Quantum Simulation Of Chiral Currents With Periodic Driving

As a new research field quantum information technology has been expected to sur-pass classical tasks such as computation,simulation and communication.Quantum information technology is a product of the combination of quantum mechanics and in-formation science,mainly including quantum computation and quantum communica-tion.In recent years,due to the continuous improvement of experimental techniques based on quantum mechanics,it has become possible to use some quantum systems to implement certain special quantum computing functions.Such quantum computers that realize special tasks are quantum simulators.There are generally two methods to realize quantum simulation.One is to use a known and controllable system to simulate systems we studied but difficult to be implemented,which is called analog quantum simulation.The other is using quantum computers to process enormous task in quantum systems,called digital quantum simulation.In quantum systems,there is generally no direct many-body interaction,but the quantum simulation of many-body interaction can be achieved under frequency mod-ulation of external driving field by the means of quantum simulation.Although the three-body interaction is relatively easy to be realized,it also has important research value.The chiral spin operator?=?₁??（?₂?×?₃?_）is a kind of three-body interaction,which first appeared in the research of spin chain model.The synthesis of chiral spin currents based on quantum simulation in different systems is of great significance for the quantum simulation of chiral spin currents and its application in quantum information.In this paper,we propose a method for generating chiral spin currents by applying a periodic driving field,which can be implemented in superconducting circuits.Ac-cording to the arrangement of qubits,we consider quantum simulation in the triangular closed chain and the one-dimensional open chain respectively.In the triangular closed chain we seek a mapping between the original Hamiltonian and the target Hamilto-nian based on the idea of analog quantum simulation.Firstly,periodic external fields are applied to the three qubits based on the Floquet theory,so that the qubits can cou-ple to each other.The interaction between each two qubits can be eliminated through frequency regulation.Then by means of Jacobi-Anger expansion and high-frequency approximation,deduce the effective Hamiltonian of the chiral spin operator.In the one-dimensional open chain,we also use the analog quantum simulation but only get one component of the chiral spin operator.To solve this problem we introduce digital quan-tum simulation,by first transform the system into the Toggling framework and then add pulses to the qubits by means of the first and the second order Trotter formulas to obtain the other two components of the chiral spin operator.To verify the above scheme,we perform numerical calculation in the two models respectively,demonstrate the popu-lations of the quantum states and investigate the validity of the approximation method under different parameters.Meanwhile,We investigate the effect of the initial phases on the directions of the chiral spin currents and find that different directions of chiral spin currents can be achieved by the phase modulation.All the numerical calculations above demonstrate the validity of our theoretical derivation.Summarily,the scheme studied in this paper provides a new idea for the transmission of quantum states.