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At least 127 records · Page 7
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DOE OSTI2020

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman–von Neumann formulation of classical mechanics. The Koopman–von Neumann formulation implies that the conservation of the probability distribution function on phase space, as expressed by the Liouville equation, can be recast as an equivalent Schrödinger equation on Hilbert space with a Hermitian Hamiltonian operator and a unitary propagator. This Schrödinger equation is linear in the momenta because it derives from a constrained Hamiltonian system with twice the classical phase-space dimension. A quantum computer with finite resources can be used to simulate a finite-dimensional approximation of this unitary evolution operator. Quantum simulation of classical dynamics is exponentially more efficient than a deterministic Eulerian discretization of the Liouville equation if the Koopman–von Neumann Hamiltonian is sparse. Utilizing quantum walk techniques for state preparation and amplitude estimation for the calculation of observables leads to a quadratic improvement over classical probabilistic Monte Carlo algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Diverging Quantum Speed Limits: A Herald of Classicality

When is the quantum speed limit (QSL) really quantum? While vanishing QSL times often indicate emergent classical behavior, it is still not entirely understood what precise aspects of classicality are at the origin of this dynamical feature. Here, we show that vanishing QSL times (or, equivalently, diverging quantum speeds) can be traced back to reduced uncertainty in quantum observables and can thus be understood as a consequence of emerging classicality for these particular observables. We illustrate this mechanism by developing a QSL formalism for continuous-variable quantum systems undergoing general Gaussian dynamics. For these systems, we show that three typical scenarios leading to vanishing QSL times, namely large squeezing, small effective Planck’s constant, and large particle number, can be fundamentally connected to each other. In contrast, by studying the dynamics of open quantum systems and mixed states, we show that the classicality that emerges due to incoherent mixing of states from the addition of classical noise typically increases the QSL time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Emulation of quantum correlations by classical dynamics in a spin-$\frac{1}{2}$ Heisenberg chain

We simulate the dynamical spin structure factor (DSSF) 𝒮⁡(𝑞,𝜔) of the spin-1/2 Heisenberg antiferromagnetic chain using classical simulations. By employing Landau-Lifshitz Dynamics, we emulate quantum correlations through temperature-dependent corrections, including rescaling of magnetic dipoles and renormalization of exchange interactions. Here, our results closely match Quantum Monte-Carlo calculations for 𝑘 B⁢ 𝑇/𝐽≳1, extending the applicability of classical dynamics to the challenging case of gapless excitations. At higher temperatures, our simulations comply with general predictions for uncorrelated paramagnetic fluctuations in the infinite temperature limit. Entanglement witnesses derived from the quantum-equivalent DSSF act as sensitive diagnostics for the quantum-to-classical crossover. Their reliability stems from their dependence on spectral features alone, enabling classical dynamics to emulate quantum thresholds without genuine entanglement. This framework also reproduces transverse spin correlations in finite magnetic fields, in agreement with quantum simulations. Together, our results establish quantum-corrected classical dynamics as a scalable and predictive tool for interpreting scattering experiments and exploring quantum correlations in strongly correlated spin systems.

Inelastic neutron scattering↗
DOE OSTI2015

Reexamining classical and quantum models for the D-Wave One processor: The role of excited states and ground state degeneracy

We revisit the evidence for quantum annealing in the D-Wave One device (DW1) based on the study of random Ising instances. Using the probability distributions of finding the ground states of such instances, previous work found agreement with both simulated quantum annealing (SQA) and a classical rotor model. Thus the DW1 ground state success probabilities are consistent with both models, and a different measure is needed to distinguish the data and the models. Here in this paper we consider measures that account for ground state degeneracy and the distributions of excited states, and present evidence that for these new measures neither SQA nor the classical rotor model correlate perfectly with the DW1 experiments. We thus provide evidence that SQA and the classical rotor model, both of which are classically efficient algorithms, do not satisfactorily explain all the DW1 data. A complete model for the DW1 remains an open problem. Using the same criteria we find that, on the other hand, SQA and the classical rotor model correlate closely with each other. To explain this we show that the rotor model can be derived as the semiclassical limit of the spin-coherent states path integral. We also find differences in which set of ground states is found by each method, though this feature is sensitive to calibration errors of the DW1 device and to simulation parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Hybrid quantum-classical algorithms for approximate graph coloring

