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Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 − δ while only requiring a single copy of the initial state. We subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: Θ ‖ H ‖ | t | + ln (1 / ϵ) + ln (1 / δ) . Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H2 molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields. [ABSTRACT FROM AUTHOR]

While closed-loop control of quantum dynamics in the laboratory is proving to be broadly successful, the control mechanisms induced by the fields are often left obscure. Hamiltonian encoding (HE) was originally introduced as a method for understanding mechanisms in quantum dynamics in the context of computational simulations, based on access to the system wavefunction. As a step towards laboratory implementation of HE, this paper addresses the issues raised by the use of observables rather than the wavefunction in HE. The goal of laboratory based HE is to obtain an understanding of control mechanism through a sequence of systematic control experiments, whose collective information can identify the underlying control mechanism defined as the set of significant amplitudes connecting the initial and final states. Mechanism is determined by means of observing the dynamics of special sequences of system Hamiltonians encoded through the control field. The proposed algorithm can handle complex systems, operates with no recourse to dynamical simulations, and functions with limited understanding of the system Hamiltonian. As with the closed-loop control experiments, the HE control mechanism identification algorithm performs a new experiment each time the dynamical outcome from an encoded Hamiltonian is called for. This paper presents the basic HE algorithm in the context of physical systems described by a finite dimensional Hilbert space. The method is simulated with simple models, and the extension to more complex systems is discussed. [ABSTRACT FROM AUTHOR]

In this paper, we present a path integral hybrid Monte Carlo (PIHMC) method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids [S. Miura and J. Tanaka, J. Chem. Phys. 120, 2160 (2004)] to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurational-bias technique for efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium-4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed. [ABSTRACT FROM AUTHOR]

Expanding the set of stable, accurate, and scalable methods for simulating molecular quantum dynamics is important for accelerating the computational exploration of molecular processes. In this paper, we adapt the signed particles Monte Carlo algorithm for solving the transient Wigner equation to scenarios of chemical interest. This approach was used in the past to study electronic processes in semi-conductors, but to the best of our knowledge, it had never been applied to molecular modeling. We present the algorithm and demonstrate its excellent performance on harmonic and double well potentials for electronic and nuclear systems. We explore the stability of the algorithm, discuss the choice of hyper-parameters, and cautiously speculate that it may be used in quantum molecular dynamics simulations. [ABSTRACT FROM AUTHOR]

Most of the numerical simulation in quantum (bilinear) control have used one of the monotonically convergent algorithms of Krotov (introduced by Tannor et al.) or of Zhu and Rabitz. However, until now no explicit relationship has been revealed between the two algorithms in order to understand their common properties. Within this framework, we propose in this paper a unified formulation that comprises both algorithms and that extends to a new class of monotonically convergent algorithms. Numerical results show that the newly derived algorithms behave as well as (and sometimes better than) the well-known algorithms cited above. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Variational basis-set formulations of the quantum mechanical reactive scattering problem lead to large, dense sets of equations. In previous work, we showed that the generalized minimal residual (GMRes) algorithm is sometimes competitive in terms of computer time with direct methods for these dense matrices, even when complex-valued boundary conditions are used, leading to non-Hermitian matrices. This paper presents a preconditioning scheme to accelerate convergence and improve performance. We block the potential energy coupling into a series of distortion blocks, and we employ the outgoing wave variational principle with nonorthogonal basis functions, including both dynamically adapted Green’s functions for the distortion blocks and also square integrable functions. The coefficient matrix of the resulting linear system couples the blocks. We have found that preconditioners formed from diagonal blocks of the coefficient matrix corresponding to the distortion blocks and vibrational blocks are effective at accelerating the iterative method in every test case, by factors of 2.9–20, with an average speedup of a factor of 6.5. The storage requirements and computational efficiency of the new scheme compare favorably to those for preconditioners based on banded matrices of variable bandwidth. The new preconditioners yield converged transition probabilities in less computer time than a direct solver even in cases which do not converge in a reasonable amount of time without preconditioning, and the average speedup compared to the direct solution is a factor of 7.6. [ABSTRACT FROM AUTHOR]

