Quantum Simulation Of Many-body System With Optical Method

A quantum many-body system refers to a microscopic system composed of a large number of particles.The precise solution of quantum many-body problems is an important topic in physics.The interactions between multiple particles make the system’s wave function contain a large amount of information,which makes classical computers unable to solve large-scale quantum many-body systems.Therefore,people have begun to seek new solutions,such as building quantum computers with quantum properties.Currently,in the laboratory,the manipulation of noisy intermediate-scale quantum(NISQ)systems has been achieved,but universal quantum computers are still far from being realized.Further research can be divided into two aspects:on the one hand,continuously improving the ability to control quantum systems to eventually achieve universal quantum computing;on the other hand,using existing NISQ systems to construct specialized quantum computers for specific many-body systems,namely quantum simulators.In quantum computing and quantum simulation,light plays a crucial role.Firstly,light is an important means of controlling quantum systems.Electromagnetic interaction is the main interaction in microscopic systems at the atomic scale,and photons are the medium for transmitting electromagnetic interaction.Thanks to the development of laser technology,people have achieved precise and rapid control of atoms and ions,thus developing quantum simulation experimental platforms such as neutral atom systems and trapped ion systems.Secondly,light is an excellent carrier for encoding quantum information.Photons have many degrees of freedom,such as frequency,polarization,orbital angular momentum,and spatial mode,providing rich choices for information encoding.Moreover,the interaction between photons and the environment is weaker than that of material quantum bits,so optical quantum bits are easier to maintain coherence and are very suitable as carriers for quantum information.Based on the two functions of optical methods in quantum simulation as a means of control and as a carrier of information,I have completed the following three works around the topic of solving quantum many-body systems:1.Using lasers and microwaves to manipulate the dynamics of ions,an experimental demonstration of quantum simulation of the slow quenching process in a one-dimensional transverse-field Ising model was performed,and the unique dynamic topological order parameter oscillation phenomenon in the slow quenching process was successfully observed.Using the change in the dynamic topological order parameter as a criterion for determining the occurrence of dynamic phase transitions,the occurrence of dynamic phase transitions was controlled by changing the quenching rate,which experimentally demonstrated that dynamic phase transitions also exist in the quenching process between the same phases.The simulation process we proposed provides a universal scheme for experimentally observing dynamic phase transitions.2.By using photon number encoding and studying fully quantum secondorder nonlinear optical processes,a correspondence between nonlinear optics and many-body physics Hamiltonians was established,and a quantum simulation of the one-dimensional XY model was achieved.Through cascaded nonlinear processes,the nonlinear optical quantum simulator was extended from one dimension to two dimensions.Using this nonlinear optical quantum simulator,we numerically simulated controllable quantum state transfer of mass through a one-dimensional XY spin chain by adjusting the interaction strength between spins.From the perspective of quantum thermodynamics,we explained the reason for the decrease in quantum state transfer quality by the relationship between quantum state transfer quality and spin chain energy levels,providing a new perspective for the study of this problem.Our quantum simulation scheme has the advantages of both scalability and tunability of parameters.Additionally,this scheme provides theoretical guidance for preparing complex multiphoton states using single nonlinear processes.3.By using optical loop structures to generate optical tensor network states,and optimizing the parameters of the optical tensor network simulator,the process of tensor network contraction was accelerated in a quantum-classical hybrid way.By adding a second loop and post-processing with classical tensors,we improved the modeling capability of the tensor network simulator.Using the one-dimensional quantum transverse Ising model and the one-dimensional antiferromagnetic Heisenberg model as examples,we numerically studied the expressivity of different optical tensor network simulators for quantum states.The numerical results demonstrate the effectiveness of our proposed optimization scheme for the tensor network simulator.