We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX- k -CUT, the problem of finding an approximate k -vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p : the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level- 1 QAOA and level- 1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level- 1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3 -colorable constant-degree graphs. We find that level- 1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Linking classical PRA models to a dynamic PRA

Here, this paper presents a series of methods designed to incorporate classical Probabilistic Risk Assessment (PRA) models such as Event Trees (ETs) and Fault Trees (FTs) into dynamic PRA. In contrast to classical PRA, dynamic PRA couples stochastic methods with system simulators to determine the risks associated with complex systems such as nuclear power plants. Compared with classical PRA methods, they can evaluate with higher resolution the safety impact of timing and sequencing of events on the progression of the accident. As part of a dynamic PRA analysis, it is not uncommon that parts of the system to be analyzed might not require a computationally expensive simulation model. These parts could be in fact modeled by employing classical PRA models (e.g., a FT). Here, we present a set of methods and tools that can be used to link the most common classical PRA models (ETs, FTs, reliability block diagrams and Markov models) to simulation codes such as RELAP5-3D: creating a “hybrid PRA.” In order to show the potential of such an hybrid PRA we employ this method to verify ET modeling assumptions (e.g., success criteria) using a large break loss of coolant accident initiating event as a test case. In this respect, we link a set of FTs from the original PRA to the RELAP5-3D code and perform a hybrid PRA. The FTs are employed to model the control logic of several safety systems and to propagate component failures throughout the system. Provided the generated dynamic PRA data, we show how conservative assumptions in the original PRA can be identified and how such original PRA can be modified by updating success criteria captured by the set of RELAP5-3D simulation runs.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2018

CD40L and TNF both activate the classical NF-κB pathway, which is not required for the CD40L induced alternative pathway in endothelial cells

Highlights: • In endothelial cells TNF induces a stronger response in gene expression as compared to CD40L. • There are no CD40L-specific genes expressed. • CD40L activates both the classical and the alternative pathway. • Activation of the alternative pathway is independent from the classical pathway. CD40L and TNF signal through engagement of their respective receptors, which are both members of the TNF receptor family. They use partially common signaling molecules leading, among others, to activation of the NF-κB pathway. However, whereas TNF activates the classical, CD40L has been reported to activate the alternative NF-κB pathway, leading to the anticipation that differences in the pattern of inflammatory gene expression would occur. Here, we have compared the gene expression repertoire of CD40L (CD154) and TNF stimulated HUVEC and report that unexpectedly, apart from a stronger response to TNF, no major qualitative differences could be observed. This applies for the period of up to 6 h, a time where the alternative pathway has already been activated. Analysis of the early events after receptor engagement revealed that both TNF and CD40L activate the classical NF-κB pathway, and confirm activation of the alternative by the latter. Furthermore, using genetic and pharmacological inhibition of the classical pathway we show that activation of the alternative occurs independently of the former. This reveals novel insights into NF-κB signaling by CD40L and TNF in endothelial cells.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Finding quantum effects in strong classical potentials

The long-standing challenge to describing charged particle dynamics in strong classical electromagnetic fields is how to incorporate classical radiation, classical radiation reaction and quantized photon emission into a consistent unified framework. The current, semiclassical methods to describe the dynamics of quantum particles in strong classical fields also provide the theoretical framework for fundamental questions in gravity and hadron–hadron collisions, including Hawking radiation, cosmological particle production and thermalization of particles created in heavy-ion collisions. However, as we show, these methods break down for highly relativistic particles propagating in strong fields. They must therefore be improved and adapted for the description of laser–plasma experiments that typically involve the acceleration of electrons. Theory developed from quantum electrodynamics, together with dedicated experimental efforts, offer the best controllable context to establish a robust, experimentally validated foundation for the fundamental theory of quantum effects in strong classical potentials.

