Quantum Simulation On Superconducting Circuits

In recent years,using artificial quantum systems to simulate quantum many-body physics,termed quantum simulation,has attracted great research interests.As a type of synthetic quantum system,the superconducting circuit has the advantages of good scalability,long coherence time,and flexible control with high precision.Therefore,superconducting circuits are considered to be one of the most competitive candidates for achieving universal quantum computation,and multi-qubit superconducting circuits are also an excellent platform for performing quantum simulations.This thesis mainly focuses on the quantum simulation based on multi-qubit superconducting processor.In the first part,we mainly review the basic knowledge of superconducting quan-tum circuits,including the implementation,control,readout,coupling and integration.Through the introduction of these basic knowledge,we can understand the advantages of superconducting circuits.Meanwhile,it also lays a theoretical foundation for the following specific quantum simulation works on superconducting circuits.In the second part,we study the dynamics of the Bose-Hubbard ladder model,especially the dynamics of the double-boson system.Through analytical and numerical calculations,it is found that there exists a novel localization mode of boson pairs in the system,which is induced by strong on-site interactions and special lattice symmetries.Then,we present an experiment about simulating the dynamics of the Bose-Hubbard ladder model in a 24-qubit ladder-type superconducting processor.In this experiment,we observed the above phenomenon of the boson-pair localization.In the third part,we introduce quantum simulations of Bloch oscillations and Wanier-Stark localizations in one-dimensional superconducting circuits.In this experiment,we firstly use the single qubit readout to show that the spin exhibits localization under the linear potential.Furthermore,we also study the heat transport of the system by using the joint readout of two qubits.Experimental results show that the kinetic energy transport is also suppressed under the linear potential.In the fourth part,we discuss how to use superconducting quantum circuits to ap-proximate the one-dimensional(Z₂lattice gauge theory.We construct a special effec-tive Hamiltonian based on a one-dimensional superconducting quantum circuit.The Hamiltonian consists of a(Z₂lattice gauge theory and a gauge-broken term.Then,the ground-state and dynamical physics of this effective model are systematically studied.Through numerical calculation,we find that,although the effective model itself has no gauge invariance,(Z₂ gauge structure can still emerge in the ground state and is in the confined phase under the strong transverse field.Moreover,the physics of the confine-ment can also be represented by dynamics,which is expected to be observed in the future quantum-simulation experiments.In the fifth part,we give a brief introduction of other two types of special quantum many-body systems,i.e.,the non-hermitian topological band system and the mang-body localized system.Here,we understand the non-hermitian topological band theory main-ly through the Dirac equation and the conservation current equation,and understand the many-body localization through the many-body eigenstates.Our work,on the one hand,has a certain enlightenment to the understanding of quantum many-body physics,specifically the non-equilibrium dynamics.On the oth-er hand,it also lays a foundation for further large-scale quantum simulation based on superconducting quantum circuits in the future.