This paper presents a new, quantum mechanical, time dependent approach to the photodissociation of triatomic molecules in Jacobi coordinates. The algorithm is based on a nested interaction representation, designed to make the representation of the time evolving wave packet as compact as possible. The new equations of motion are solved numerically using a synthesis of grid techniques: the fast Fourier transform (FFT) method is used in Cartesian-like coordinates, and the discrete variable representation (DVR) method in the angular or bending coordinate. A variant on the short iterative Lanczos (SIL) procedure is used for the temporal propagation of the wave packet. Rotational state distributions obtained from this new algorithm are presented for the single surface photodissociation of ClCN and for the two surface photodissociation of ICN. The ClCN results are in good agreement with the semiclassical results of Barts and Halpern [J. Phys. Chem. 93, 7346 (1989)] and in excellent agreement with the time independent quantum results of Schinke [J. Chem. Phys. 92, 2397 (1990)]. Rotational state distributions for the two electronic surface photodissociation of ICN are in good agreement with the time independent quantum results of Guo and Schatz [J. Chem. Phys. 92, 1634 (1990)] and illustrate the flexibility of the method for dealing with nonadiabatic processes. The numerical efficiency of the method is comparable with standard time independent techniques, but has the attractive feature of yielding final state distributions at all energies from a single wave packet propagation. [ABSTRACT FROM AUTHOR]

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule. [ABSTRACT FROM AUTHOR]

A controlled quantum system possesses a search landscape defined by the target physical objective as a function of the controls. This paper focuses on the landscape for the transition probability Pi → f between the states of a finite level quantum system. Traditionally, the controls are applied fields; here, we extend the notion of control to also include the Hamiltonian structure, in the form of time independent matrix elements. Level sets of controls that produce the same transition probability value are shown to exist at the bottom Pi → f = 0.0 and top Pi → f = 1.0 of the landscape with the field and/or Hamiltonian structure as controls. We present an algorithm to continuously explore these level sets starting from an initial point residing at either extreme value of Pi → f. The technique can also identify control solutions that exhibit the desirable properties of (a) robustness at the top and (b) the ability to rapidly rise towards an optimal control from the bottom. Numerical simulations are presented to illustrate the varied control behavior at the top and bottom of the landscape for several simple model systems. [ABSTRACT FROM AUTHOR]

Open-system quantum optimal control theory for optical control of the dynamics of a quantum system in contact with a dissipative bath is used here for explicitly time-dependent target operators, O⁁(t). Global and local control strategies are combined in a novel algorithm by defining a set of time slices, into which the total control time is subdivided. The optimization then proceeds locally forward in time from subinterval to subinterval, while within each subinterval global control theory is used with iterative forward-backward propagation. The subintervals are connected by appropriate boundary conditions. In the present paper, all operators are represented in the basis of the eigenstates of the field-free system Hamiltonian. The algorithm is first applied to and its computational performance tested for a two-level system with energy and phase relaxation, and later extended to a many-level model. Model parameters are chosen to represent the IR pulse excitation of the adsorbate-surface stretch mode of vibrationally relaxing CO on a Cu(100) surface. Various time-dependent targets are formulated to achieve (i) population inversion, (ii) the creation of a wavepacket, and (iii) overtone excitation by “ladder climbing.” [ABSTRACT FROM AUTHOR]

An approach is developed in the replica exchange framework to enhance conformational sampling for the quantum mechanical (QM) potential based molecular dynamics simulations. Importantly, with our enhanced sampling treatment, a decent convergence for electronic structure self-consistent-field calculation is robustly guaranteed, which is made possible in our replica exchange design by avoiding direct structure exchanges between the QM-related replicas and the activated (scaled by low scaling parameters or treated with high “effective temperatures”) molecular mechanical (MM) replicas. Although the present approach represents one of the early efforts in the enhanced sampling developments specifically for quantum mechanical potentials, the QM-based simulations treated with the present technique can possess the similar sampling efficiency to the MM based simulations treated with the Hamiltonian replica exchange method (HREM). In the present paper, by combining this sampling method with one of our recent developments (the dual-topology alchemical HREM approach), we also introduce a method for the sampling enhanced QM-based free energy calculations. [ABSTRACT FROM AUTHOR]

