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A machine-learning approach to draw landscape maps in a low-dimensional control-parameter space is examined through a case study of three-dimensional alignment control of the asymmetric-top molecule SO2. As a minimal model, we consider the control by using a set of mutually orthogonal, linearly polarized laser pulses that are parameterized by the time delay and fluence ratio. The parameters are represented either by points in the parameter space or by time- and frequency-resolved spectra. Machine-learning models based on convolutional neural networks together with two considerably different representations, which are trained by using a reasonably small number of training samples, construct maps that have sufficient accuracy to predict temperature-dependent control mechanisms. [ABSTRACT FROM AUTHOR]

Reducing decoherence is an essential step toward realizing general‐purpose quantum computers beyond the present noisy intermediate‐scale quantum (NISQ) computers. To this end, dynamical decoupling (DD) approaches in which external fields are applied to qubits are often adopted. We numerically study DD using a two‐level model system (qubit) under the influence of Markovian decoherence by using quantum optimal control theory with slightly modified settings, in which the physical objective is to maximally create and maintain a specified superposition state in a specified control period. An optimal pulse is numerically designed while systematically varying the values of dephasing, population decay, pulse fluence, and control period as well as using two kinds of objective functionals. The decrease in purity due to the decoherence limits the ability to maintain a coherent superposition state; we refer to the state of maximal purity that can be maintained as the saturated value. The optimally shaped pulse minimizes the negative effect of decoherence by gradually populating and continuously replenishing the state of saturated purity. [ABSTRACT FROM AUTHOR]

The local control theory has been extended to deal with nonlinear interactions, such as polarizability interaction, as well as a combination of dipole and polarizability interactions. We explain herein how to implement the developed pulse-design algorithm in a standard computer code that numerically integrates the Liouville equation and/or the Schrödinger equation without incurring additional high computational cost. Through a case study of the rotational dynamics control of crystalline orbital molecules, the effectiveness of the locally optimized control pulses is demonstrated by adopting four types of control objectives, namely, two types of state-selective excitation, alignment, and orientation control. [ABSTRACT FROM AUTHOR]

We apply nonlinear optimal control simulation to design a non-resonant control pulse that maximizes the probability of specified photodissociation of IBr by utilizing the non-resonant dynamic Stark effect in the presence of a predetermined pump pulse. The optimal pulses are always composed of several subpulses that increase the target probability considerably depending on the wavelength of the pump pulse. Focusing on the cases of high target probabilities, we systematically examine how the subpulses cooperate with each other on the basis of pulse-partitioning analyses.We show that the subpulses largely cooperate with the pump pulse, which can explain their irradiation timings. On the other hand, the cooperation between the subpulses is mainly expressed as the sum of the contribution from each subpulse. [ABSTRACT FROM AUTHOR]

Alignment control of an ensemble of nonpolar molecules is numerically studied by means of optimal control simulation. A nitrogen molecule that is modeled by a quantum rigid rotor is adopted. Controlled rotational wave packets are created through nonresonant optical transitions induced by polarizability coupling. Optimal pulses are designed to achieve the alignment control at a specified time in the absence/presence of external static fields in zero- and finite-temperature cases, as well as to maintain an aligned state. When maintaining an aligned state over a specified time interval is chosen as a target, the control mechanism is primarily attributed to a dynamical one. Multiple optimal solutions that lead to virtually the same control achievement are found, which are consistent with the topology of the quantum control landscape. [ABSTRACT FROM AUTHOR]

The question as to whether state-selective population of molecular vibrational levels by shaped infrared laser pulses is possible in a condensed phase environment is of central importance for such diverse fields as time-resolved spectroscopy, quantum computing, or “vibrationally mediated chemistry.” This question is addressed here for a model system, representing carbon monoxide adsorbed on a Cu(100) surface. Three of the six vibrational modes are considered explicitly, namely, the CO stretch vibration, the CO-surface vibration, and a frustrated translation. Optimized infrared pulses for state-selective excitation of “bright” and “dark” vibrational levels are designed by optimal control theory in the framework of a Markovian open-system density matrix approach, with energy flow to substrate electrons and phonons, phase relaxation, and finite temperature accounted for. The pulses are analyzed by their Husimi “quasiprobability” distribution in time-energy space. [ABSTRACT FROM AUTHOR]

