources of the hybrid variational method are much less than the adiabatic evolution.Nonetheless,classical optimization,which is the essential component in the hybrid method,will be a drawback with slow convergence.2.I developed two different strategies to improve the speed of convergence of the classical optimizer.These methods intend to start the optimization procedure with a better choice of initial parameters of the variational circuit.I presented the numerical simula-tion result of a wide range of Hamiltonian which proved that the accelerate strategies are general for many-body spin system ground state preparation and indeed can improve the optimization of the hybrid method.