Trajectories of duration τ joining two points q0 and q1 in the configuration space of a classical system satisfy Hamilton’s principle: they are stationary points of the classical action. The second variation (fluctuations) of the action around the stationary point signals whether the latter is or not a minimum and delivers the density in trajectory space around the points q0 and q1. This concept of density of paths is of great importance in semiclassical quantum theory, where it weights the contribution to the propagator from the single classical trajectories. In this paper, two algorithms based on the concepts of molecular dynamics simulation are introduced for computing the density of paths, also called van Vleck [Proc. Natl. Acad. Sci. U.S.A. 14, 178 (1928)] determinant. Examples for realistic systems are presented, together with a suggestion about possible applications in the field of rare events in physics and chemistry. [ABSTRACT FROM AUTHOR]

The key factors that distinguish algorithms for nonadiabatic mixed quantum/classical (MQC) simulations from each other are how they incorporate quantum decoherence—the fact that classical nuclei must eventually cause a quantum superposition state to collapse into a pure state—and how they model the effects of decoherence on the quantum and classical subsystems. Most algorithms use distinct mechanisms for modeling nonadiabatic transitions between pure quantum basis states ("surface hops") and for calculating the loss of quantum-mechanical phase information (e.g., the decay of the off-diagonal elements of the density matrix). In our view, however, both processes should be unified in a single description of decoherence. In this paper, we start from the density matrix of the total system and use the frozen Gaussian approximation for the nuclear wave function to derive a nuclear-induced decoherence rate for the electronic degrees of freedom. We then use this decoherence rate as the basis for a new nonadiabatic MQC molecular-dynamics (MD) algorithm, which we call mean-field dynamics with stochastic decoherence (MF-SD). MF-SD begins by evolving the quantum subsystem according to the time-dependent Schrödinger equation, leading to mean-field dynamics. MF-SD then uses the nuclear-induced decoherence rate to determine stochastically at each time step whether the system remains in a coherent mixed state or decoheres. Once it is determined that the system should decohere, the quantum subsystem undergoes an instantaneous total wave-function collapse onto one of the adiabatic basis states and the classical velocities are adjusted to conserve energy. Thus, MF-SD combines surface hops and decoherence into a single idea: decoherence in MF-SD does not require the artificial introduction of reference states, auxiliary trajectories, or trajectory swarms, which also makes MF-SD much more computationally efficient than other nonadiabatic MQC MD algorithms. The unified definition of decoherence in MF-SD requires only a single ad hoc parameter, which is not adjustable but instead is determined by the spatial extent of the nonadiabatic coupling. We use MF-SD to solve a series of one-dimensional scattering problems and find that MF-SD is as quantitatively accurate as several existing nonadiabatic MQC MD algorithms and significantly more accurate for some problems. [ABSTRACT FROM AUTHOR]

