System Identification For Quantum Systems Subject To Colored Noise

Since the late 20th century,investigation on quantum physics has boosted the development of quantum information technology such as quantum computation,quantum communication and quantum metrology,etc.These quantum technologies are supported by quantum control theory in which quantum system identification is a fundamental branch to calibrate models of quantum systems.However,existing works on this issue rarely take colored noise disturbance and quantum colored noise into account.Therefore,in this paper we consider identification problems involving both colored measurement noise and quantum colored noise.The sketch of our work is listed as follows:1)With regard to colored measurement noise,we present a Model-augmentation-based Hamiltonian identification method for closed quantum systems.A system realization for colored measurement noise can be established by applying spectrum factorizing theorem and thus closed quantum system model can be augmented.Meanwhile we can obtain a system realization from output data by using Eigenstate Realization Algorithm(ERA).Due to the equivalence between the obtained realization and the augmented model,a set of polynomial equations on unknown Hamiltonian parameters can be derived and numerically solved.The effectiveness of this method is shown by an example on a two-qubit system.2)On the other hand,quantum system may also disturbed by quantum colored noise.To identify the power spectrum density(PSD)of quantum colored noise,we present a method based on model transformation.Firstly,a linear model for the quantum colored noise field is obtained by applying quantum spectrum factorization theorem and is used to augment the model of the prober—a quantum oscillator.The prober is driven by coherent white noise field to obtain the response of the whole system.In addition,with the response,the unknown parameters of the linear model can be estimated by our method such that the corresponding PSD can be extracted.We verify this method in two examples on identification of quantum colored noise fields with Lorentzian and double Lorentzian spectra.3)In a class of time-convolution-less master equations,quantum colored noises are embedded in damping rate functions and thus the problem on identification of quantum colored noise is converted to that of damping rate functions.To identify the damping rate function of a singlequbit system,we propose a linear-least-square identifier.For single qubit,we transform the time-convolution-less master equation into Bloch vector representation,and express the unknown damping rate function as a polynomial with unknown coefficients.A matrix equation between measured data and unknown coefficients can be derived and solved by linear least squared method.However,this method is difficult to be generalized to multi-qubit system.Further,we present an inverse-system method to iteratively identify several different damping rate functions simultaneously in a multi-qubit system.We construct an estimation expression for the unknown damping rate functions in terms of experimental data and density matrix.And thus we obtain a necessary condition on the identifiability based on inverse system theory.With this condition,an algorithm is designed to identify the damping rate functions.Simulation results on a three-qubit system demonstrate the effectiveness of our method.