Optimal control simulation is used to examine the control mechanisms in the photodissociation of phenol within a two-dimensional, three-electronic-state model with two conical intersections. This model has two channels for H-atom elimination, which correspond to the 2π and 2σ states of the phenoxyl radical. The optimal pulse that enhances 2σ dissociation initially generates a wave packet on the S1 potential-energy surface of phenol. This wave packet is bifurcated at the S2-S1 conical intersection into two components with opposite phases because of the geometric phase effect. The destructive interference caused by the geometric phase effect reduces the population around the S1-S0 conical intersection, which in turn suppresses nonadiabatic transitions and thus enhances dissociation to the 2σ limit. The optimal pulse that enhances S0 dissociation, on the other hand, creates a wave packet on the S2 potential-energy surface of phenol via an intensity borrowing mechanism, thus avoiding geometric phase effects at the S2-S1 conical intersection. This wave packet hits the S1-S0 conical intersection directly, resulting in preferred dissociation to the 2π limit. The optimal pulse that initially prepares the wave packet on the S1 potential-energy surface (PES) has a higher carrier frequency than the pulse that prepares the wave packet on the S2 PES. This counterintuitive effect is explained by the energy-level structure and the S2-S1 vibronic coupling mechanism. [ABSTRACT FROM AUTHOR]

We numerically propose a way to perform quantum computations by combining an ensemble of molecular states and weak laser pulses. A logical input state is expressed as a superposition state (a wave packet) of molecular states, which is initially prepared by a designed femtosecond laser pulse. The free propagation of the wave packet for a specified time interval leads to the specified change in the relative phases among the molecular basis states, which corresponds to a computational result. The computational results are retrieved by means of quantum interferometry. Numerical tests are implemented in the vibrational states of the B state of I2 employing controlled-NOT gate, and 2 and 3 qubits Fourier transforms. All the steps involved in the computational scheme, i.e., the initial preparation, gate operation, and detection steps, are achieved with extremely high precision. [ABSTRACT FROM AUTHOR]

Optimal control simulation is applied to the cis-trans photoisomerization of retinal in rhodopsin within a two-dimensional, two-electronic-state model with a conical intersection [S. Hahn and G. Stock, J. Phys. Chem. B 104, 1146 (2000)]. For this case study, we investigate coherent control mechanisms, in which laser pulses work cooperatively with a conical intersection that acts as a “wave-packet cannon.” Optimally designed pulses largely consist of shaping subpulses that prepare a wave packet, which is localized along a reaction coordinate and has little energy in the coupling mode, through multiple electronic transitions. This shaping process is shown to be essential for achieving a high target yield although the envelopes of the calculated pulses depend on the local topography of the potential-energy surfaces around the conical intersection and the choice of target. The control mechanisms are analyzed by considering the motion of reduced wave packets in a nuclear configuration space as well as by snapshots of probability current-density maps. [ABSTRACT FROM AUTHOR]