This paper investigates the impact of control field noise on the optimal manipulation of quantum dynamics. Simulations are performed on several multilevel quantum systems with the goal of population transfer in the presence of significant control noise. The noise enters as run-to-run variations in the control amplitude and phase with the observation being an ensemble average over many runs as is commonly done in the laboratory. A genetic algorithm with an improved elitism operator is used to find the optimal field that either fights against or cooperates with control field noise. When seeking a high control yield it is possible to find fields that successfully fight with the noise while attaining good quality stable results. When seeking modest control yields, fields can be found which are optimally shaped to cooperate with the noise and thereby drive the dynamics more efficiently. In general, noise reduces the coherence of the dynamics, but the results indicate that population transfer objectives can be met by appropriately either fighting or cooperating with noise, even when it is intense. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The present paper is devoted to a detailed study of the intramolecular vibrational energy redistribution in fluoroform initiated by a local mode excitation of the CH stretch [nνCH (n=1,...,4)]. All nine internal degrees of freedom are explicitly taken into account and the full quantum mechanical simulation is performed by means of the multiconfiguration time-dependent Hartree algorithm. The existence of different time scales considerably complicates the dynamics. The mode-to-mode energy transfer is analyzed by calculating the evolution of the partial energies of all vibrational modes. This study emphasizes the crucial role played by the two-dimensional FCH bending modes which act as an energy reservoir. The fast energy flow into these bending modes significantly hinders an energy flow from the CH chromophore. Finally, our results are compared with those obtained previously with the wave operator sorting algorithm approach. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The objective of this paper is to create a new kind of dynamical systems—a quantum-classical hybrid—that would preserve superposition and entanglement of random solutions while allowing one to measure their state variables by using classical methods. Such an optimal combination of characteristics is a perfect match for quantum-inspired computing. The model is represented by a modified Madelung equation in which the quantum potential is replaced by a different, specially chosen “computational” potential. As a result, the dynamics attains both quantum and classical properties. Similarities and differences of the proposed model with quantum systems are outlined. As an application, an algorithm for the global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithms is very simple: based on the quantum-inspired maximizer, introduce a positive function to be maximized as the probability density to which the solution is attracted. Then, the larger value of this function will have the higher probability to appear. Special attention is paid to the simulation of integer programming, NP-complete problems and information retrieval. [ABSTRACT FROM AUTHOR]

Reduction of a state of a quantum system to a subsystem gives partial quantum information about the true state of the total system. In connection with optimal state determination for two qubits, the question was raised about the maximum number of pairwise complementary reductions. The main result of the paper tells that the maximum number is 4, that is, if A1,A2,...,Ak are pairwise complementary (or quasiorthogonal) subalgebras of the algebra M4(C) of all 4×4 matrices and they are isomorphic to M2(C), then k≼4. The proof is based on a Cartan decomposition of SU(4). In the way to the main result, contributions are made to the understanding of the structure of complementary reductions. [ABSTRACT FROM AUTHOR]

In this paper we construct quantum mechanical observables of a single free particle that lives on the surface of the two-sphere S2 by implementing the Fedosov *-formalism. The Fedosov * is a generalization of the Moyal star product on an arbitrary symplectic manifold. After their construction we show that they obey the standard angular momentum commutation relations in ordinary nonrelativistic quantum mechanics. The purpose of this paper is threefold. One is to find an exact, nonperturbative solution of these observables. The other is to verify that the commutation relations of these observables correspond to angular momentum commutation relations. The last is to show a more general computation of the observables in Fedosov *-formalism; essentially an undeformation of Fedosov’s algorithm. [ABSTRACT FROM AUTHOR]

By means of complex representation and companion vector, in this paper we introduce a definition of rank of a quaternion matrix, study the problems of quaternionic linear equations, and obtain an algorithm for quaternionic linear equations in quaternionic quantum theory. [ABSTRACT FROM AUTHOR]

In this article, we demonstrate that Tully's fewest-switches surface hopping (FSSH) algorithm approximately obeys the mixed quantum-classical Liouville equation (QCLE), provided that several conditions are satisfied - some major conditions, and some minor. The major conditions are: (1) nuclei must be moving quickly with large momenta; (2) there cannot be explicit recoherences or interference effects between nuclear wave packets; (3) force-based decoherence must be added to the FSSH algorithm, and the trajectories can no longer rigorously be independent (though approximations for independent trajectories are possible). We furthermore expect that FSSH (with decoherence) will be most robust when nonadiabatic transitions in an adiabatic basis are dictated primarily by derivative couplings that are presumably localized to crossing regions, rather than by small but pervasive off-diagonal force matrix elements. In the end, our results emphasize the strengths of and possibilities for the FSSH algorithm when decoherence is included, while also demonstrating the limitations of the FSSH algorithm and its inherent inability to follow the QCLE exactly. [ABSTRACT FROM AUTHOR]

