Quantum Trajectory Theory And Applications

It is necessary to output the information of the measurement system in quantum computing process,and the process of extracting information is regarded as quantum measurement,especially,the quantum trajectory approach proposed to simplify the study of the stochastic evolution of the system state conditioned on the measurement record.besides that,superconducting circuit quantum electrodynamics(QED)is an ideal platform for quantum measurement and a promising candidate for quantum processing.in this paper,we first to reveal how the quantum trajectory equation describing continuous quantum measurement are derived.Second,we study the quantum trajectory equation in QED system,which may reveal the process of obtaining information by homodyne measurement,and propose two schemes to eliminate the degrees of freedom of the cavity photons.At last,the quantum trajectory approach is introduced into the highly concerned nonadiabatic mixed quantum classicl molecular dynamics simulation,which implies an effective measurement on the electronic state due to continuously test the classical atomic force,and provides a easier approach to the nonadiabatic molecular dynamics simulation.The main contents of this paper can be concluded as the following two aspects:(I)In circuit QED system,the coupling between photons and qubit cannot be overlooked.therefore,when some quantum measurement and control are performed on this system,owing to the existence of large number of photons in the cavity,the degrees of freedom of the system state is increased and will increase a large amount of computation in simulation process.To improve the simulation efficiency,It is enjoyable and beneficial to eliminate the degrees of freedom of the cavity photons,and get an effective evolution equation which includes only highly focused qubit state.and then,The adiabatic and polaron elimination scheme are proposed according to the coupling strength between the photon and qubit in the displacement.we also simulate the evolution of qubit by above two schemes and compare results with exact numerical simulations.We find that in strong coupling and weak cavity damping regime,the adiabatic scheme is inferior to the polaron method,but out of regime,The difference between the simulation results has become insignificant.(II)In the study of nonadiabatic molecular dynamics systems,full quantum dynamics simulation scheme would quickly becoming challenging with the increase of atomic degrees of freedom.A series of mixed quantum-classical(MQC)molecular dynamics simulation methods were developed and proved to be the most powerful tool for nonadiabatic molecular dynamics simulaion.these schemes believe that continuously tracking the classical atomic force can be described as a quantum measurement on the electronic state.Based on this view,quantum trajectory(QT)scheme for the description of nonadiabatic molecular dynamics be proposed.And we simulate in the work several typical potential-surface models,including the single avoided crossing,dual avoided crossing,extended coupling,dumbbell and double arch potentials.In particular,we simulate and compare three decoherence rates,which are from different physical considerations.We also design simulation algorithm to properly account for the energy conservation and force direction change associated with the surface hopping.In most cases,we find that the QT-MQC results are in good agreement with the full quantum dynamics,not sensitive to the form of the decoherence rate.But for the model involving strong quantum interference,the MQC approach cannot give desirable results.