A linearized optimal control method in combination with mixed quantum/classical molecular dynamics simulation is used for numerically investigating the possibility of controlling photodissociation wave packets of I2- in water. Optimal pulses are designed using an ensemble of photodissociation samples, aiming at the creation of localized dissociation wave packets. Numerical results clearly show the effectiveness of the control although the control achievement is reduced with an increase in the internuclear distance associated with a target region. We introduce effective optimal pulses that are designed using a statistically averaged effective dissociation potential, and show that they semiquantitatively reproduce the control achievements calculated by using optimal pulses. The control mechanisms are interpreted from the time- and frequency-resolved spectra of the effective optimal pulses. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An optimal control theory for open quantum systems is constructed containing non-Markovian dissipation manipulated by an external control field. The control theory is developed based on a novel quantum dissipation formulation that treats both the initial canonical ensemble and the subsequent reduced control dynamics. An associated scheme of backward propagation is presented, allowing the efficient evaluation of general optimal control problems. As an illustration, the control theory is applied to the vibration of the hydrogen fluoride molecule embedded in a non-Markovian dissipative medium. The importance of control-dissipation correlation is evident in the results. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to “trapping” and that relaxation processes may remove such unfavorable behavior. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Optimal control within the density matrix formalism is applied to the creation of a specified superposition state in condensed phases. The primary system modeled by a displaced harmonic oscillator is surrounded by a boson heat bath, the dynamics of which is described by a non-Markovian master equation. A newly developed monotonically convergent algorithm is used to solve the pulse design equations. The control mechanisms are strongly dependent on the bath correlation time that is characterized by the inverse of an exponential decay constant, γ. If the correlation time is shorter than the temporal width of a typical subpulse involved in an optimal pulse, the solution is reduced to that in the Markovian case. If we assume a longer correlation time, by weighing less physical significance on the penalty due to pulse fluence, an optimal pulse with high intensity is obtained, the temporal width of which approaches ∼1/γ. We also see considerable changes in the shape of the optimal pulse with increasing intensity, suggesting that strong fields open up control mechanisms that are qualitatively different from those in weak fields. [ABSTRACT FROM AUTHOR]

In order to achieve optimal control of unbounded molecular dynamics, we develop an algorithm to deal with a spatially delocalized final condition of homogeneous pulse design equations that are derived from a typical optimal control procedure. We introduce a quasiprojector to specify a spatially delocalized physical objective, while we store wave packet components that spread beyond the grid region in memory. The quasiprojector, which can explicitly identify target products in photodissociation and bimolecular reactions, is a weighted sum of projectors, whose weight function is constant outside the grid region. This algorithm, combined with an efficient iteration method, is applied to the control of NaI predissociation with the aim of obtaining a high dissociation probability within one cycle of nuclear vibration. We discuss how the control mechanisms are changed depending on the potential coupling strengths and restriction imposed on the optical interaction region. The effects of molecular orientation on a control pathway are also examined using a two-orientation model with the assumption of a frozen rotational wave packet. [ABSTRACT FROM AUTHOR]

Focuses on the extension of a monotonically convergent algorithm for quantum optimal control to treat systems with dissipation. Exhibition of quadratic and monotonic convergence of the algorithm working with the density matrix; Exploitation of the model to control various targets including the expectation value of Hermitian operator.

The quantum control theory indicates that chiral molecular motors can be effectively driven in predesired directions by applying linearly polarized laser pulses with optimized electric fields. The direction of rotation of a chiral molecular motor is toward its gentle slope of the asymmetric potential, namely, the intuitive direction.

Fluence-specified optimal control simulation is applied to C16O/C18O and14N2/15N2mixtures to numerically design laser pulses that best achieve isotope-selective alignment. The degree of control is measured in terms of selectivity, which is defined by the difference in the degree of alignment between a heavy isotopologue (HI) and a light isotopologue (LI). Optimal pulses are composed of several subpulses that cooperate with the so-called revivals of the rotational wave packets. Although the two mixtures have slightly different molecular parameters and isotope shifts, it turns out that the optimal pulses share common multi-pulse structures. We also develop a pulse-partitioning analysis to quantitatively and systematically examine the role of inter-subpulse cooperation in the improvement of the isotope-selective alignment. According to the analyses, we find that the ‘coherent’ and the ‘incoherent’ inter-subpulse cooperation almost equally contribute to the improvement of the degree of alignment (HI) as well as that of anti-alignment (LI). [ABSTRACT FROM AUTHOR]

Molecular orientation with combinations of near-single-cycle THz and non-resonant laser pulses is studied by means of optimal control simulation with CO molecules at 5 K. We optimize non-resonant laser pulses with optimally determined final times while assuming fixed THz pulses and focusing on the carrier-envelope phase (CEP) effects. Although almost the same high degrees of orientation are achieved by the combined control independent of CEPs, the structures of the optimal non-resonant laser pulses considerably depend on CEPs and the central frequencies of the THz pulses. From a practical viewpoint, simplified treatments are also discussed. [ABSTRACT FROM AUTHOR]