Pulay’s original expression for the basis-set dependent adjustment term to the Hellmann–Feynman force in electronic structure theory, which occurs for nonorthogonal local basis-set representations, is based on the idempotency condition of a pure ensemble. At finite electronic temperatures with a fractional occupation of the states, the conventional expression of the Pulay force is therefore no longer valid. Here we derive a simple and computationally efficient expression for a generalized Pulay force, which is suitable for large-scale ab initio simulations at finite electronic temperatures using local nonorthogonal basis-set representations. The generalized Pulay force expression is given in terms of the temperature-dependent density matrix. For the construction of the density matrix, we propose a recursive Fermi operator expansion algorithm that automatically converges to the correct chemical potential. [ABSTRACT FROM AUTHOR]

We provide a rigorous proof that the Hohenberg-Kohn theorem holds for spin densities by extending Lieb’s Legendre-transform formulation to spin densities. The resulting spin-density-functional theory resolves several troublesome issues. Most importantly, the present paper provides an explicit construction for the spin potentials at any point along the adiabatic connection curve, thus providing a formal basis for the use of exchange-correlation functionals of the spin density in the Kohn-Sham density-functional theory (DFT). The practical implications of this result for unrestricted Kohn-Sham DFT calculations is considered, and the existence of holes below the Fermi level is discussed. We argue that an orbital’s energy tends to increase as its occupation number increases, which provides the basis for a computational algorithm for determining the occupation numbers in Kohn-Sham DFT and helps explain the origin of Hund’s rules and holes below the Fermi level. [ABSTRACT FROM AUTHOR]

Rigorous simulations of quantum tunneling dynamics in model systems with up to 20 coupled degrees of freedom are reported. The simulations implement an extension of the recently developed matching-pursuit/split-operator Fourier-transform method to complex-valued coherent-state representations. The resulting method recursively applies the time-evolution operator, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state representations generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The matching-pursuit algorithm is implemented to develop an extension of the split-operator Fourier transform method to a nonorthogonal, nonuniform and dynamically adaptive coherent-state representation. The accuracy and efficiency of the computational approach are demonstrated in simulations of deep tunneling and long time dynamics by comparing our simulation results with the corresponding benchmark calculations. [ABSTRACT FROM AUTHOR]

Presents a general self-guided algorithm for direct laboratory learning of controls to manipulate quantum-mechanical systems. Focus on an algorithm based on the learning of a linear laboratory input-output map from a sequence of controls; Self-guided iterative learning control; Incorporation of input and output basis functions.

The sum-of-products finite-basis-representation (SOP-FBR) approach for the automated multidimensional fit of potential energy surfaces (PESs) is presented. In its current implementation, the method yields a PES in the so-called Tucker sum-of-products form, but it is not restricted to this specific ansatz. The novelty of our algorithm lies in the fact that the fit is performed in terms of a direct product of a Schmidt basis, also known as natural potentials. These encode in a non-trivial way all the physics of the problem and, hence, circumvent the usual extra ad hoc and a posteriori adjustments (e.g., damping functions) of the fitted PES. Moreover, we avoid the intermediate refitting stage common to other tensor-decomposition methods, typically used in the context of nuclear quantum dynamics. The resulting SOP-FBR PES is analytical and differentiable ad infinitum. Our ansatz is fully general and can be used in combination with most (molecular) dynamics codes. In particular, it has been interfaced and extensively tested with the Heidelberg implementation of the multiconfiguration time-dependent Hartree quantum dynamical software package. [ABSTRACT FROM AUTHOR]

Compares the sensitivity behavior between direct and long-lived classical trajectories and quantum wave packets in a H-H[sub 2] reaction. Response to perturbations; Sensitivities of trajectories to variations in the potential; Algorithm that accounts for the contributions to the sensitivities from the trajectories.