Physics↗
DOE OSTI2015

A Symmetrical Quasi-Classical Spin-Mapping Model for the Electronic Degrees of Freedom in Non-Adiabatic Processes

A recent series of papers has proven that a symmetrical quasi-classical (SQC) windowing procedure applied to the Meyer-Miller (MM) classical vibronic Hamiltonian provides a very good treatment of electronically nonadiabatic processes in a variety of benchmark model systems, including systems that exhibit strong quantum coherence effects and some which other approximate approaches have difficulty in describing correctly. In this paper, a different classical electronic Hamiltonian for the treatment of electronically nonadiabatic processes is proposed (and "quantized" via the SQC windowing approach), which maps the dynamics of F coupled electronic states to a set of F spin- 1 / 2 degrees of freedom (DOF), similar to the Fermionic spin model described by Miller and White (J. Chem. Phys. 1986, 84, 5059). It is noted that this spin-mapping (SM) Hamiltonian is an exact Hamiltonian if treated as a quantum mechanical (QM) operator-and thus QM'ly equivalent to the MM Hamiltonian-but that an analytically distinct classical analogue is obtained by replacing the QM spin-operators with their classical counterparts. Due to their analytic differences, a practical comparison is then made between the MM and SM Hamiltonians (when quantized with the SQC technique) by applying the latter to many of the same benchmark test problems successfully treated in our recent work with the SQC/MM model. We find that for every benchmark problem the MM model provides (slightly) better agreement with the correct quantum nonadiabatic transition probabilities than does the new SM model. This is despite the fact that one might expect, a priori, a more natural description of electronic state populations (occupied versus unoccupied) to be provided by DOF with only two states, i.e., spin- 1 / 2 DOF, rather than by harmonic oscillator DOF which have an infinite manifold of states (though only two of these are ever occupied).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Modeling of Peptides with Classical and Novel Machine Learning Force Fields: A Comparison

The replacement of classical force fields (FFs) with novel neural-network-based frameworks is an emergent topic in molecular dynamics (MD) simulations. In contrast to classical FFs, which have proven their capability to provide insights into complex soft matter systems at an atomistic resolution, the machine learning (ML) potentials have yet to demonstrate their applicability for soft materials. However, the underlying philosophy, which is learning the energy of an atom in its surrounding chemical environment, makes this approach a promising tool. In particular for the exploration of novel chemical compounds, which have not been considered in the original parametrization of classical FFs. In this article, we study the performance of the ANI-2x ML model and compare the results with those of two classical FFs, namely, CHARMM27 and the GROMOS96 43a1 FF. We explore the performance of these FFs for bulk water and two model peptides, trialanine and a 9-mer of the α-aminoisobutyric acid, in vacuum and water. The results for water describe a highly ordered water structure, with a structure similar to those using ab initio molecular dynamics simulations. The energy landscape of the peptides described by Ramachandran maps show secondary structure basins similar to those of the classical FFs but differ in the position and relative stability of the basins. Details of the sampled structures show a divergent performance of the different models, which can be related either to the short-ranged nature of the ML potentials or to shortcomings of the underlying data set used for training. These findings highlight the current state of the applicability of ANI-2x ML potential for MD simulations of soft matter systems. Simultaneously, they provide insights for future improvements of current ML potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A Bayesian analysis of classical shadows

Abstract The method of classical shadows proposed by Huang, Kueng, and Preskill heralds remarkable opportunities for quantum estimation with limited measurements. Yet its relationship to established quantum tomographic approaches, particularly those based on likelihood models, remains unclear. In this article, we investigate classical shadows through the lens of Bayesian mean estimation (BME). In direct tests on numerical data, BME is found to attain significantly lower error on average, but classical shadows prove remarkably more accurate in specific situations—such as high-fidelity ground truth states—which are improbable in a fully uniform Hilbert space. We then introduce an observable-oriented pseudo-likelihood that successfully emulates the dimension-independence and state-specific optimality of classical shadows, but within a Bayesian framework that ensures only physical states. Our research reveals how classical shadows effect important departures from conventional thinking in quantum state estimation, as well as the utility of Bayesian methods for uncovering and formalizing statistical assumptions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Classical molecular dynamics simulation of electronically non-adiabatic processes