In the B state of I2, strong-laser-induced interference (SLI) was recently observed in the population of each vibrational eigenstate within a wave packet, which was initially prepared by a pump pulse and then strongly modulated by an intense femtosecond near-infrared (NIR) laser pulse. It was suggested that the interference as a function of the time delay occurs between the eigenstate reached by Rayleigh scattering and that by Raman scattering. To verify this mechanism and further discuss its characteristics, we theoretically/numerically study the SLI by adopting a two-electronic-state model of I2. Numerical simulation reasonably reproduces the experimental signals and confirms the theoretical consequences, which include the π-phase shifts between Stokes and anti-Stokes transitions and (practically) no contribution from the energy shifts induced by the NIR pulse. [ABSTRACT FROM AUTHOR]

In this paper, molecular quantum computation is numerically studied with the quantum search algorithm (Grover's algorithm) by means of optimal control simulation. Qubits are implemented in the vibronic states of I2, while gate operations are realized by optimally designed laser pulses. The methodological aspects of the simulation are discussed in detail. We show that the algorithm for solving a gate pulse-design problem has the same mathematical form as a state-to-state control problem in the density matrix formalism, which provides monotonically convergent algorithms as an alternative to the Krotov method. The sequential irradiation of separately designed gate pulses leads to the population distribution predicted by Grover's algorithm. The computational accuracy is reduced by the imperfect quality of the pulse design and by the electronic decoherence processes that are modeled by the non-Markovian master equation. However, as long as we focus on the population distribution of the vibronic qubits, we can search a target state with high probability without introducing error-correction processes during the computation. A generalized gate pulsedesign scheme to explicitly include decoherence effects is outlined, in which we propose a new objective functional together with its solution algorithm that guarantees monotonic convergence. [ABSTRACT FROM AUTHOR]

Abstract: We numerically study molecular quantum computation using qubits that are implemented in the vibrational states of I2. Logical gate operations are realized by laser pulses designed by an optimal control method within the density matrix formalism. Optimally designed gate pulses are shown to act as universal gates through a case study of the simulation of the Deutsch–Jozsa algorithm. [Copyright &y& Elsevier]

A hybrid quantum control scheme that combines incoherent excitation processes with coherent excitation processes in desorption induced by multiple electronic transitions (DIMET) is proposed on the basis of optimal control theory. The desorption is induced by hot electrons (incoherent excitation), while the initial configuration and/or kinetic energy of the adsorbate complex is coherently controlled by optimal IR pulses. To show its effectiveness, the results of application of this hybrid control to a `toy model'' representing DIMET of NO/Pt(1 1 1) are presented by solving the pulse design equations under the influence of strong dissipation. [Copyright &y& Elsevier]

An optimal control procedure is presented to design a field that transfers a molecule into an objective state that is specified by the expectation values of multiple target operators. This procedure explicitly includes constraints on the time behavior of specified operators during the control period. To calculate the optimal control field, we develop a new monotonically and quadratically convergent algorithm by introducing a quadruple space that consists of a direct product of the double (Liouville) space. In the absence of the time-dependent constraints, the algorithm represented in the quadruple-space notation reduces to that of the double-space notation. This simplified formulation is applied to a two dimensional system which models intramolecular vibrational energy redistribution (IVR) processes in polyatomic molecules. An optimal pulse is calculated that exploits IVR to transfer a specific amount of population to an optically inactive state, while the other portion of the population remains in the initial state at a control time. Using trajectory plots in quantum-number space, we numerically analyze how the control pathway changes depending on the amount of the excited population. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In the B state of I2, strong-laser-induced interference (SLI) was recently observed in the population of each vibrational eigenstate within a wave packet, which was initially prepared by a pump pulse and then strongly modulated by an intense femtosecond near-infrared (NIR) laser pulse. It was suggested that the interference as a function of the time delay occurs between the eigenstate reached by Rayleigh scattering and that by Raman scattering. To verify this mechanism and further discuss its characteristics, we theoretically/numerically study the SLI by adopting a two-electronic-state model of I2. Numerical simulation reasonably reproduces the experimental signals and confirms the theoretical consequences, which include the π-phase shifts between Stokes and anti-Stokes transitions and (practically) no contribution from the energy shifts induced by the NIR pulse.