In this paper, we present a study of discrete time quantum walks whose underlying graph is a d-dimensional lattice. The dynamical behavior of these systems is of current interest because of their applications in quantum information theory as tools to design quantum algorithms. We assume that, at each step of the walk evolution, the coin transformation is allowed to change so that we can use it as a control variable to drive the evolution in a desired manner. We give an exact description of the possible evolutions and of the set of possible states that can be achieved with such a system. In particular, we show that it is possible to go from a state where there is probability 1 for the walker to be found in a vertex to a state where all the vertices have equal probability. We also prove a number of properties of the set of admissible states in terms of the number of steps needed to obtain them. We provide explicit algorithms for state transfer in low dimensional cases as well as results that allow to reduce algorithms on two-dimensional lattices to algorithms on the one-dimensional lattice, the cycle. [ABSTRACT FROM AUTHOR]

By means of complex representation and companion vector, this paper studies the problems of eigenvalues and eigenvectors of quaternion matrices, and gives a technique of computing the eigenvalues and eigenvectors of the quaternion matrices in quaternionic quantum mechanics. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We demonstrate an efficient algorithm for inverse problems in time-dependent quantum dynamics based on feedback loops between Hamiltonian parameters and the solutions of the Schrödinger equation. Our approach formulates the inverse problem as a target vector estimation problem and uses Bayesian surrogate models of the Schrödinger equation solutions to direct the optimization of feedback loops. For the surrogate models, we use Gaussian processes with vector outputs and composite kernels built by an iterative algorithm with the Bayesian information criterion (BIC) as a kernel selection metric. The outputs of the Gaussian processes are designed to model an observable simultaneously at different time instances. We show that the use of Gaussian processes with vector outputs and the BIC-directed kernel construction reduces the number of iterations in the feedback loops by, at least, a factor of 3. We also demonstrate an application of Bayesian optimization for inverse problems with noisy data. To demonstrate the algorithm, we consider the orientation and alignment of polyatomic molecules SO2 and propylene oxide (PPO) induced by strong laser pulses. We use simulated time evolutions of the orientation or alignment signals to determine the relevant components of the molecular polarizability tensors. We show that, for the five independent components of the polarizability tensor of PPO, this can be achieved with as few as 30 quantum dynamics calculations. [ABSTRACT FROM AUTHOR]

In a recent paper, we presented a road map for how Tully's fewest switches surface hopping (FSSH) algorithm can be derived, under certain circumstances, from the mixed quantum-classical Liouville equation. In this communication, we now demonstrate how this new interpretation of surface hopping can yield significantly enhanced results for electronic properties in nonadiabatic calculations. Specifically, we calculate diabatic populations for the spin-boson problem using FSSH trajectories. We show that, for some Hamiltonians, without changing the FSSH algorithm at all but rather simply reinterpreting the ensemble of surface hopping trajectories, we recover excellent results and remove any and all ambiguity about the initial condition problem. [ABSTRACT FROM AUTHOR]

Discusses the metric and coordinate invariance of the helicity of the magnetic field intensity vector H. Introduction of a complexified time dependent helicity functional; Details on Wexler's algorithm; Time dependent version of the helicity functional and the relevance of metric independence in the solution of inverse problems.

Trajectory surface hopping (TSH) methods have been widely used for the study of nonadiabatic molecular dynamics. In the present work, the accuracy of two TSH algorithms, Tully's fewest switching algorithm and an algorithm based on the Landau-Zener formula, has been critically evaluated in comparison with exact nonadiabatic quantum dynamics calculations for a model of the photoinduced hydrogen-atom dissociation reaction in phenol. The model consists of three electronic states (S0, ¹ππ*, ¹πσ*) and two nuclear degrees of freedom (the OH stretching coordinate and CCOH dihedral angle) and displays two successive conical intersections (¹ππ*/¹πσ* and ¹πσ*/S0). Considering instantaneous photoexcitation from different vibrational levels of the S0 state to the ¹ππ* state, we examined the time-dependent electronic population dynamics as well as the branching ratio of the two dissociation channels. The results of fully converged trajectory calculations are compared with the results of exact quantum wave-packet calculations. It is found that both TSH algorithms describe the dynamics at the ¹πσ*/S0 conical intersection, which is accessed with high excess energy, with good accuracy. The ¹ππ*/¹πσ* conical intersection, on the other hand, is accessed with little excess energy so tunneling effects as well as wave-packet interference effects which cannot be reproduced with classical trajectory calculations become relevant. Overall, the performance of the fewest-switching and Landau-Zener surface-hopping algorithms for the photodissociation of phenol is very similar. The populations of the adiabatic S¹ and S² states are found to exhibit fast oscillations which reflect nonadiabatic electronic transitions driven by coherent dynamics in the OH stretching mode. These electronic population oscillations are qualitatively reproduced by both TSH algorithms. [ABSTRACT FROM AUTHOR]

