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Extracting quantum dynamics from genetic learning algorithms through principal component analysis

J. L. White, Brett J. Pearson, P. H. Bucksbaum

Published Jan 6, 2004• 0 citations
OpenAlex

Abstract

Genetic learning algorithms are widely used to control ultrafast optical pulse shapes for photo-induced quantum control of atoms and molecules. An outstanding issue is how to use the solutions found by these algorithms to learn about the system's quantum dynamics. We propose a simple method based on principal component analysis of the control space, which can reveal the degrees of freedom responsible for control, and aid in the construction of an effective Hamiltonian for the dynamics.

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Genetic learning algorithms are widely used to control ultrafast optical pulse shapes for photo-induced quantum control of atoms and molecules. An outstanding issue is how to use the solutions found by these algorithms to learn about the system's quantum dynamics. We propose a simple method based on principal component analysis of the control space, which can reveal the degrees of freedom responsible for control, and aid in the construction of an effective Hamiltonian for the dynamics.
Genetic learning algorithms are widely used to control ultrafast optical pulse shapes for photo-induced quantum control of atoms and molecules. An unresolved issue is how to use the solutions found by these algorithms to learn about the system's quantum dynamics. We propose a simple method based on covariance analysis of the control space, which can reveal the degrees of freedom in the effective control Hamiltonian. We have applied this technique to stimulated Raman scattering in liquid methanol. A simple model of two-mode stimulated Raman scattering is consistent with the results.
A longstanding goal in chemical physics has been the control of atoms and molecules using coherent light fields. This paper provides a brief overview of the field and discusses experiments that use a programmable pulse shaper to control the quantum state of electronic wavepackets in Rydberg atoms and electronic and nuclear dynamics in molecular liquids. The shape of Rydberg wavepackets was controlled by using tailored ultrafast pulses to excite a beam of caesium atoms. The quantum state of these atoms was measured using holographic techniques borrowed from optics. The experiments with molecular liquids involved the construction of an automated learning machine. A genetic algorithm directed the choice of shaped pulses which interacted with the molecular system inside a learning control loop. Analysis of successful pulse shapes that were found by using the genetic algorithm yield insight into the systems being controlled.
The control of atoms and molecules using coherent light fields has been a long-standing goal in chemical physics. This thesis discusses experiments which use a programmable pulse shaper to control the quantum state of electronic wavepackets in Rydberg atoms and electronic and nuclear dynamics in molecular liquids. The shape of Rydberg wavepackets was controlled by using tailored ultrafast pulses to excite a beam of cesium atoms. The quantum state of these atoms was measured using holographic techniques borrowed from optics. The experiments with molecular liquids involved the construction of an automated learning machine. A Genetic Algorithm directed the choice of shaped pulses which interacted with the molecular system inside a learning control loop. Analysis of successful pulse shapes that were found by using the GA yield insight into the systems being controlled.
Coherent control of light and matter is a major tool in current atomic physics and physical chemistry research. Technological advances in ultrafast laser pulse shaping allow control over the dynamics of molecular systems on sub-picosecond timescales. This thesis demonstrates feedback control over a variety of quantum systems and describes an adaptive genetic algorithm used in the experiments. In the gas phase, we examine control of multi-photon, dissociative ionization in diatomic sodium. The learning algorithm achieves control over the dissociative fraction primarily by adjusting the peak intensity of the laser field. We also investigate control of multi-mode stimulated Raman scattering in liquid phase methanol. Analysis of the results leads to identification of quasi-impulsive Raman coupling as a possible control mechanism. Further experiments, combined with numerical simulations of the interaction, demonstrate that an impulsive coupling of the two modes by the pump pulse can control the Raman gain. We extend the Raman control experiments to ethanol and isopropanol. Finally we apply feedback control techniques in an initial investigation of a liquid-phase chemical reaction. Specifically, we examine the ring-opening conversion of cyclohexadiene into hexatriene. The reaction dynamics occur on an excited state potential energy surface. Through control of the excitation pulse shape, we seek to guide the wavepacket evolution on the excited state to exert control over the reaction branching ratio.
Principal component analysis (PCA) is a widely applied but rather time-consuming tool in machine learning techniques. In 2014, Lloyd, Mohseni, and Rebentrost proposed a quantum PCA (qPCA) algorithm [Lloyd, Mohseni, and Rebentrost, Nat. Phys. 10, 631 (2014)NPAHAX1745-247310.1038/nphys3029] that still lacks experimental demonstration due to the experimental challenges in preparing multiple quantum state copies and implementing quantum phase estimations. Here, we propose a new qPCA algorithm using the hybrid classical-quantum control, where parameterized quantum circuits are optimized with simple measurement observables, which significantly reduces the experimental complexity. As one important PCA application, we implement a human face recognition process using the images from the Yale Face Dataset. By training our quantum processor, the eigenface information in the training dataset is encoded into the parameterized quantum circuit, and the quantum processor learns to recognize new face images from the test dataset with high fidelities. Our work paves a new avenue toward the study of qPCA applications in theory and experiment.
We have constructed an automated learning apparatus to control quantum systems. By directing intense shaped ultrafast laser pulses into a variety of samples and using a measurement of the system as a feedback signal, we are able to reshape the laser pulses to direct the system into a desired state. The feedback signal is the input to an adaptive learning algorithm. This algorithm programs a computer-controlled, acousto-optic modulator pulse shaper. The learning algorithm generates new shaped laser pulses based on the success of previous pulses in achieving a predetermined goal.