Quantum Simulation Of Many-body Quantum Systems And Its Physical Realization

In the past two decades,tremendous progress has been made in quantum technologies.In particular,the controllability,scalability and coherence of artificial quantum systems have seen a considerable improvement.Quantum simulation,as a process of employing artificial quantum systems to mimic other complex systems,has opened up new avenues of studying physical phenomena not accessible via other experimental methods.Quantum simulation has opened up completely new horizons for exploring and understanding non-equilibrium phases or dynamical processes of quantum many-body systems.Here,we mainly focus on how to use the quantum simulation to study emergent intriguing phenomena in the out-of-equilibrium dynamics of quantum many-body systems.We pay attention to the circuit consisting of superconducting qubits and the Rydberg atom arrays,being the physical systems that can realize the quantum simulation.In the first part,we mainly discuss the quantum thermalization and information scrambling.Making use of superconducting qubits,we realize the analog quantum simulation of strong and weak thermalization.By measuring the tripartite mutual information and entanglement entropy,we observe the signature of information scrambling and thermalization in the superconducting quantum circuit with ladder-type geometry,respectively.For the first time,our experiment characterizes the information scrambling via measuring the stable negative value of the tripartite mutual information during its time evolution.We then numerically study the dependence of information scrambling on strong and weak thermalization,revealing a close relationship between the dynamics of tripartite mutual information and the effective temperature of the chosen initial states.In the second part,we mainly discuss the analog quantum simulation of the transverse-field Ising model with infinite-range interactions by employing the superconducting quantum circuit with all-to-all connectivity,and the observation of dynamical phase transitions in this model.Moreover,we realize the analog quantum simulation of one-axis twisting.By measuring the spin-squeezing parameter and the Fisher information,we characterize the Gaussian spin-squeezed states and nonGaussian entangled states generated by the one-axis twisting.Finally,we innovatively design a variational spin-squeezing algorithm.By optimizing the variational parameters in the quantum circuit,the algorithm can generate a spin-squeezed state whose squeezing is stronger than the best squeezing generated from the one-axis twisting.In the third part,we present an analog quantum simulation of the mobility edge of many-body localization based on superconducting qubits.The innovation of the experiment lies in the generalization of the definition of imbalance,and further charactering the mobility edge via the non-equilibrium dynamics of the generalized imbalance,which directly corresponds to the analog quantum simulation.Next,we numerically simulate the non-equilibrium dynamics of diagonal entropy in many-body localized systems,and perform the finite-size scaling analysis of the data of diagonal entropy,obtaining the location of the critical point of the transition between quantum thermalization and the many-body localized phase.The numerical results about the diagonal entropy provide an experimentally feasible protocol for studying the manybody localization transition via the quantum simulation.Finally,we present an experimental scheme for studying the protection of the quantum order of ground states on the non-equilibrium dynamics by using the digital quantum simulation.In the fourth part,we study the variational quantum simulation based on the quantum approximate optimization algorithm.We numerically investigate the dependence of the performance of the algorithm for generating the ground states of quantum many-body systems and the Greenberg-Horne-Zeilinger state on the translational-invariant symmetry of the quantum circuit.We propose an improved quantum approximate optimization algorithm for the quantum simulators where the translational-invariant symmetry of the quantum circuit is absent.In comparison with the conventional quantum approximate optimization algorithm,the improved version can prepare the ground states of quantum many-body systems and the GreenbergHorne-Zeilinger state with higher fidelities.We also present an experimental scheme for realizing the improved quantum approximate optimization algorithm based on the Rydberg-dressed atoms.This work presents a series of experimental results of analog quantum simulations,and at the same time,performs numerical and theoretical studies of the non-equilibrium dynamics of quantum many-body systems.On the one hand,quantum simulation can provide experimental demonstration of the emergent non-trivial phenomena in out-ofequilibrium quantum matter,and on the other hand,the theoretical and numerical studies in this field can provide a source of inspiration for designing new protocols for quantum simulations of non-equilibrium phenomena.With the rapid development of quantum technologies,the digital and variational quantum simulation,with larger flexibility than the analog quantum simulation,can be experimentally realized,obtaining results with high accuracy.It is my expectation that more and more novel equilibrium quantum phases can be revealed,and challenging problems in this field can be solved via the quantum simulation.