The iterative decomposition of the blip-summed path integral [N. Makri, J. Chem. Phys. 141, 134117 (2014)] is described. The starting point is the expression of the reduced density matrix for a quantum system interacting with a harmonic dissipative bath in the form of a forward-backward path sum, where the effects of the bath enter through the Feynman-Vernon influence functional. The path sum is evaluated iteratively in time by propagating an array that stores blip configurations within the memory interval. Convergence with respect to the number of blips and the memory length yields numerically exact results which are free of statistical error. In situations of strongly dissipative, sluggish baths, the algorithm leads to a dramatic reduction of computational effort in comparison with iterative path integral methods that do not implement the blip decomposition. This gain in efficiency arises from (i) the rapid convergence of the blip series and (ii) circumventing the explicit enumeration of between-blip path segments, whose number grows exponentially with the memory length. Application to an asymmetric dissipative two-level system illustrates the rapid convergence of the algorithm even when the bath memory is extremely long. [ABSTRACT FROM AUTHOR]

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task--especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version. [ABSTRACT FROM AUTHOR]

Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy. [ABSTRACT FROM AUTHOR]

We investigate the incorporation of the surface-leaking (SL) algorithm into Tully's fewest-switches surface hopping (FSSH) algorithm to simulate some electronic relaxation induced by an electronic bath in conjunction with some electronic transitions between discrete states. The resulting SL-FSSH algorithm is benchmarked against exact quantum scattering calculations for three one-dimensional model problems. The results show excellent agreement between SL-FSSH and exact quantum dynamics in the wide band limit, suggesting the potential for a SL-FSSH algorithm. Discrepancies and failures are investigated in detail to understand the factors that will limit the reliability of SL-FSSH, especially the wide band approximation. Considering the easiness of implementation and the low computational cost, we expect this method to be useful in studying processes involving both a continuum of electronic states (where electronic dynamics are probabilistic) and processes involving only a few electronic states (where non-adiabatic processes cannot ignore short-time coherence). [ABSTRACT FROM AUTHOR]

The objective of pure-sampling quantum Monte Carlo is to calculate physical properties that are independent of the importance sampling function being employed in the calculation, save for the mismatch of its nodal hypersurface with that of the exact wave function. To achieve this objective, we report a pure-sampling algorithm that combines features of forward walking methods of pure-sampling and reptation quantum Monte Carlo (RQMC). The new algorithm accurately samples properties from the mixed and pure distributions simultaneously in runs performed at a single set of time-steps, over which extrapolation to zero time-step is performed. In a detailed comparison, we found RQMC to be less efficient. It requires different sets of time-steps to accurately determine the energy and other properties, such as the dipole moment. We implement our algorithm by systematically increasing an algorithmic parameter until the properties converge to statistically equivalent values. As a proof in principle, we calculated the fixed-node energy, static a polarizability, and other one-electron expectation values for the ground-states of LiH and water molecules. These quantities are free from importance sampling bias, population control bias, time-step bias, extrapolation-model bias, and the finite-field approximation. We found excellent agreement with the accepted values for the energy and a variety of other properties for those systems. [ABSTRACT FROM AUTHOR]