Quantum Many-Body Equilibrium And Non-Equilibrium Problems In Superconducting Quantum Simulation

Due to the exponential growth of the Hilbert space,the quantum many-body problem is highly complex and difficult to study,especially for strongly correlated systems.Currently,there is no general theory or numerical method to deal with it.The research of quantum many-body physics is the basis of many breakthrough types of research,such as the mechanism of high-temperature superconductivity,quantum computing,quantum information and quantum gravity,etc.As a way of using quantum resources to study quantum physics,the quantum simulation itself utilizes the quantum superposition effect,which is expected to realize the effective simulation of quantum many-body physics.At this stage,quantum control technology is developing rapidly.At present,rapid development in quantum control technology has led to a variety of platforms for simulating physical systems based on cold atoms,ion traps and superconducting qubits showing great potential and application prospects.Among them,superconducting quantum circuits have become the main platform for quantum simulation due to their high scalability and controllability.Superconducting quantum chips with different topological structures can not only be used to directly simulate non-equilibrium dynamics of various quantum many-body models,but also to study equilibrium physics through variable quantum algorithms.This paper first introduces some background knowledge,including the basic principles of superconducting quantum circuits and some important concepts in quantum non-equilibrium dynamics.Our work then focuses on simulating the equilibrium and non-equilibrium states of quantum many-body systems using superconducting qubit systems.A new type of localization phenomenon has been discovered in recent simulation experiments of superconducting quantum ladders,but its mechanism has not been well explained.In the first work,we conducted an in-depth theoretical study of this phenomenon,revealing that the localization originates from the zero-energy flat band,and that the formation of the flat band is caused by a new mechanism.In the third work,we mainly use superconducting quantum devices and variational quantum algorithms to prepare finite temperature equilibrium states.Most of the current experimental work focuses on the preparation of the ground state of the quantum system,while for the thermal state and highly excited state,the preparation is more challenging in the experimental realization.Our work prepares the thermal state of 5 qubits on a quantum device,which is the largest thermal simulation to date.Furthermore,we demonstrate for the first time the preparation of all excited states of the system using aIn the second work,we propose a disordered fully connected model with a fast scrambling phenomenon.Most previous works of fast scrambling depend on the semiclassical limit.Through the numerical simulation using large-scale tensor networks,we obtained the fast scrambling in the quantum model that does not depend on the semi-classical limit.In addition,there are few studies on the many-body localization phenomenon of quantum models.By studying the energy spectrum and entanglement entropy of the system,we obtained the many-body localization phase transition in quantum models for the first time.quantum computer.Our work demonstrates the great potential of superconducting quantum platforms by studying the many-body problem in superconducting quantum simulations and also lays the foundation for using superconducting quantum simulations to solve major and breakthrough physical problems.