Quantum Simulation With External Drives In Superconducting Circuits

Recently,quantum simulation based on superconducting circuits has attracted much attention due to their unique advantages.In this thesis work,we study nonequilibrium dynamics via quantum simulation in a superconducting 10-qubit chain under external driving.Superconducting qubits have multiple energy levels and coupled qubits are governed by the Bose-Hubbard model.Applying an external driving can further ma-nipulate the Hamiltonian so specific system properties can be investigated.For exam-ple,with longitudinal-field driving,the strength and phase of the qubit coupling can be tuned to realize time-reversed evolution of the system.On the other hand,the qubit chain becomes a controllable nonintegrable system under transverse-field driving,being chaotic and undergoing thermalization,which are of great significance for the studies of nonequilibrium dynamics of the system.After briefly introducing superconducting circuits,quantum simulation,and nonequilibrium dynamics of isolated systems,we will present an in-depth discussion on superconducting qubits and their controls,as well as the calibration and optimization of the system parameters.Further studies are divided into three parts and the results are summarized as follows:(1)Two-level approximation of transmon qubits:The hard-core boson and spin models based on the qubit two-level approximation are often used in the quantum simu-lation experiments.However,it is inevitable that the qubit two energy levels in compu-tational subspace has particle exchange with high-energy levels beyond the subspace.We calculate the fidelity that decays with time due to the state leakage to the qubit high-energy levels for two kinds of experiments with time reversal and time evolution in one direction,respectively.The results for different system Hamiltonians with various ini-tial state,qubit coupling strength,and external driving are presented,which provide precise estimates for the applicability of the qubit two-level approximation.(2)Longitudinal-field driving,Loschmidt echo,and mixed state:The Loschmidt echo is concerned with the time reversal of a quantum system,which has been widely used for the studies of quantum chaos,decoherence,and entanglement propagation.Us-ing the longitudinal-field driving,we successfully realize the time reversal and measure the Loschmidt echo for various initial states.After reducing the effect of qubit next-nearest-neighbour coupling,the fidelity decay with time can be fairly explained by the excitations of the qubit high-level states.We further measure the density matrices of the mixed states of the subsystems with different qubit numbers,decompose them into pure states and analyse the time dependence of their eigenvalues.We find that the number of the pure states obtained from mixed state decomposition with probability larger than1/9)~2(n is the dimension of the subsystem state space)is proportional to the square root of time,typical of a diffusion process.The diffusion coefficient is found to increase with the increasing particle number.This result is important for the further study of the mixed states.(3)Transverse-field driving,nonintegrable system,and thermalization:In the quan-tum simulation experiments,the initial states are usually prepared in the two-level sub-space.In this case,the high-level excitations are relatively low and the system described by the Bose-Hubbard model is nearly integrable.When the system is applied with mi-crowave driving,the system becomes nonintegrable.The key point of the experiment is the calibration and elimination of the microwave crosstalk among the qubit control lines.We propose a convenient method to determine the crosstalk matrix and demon-strate that the microwave crosstalk can be reduced by 2 to 3 orders for a superconducting qubit chain with large crosstalk amplitudes and variations.Based on this,we success-fully observe the thermalization phenomena in the nonintegrable chaotic system with excellent agreement between experiment and theory.Our results provide a useful and realistic starting point for the further studies of the nonequilibrium dynamics in quantum many-body systems.