Nonresonant optimal control simulation is applied to a CO molecule to design two-color phase-locked laser pulses (800 nm + 400 nm) with the aim of orienting the molecule under the field-free condition. The optimal pulse consists of two subpulses: the first subpulse aligns the molecule and the second one orients it. The molecular alignment induced by the first subpulse considerably enhances the degree of orientation, the value of which is close to an ideal value at temperature T = 0 K. To confirm the effectiveness of this alignment-enhanced orientation mechanism, we adopt a set of model Gaussian pulses and calculate the maximum degrees of orientation as a function of the delay time and the intensity. In finite-temperature (T = 3.0 K and T = 5.0 K) cases, although the alignment subpulse can improve the degree of orientation, the control achievement decreases with temperature rapidly; this decrease can be attributed to the initial-state-dependent (phase-shifted) rotational wave packet motion.

Wave functions of electrically neutral systems can be used as information carriers to replace real charges in the present Si-based circuit, whose further integration will result in a possible disaster where current leakage is unavoidable with insulators thinned to atomic levels. We have experimentally demonstrated a new logic gate based on the temporal evolution of a wave function. An optically tailored vibrational wave packet in the iodine molecule implements four- and eight-element discrete Fourier transform with arbitrary real and imaginary inputs. The evolution time is 145 fs, which is shorter than the typical clock period of the current fastest Si-based computers by 3 orders of magnitudes.

The conical intersections of the dissociative 1pisigma* excited state with the lowest 1pipi* excited state and the electronic ground state of 9H-adenine have been investigated with multireference electronic structure calculations. Adiabatic and quasidiabatic potential energy surfaces and coupling elements were calculated as a function of the NH stretch coordinate of the azine group and the out-of-plane angle of the hydrogen atom, employing MultiReference Configuration-Interaction (MRCI) as well as Complete-Active-Space Self-Consistent-Field (CASSCF) methods. Characteristic properties of the 1pipi*-1pisigma* and 1pisigma*-S0 conical intersections, such as the diabatic-to-adiabatic mixing angle, the geometric phase of the adiabatic electronic wavefunctions, the derivative coupling, as well as adiabatic and diabatic transition dipole moment surfaces were investigated in detail. These data are a prerequisite for future quantum wavepacket simulations of the photodissociation and internal-conversion dynamics of adenine.

A linearized optimal control method in combination with mixed quantum/classical molecular dynamics simulation is used for numerically investigating the possibility of controlling photodissociation wave packets of I(2)(-) in water. Optimal pulses are designed using an ensemble of photodissociation samples, aiming at the creation of localized dissociation wave packets. Numerical results clearly show the effectiveness of the control although the control achievement is reduced with an increase in the internuclear distance associated with a target region. We introduce effective optimal pulses that are designed using a statistically averaged effective dissociation potential, and show that they semiquantitatively reproduce the control achievements calculated by using optimal pulses. The control mechanisms are interpreted from the time- and frequency-resolved spectra of the effective optimal pulses.

An optimal control theory for open quantum systems is constructed containing non-Markovian dissipation manipulated by an external control field. The control theory is developed based on a novel quantum dissipation formulation that treats both the initial canonical ensemble and the subsequent reduced control dynamics. An associated scheme of backward propagation is presented, allowing the efficient evaluation of general optimal control problems. As an illustration, the control theory is applied to the vibration of the hydrogen fluoride molecule embedded in a non-Markovian dissipative medium. The importance of control-dissipation correlation is evident in the results., ((c) 2004 American Institute of Physics)