Quantum ensemble classification (QEC) has significant applications in discrimination of atoms (or molecules), separation of isotopes, and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging, since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast QEC as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). First, a new discrimination method is proposed for two similar quantum systems. Then, an SLC method is presented for QEC. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.Quantum ensemble classification (QEC) has significant applications in discrimination of atoms (or molecules), separation of isotopes, and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging, since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast QEC as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). First, a new discrimination method is proposed for two similar quantum systems. Then, an SLC method is presented for QEC. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.

arXiv:1312.6945IEEE Transactions on Neural Networks and Learning SystemsMar 23, 201631 citations

On the Stochastic Control of Quantum Ensembles

Roger W. Brockett, Navin Khaneja

Kluwer international series in engineering and computer scienceJan 1, 200057 citations

On the control of quantum statistical systems

Morton H. Rubin

Journal of Statistical PhysicsMay 1, 19822 citations

Sampling-based learning control of inhomogeneous quantum ensembles

Chunlin Chen, Daoyi Dong, Ruixing Long +2 more

Compensation for parameter dispersion is a significant challenge for control of inhomogeneous quantum ensembles. In this paper, we present the systematic methodology of sampling-based learning control (SLC) for simultaneously steering the members of inhomogeneous quantum ensembles to the same desired state. The SLC method is employed for optimal control of the state-to-state transition probability for inhomogeneous quantum ensembles of spins as well as $\ensuremath{\Lambda}$-type atomic systems. The procedure involves the steps of (i) training and (ii) testing. In the training step, a generalized system is constructed by sampling members according to the distribution of inhomogeneous parameters drawn from the ensemble. A gradient flow based learning and optimization algorithm is adopted to find an optimal control for the generalized system. In the process of testing, a number of additional ensemble members are randomly selected to evaluate the control performance. Numerical results are presented, showing the effectiveness of the SLC method.Compensation for parameter dispersion is a significant challenge for control of inhomogeneous quantum ensembles. In this paper, we present the systematic methodology of sampling-based learning control (SLC) for simultaneously steering the members of inhomogeneous quantum ensembles to the same desired state. The SLC method is employed for optimal control of the state-to-state transition probability for inhomogeneous quantum ensembles of spins as well as $\ensuremath{\Lambda}$-type atomic systems. The procedure involves the steps of (i) training and (ii) testing. In the training step, a generalized system is constructed by sampling members according to the distribution of inhomogeneous parameters drawn from the ensemble. A gradient flow based learning and optimization algorithm is adopted to find an optimal control for the generalized system. In the process of testing, a number of additional ensemble members are randomly selected to evaluate the control performance. Numerical results are presented, showing the effectiveness of the SLC method.

arXiv:1308.1454Physical Review AFeb 5, 2014129 citations

Learning Control with Evolution Strategy for Inhomogeneous Open Quantum Ensembles

Chunxiang Song, Yanan Liu, David McManus +1 more

This paper investigates the application of an evolutionary algorithm, evolution strategy (ES)( $\mu+\lambda$ ) to the control design in several inhomogeneous open quantum ensembles. We apply the ES ( $\mu+\lambda$ ) to assist the sampling-based learning control (SLC) technique, by which a set of control signals is designed to drive the inhomogeneous open quantum ensemble to a given target state. We illustrate our algorithm in two-level and four-level inhomogeneous open quantum ensembles. Numerical results show the effectiveness of the proposed control algorithm. The comparison with other evolutionary algorithms such as differential evolution (DE) and genetic algorithm (GA) shows the superiority of our ES ( $\mu+\lambda$ ) both in average fidelity and stability. In a four-level open quantum ensemble, for example, the fitness error after optimization using the ES ( $\mu+\lambda$ ) is decreased by around 59% compared to DE, and the standard deviation is lowered by about 47%.This paper investigates the application of an evolutionary algorithm, evolution strategy (ES)($\mu+\lambda$) to the control design in several inhomogeneous open quantum ensembles. We apply the ES ($\mu+\lambda$) to assist the sampling-based learning control (SLC) technique, by which a set of control signals is designed to drive the inhomogeneous open quantum ensemble to a given target state. We illustrate our algorithm in two-level and four-level inhomogeneous open quantum ensembles. Numerical results show the effectiveness of the proposed control algorithm. The comparison with other evolutionary algorithms such as differential evolution (DE) and genetic algorithm (GA) shows the superiority of our ES ($\mu+\lambda$) both in average fidelity and stability. In a four-level open quantum ensemble, for example, the fitness error after optimization using the ES ($\mu+\lambda$) is decreased by around 59% compared to DE, and the standard deviation is lowered by about 47%.

Conference proceedings/Conference proceedings - IEEE International Conference on Systems, Man, and CyberneticsOct 9, 20220 citations

Ensembles in Quantum Mechanics

L. E. Ballentine

Compendium of Quantum PhysicsJan 1, 20092 citations

This paper investigates the application of an evolutionary algorithm, evolution strategy (ES)(

\mu+\lambda

) to the control design in several inhomogeneous open quantum ensembles. We apply the ES (

\mu+\lambda

) to assist the sampling-based learning control (SLC) technique, by which a set of control signals is designed to drive the inhomogeneous open quantum ensemble to a given target state. We illustrate our algorithm in two-level and four-level inhomogeneous open quantum ensembles. Numerical results show the effectiveness of the proposed control algorithm. The comparison with other evolutionary algorithms such as differential evolution (DE) and genetic algorithm (GA) shows the superiority of our ES (

\mu+\lambda

) both in average fidelity and stability. In a four-level open quantum ensemble, for example, the fitness error after optimization using the ES (

\mu+\lambda

) is decreased by around 59% compared to DE, and the standard deviation is lowered by about 47%.