Both classical and quantum mechanics (as well as hybrids thereof, i.e., semiclassical approaches) find widespread use in simulating dynamical processes in molecular systems. For large chemical systems, however, which involve potential energy surfaces (PES) of general/arbitrary form, it is usually the case that only classical molecular dynamics (MD) approaches are feasible, and their use is thus ubiquitous nowadays, at least for chemical processes involving dynamics on a single PES (i.e., within a single Born-Oppenheimer electronic state). Our paper reviews recent developments in an approach which extends standard classical MD methods to the treatment of electronically non-adiabatic processes, i.e., those that involve transitions between different electronic states. This approach treats nuclear and electronic degrees of freedom (DOF) equivalently (i.e., by classical mechanics, thereby retaining the simplicity of standard MD), and provides "quantization" of the electronic states through a symmetrical quasi-classical (SQC) windowing model. The approach is seen to be capable of treating extreme regimes of strong and weak coupling between the electronic states, as well as accurately describing coherence effects in the electronic DOF (including the de-coherence of such effects caused by coupling to the nuclear DOF). A survey of recent applications is presented to illustrate the performance of the approach. We also described is a newly developed variation on the original SQC model (found universally superior to the original) and a general extension of the SQC model to obtain the full electronic density matrix (at no additional cost/complexity).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Classical confinement and outward convection of impurity ions in the MST RFP

Impurity ion dynamics measured with simultaneously high spatial and temporal resolution reveal classical ion transport in the reversed-field pinch. The boron, carbon, oxygen, and aluminum impurity ion density profiles are obtained in the Madison Symmetric Torus [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)] using a fast, active charge-exchange-recombination-spectroscopy diagnostic. Measurements are made during improved-confinement plasmas obtained using inductive control of tearing instability to mitigate stochastic transport. At the onset of the transition to improved confinement, the impurity ion density profile becomes hollow, with a slow decay in the core region concurrent with an increase in the outer region, implying an outward convection of impurities. Impurity transport from Coulomb collisions in the reversed-field pinch is classical for all collisionality regimes, and analysis shows that the observed hollow profile and outward convection can be explained by the classical temperature screening mechanism. The profile agrees well with classical expectations. Experiments performed with impurity pellet injection provide further evidence for classical impurity ion confinement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

A mixed quantum-classical Liouville study of the population dynamics in a model photo-induced condensed phase electron transfer reaction

We apply two approximate solutions of the quantum-classical Liouville equation (QCLE) in the mapping representation to the simulation of the laser-induced response of a quantum subsystem coupled to a classical environment. These solutions, known as the Poisson Bracket Mapping Equation (PBME) and the Forward-Backward (FB) trajectory solutions, involve simple algorithms in which the dynamics of both the quantum and classical degrees of freedom are described in terms of continuous variables, as opposed to standard surface-hopping solutions in which the classical degrees of freedom hop between potential energy surfaces dictated by the discrete adiabatic state of the quantum subsystem. The validity of these QCLE-based solutions is tested on a non-trivial electron transfer model involving more than two quantum states, a time-dependent Hamiltonian, strong subsystem-bath coupling, and an initial energy shift between the donor and acceptor states that depends on the strength of the subsystem-bath coupling. In particular, we calculate the time-dependent population of the photoexcited donor state in response to an ultrafast, on-resonance pump pulse in a three-state model of an electron transfer complex that is coupled asymmetrically to a bath of harmonic oscillators through the optically dark acceptor state. Within this approach, the three-state electron transfer complex is treated quantum mechanically, while the bath oscillators are treated classically. When compared to the more accurate QCLE-based surface-hopping solution and to the numerically exact quantum results, we find that the PBME solution is not capable of qualitatively capturing the population dynamics, whereas the FB solution is. However, when the subsystem-bath coupling is decreased (which also decreases the initial energy shift between the donor and acceptor states) or the initial shift is removed altogether, both the PBME and FB results agree better with the QCLE-based surface-hopping results. These findings highlight the challenges posed by various conditions such as a time-dependent external field, the strength of the subsystem-bath coupling, and the degree of asymmetry on the accuracy of the PBME and FB algorithms.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Comparison of classical and quantal calculations of helium three-body recombination

A general method to study classical scattering in n-dimension is developed. Through classical trajectory calculations, the three-body recombination is computed as a function of the collision energy for helium atoms, as an example. Quantum calculations are also performed for the J{sup Π} = 0{sup +} symmetry of the three-body recombination rate in order to compare with the classical results, yielding good agreement for E ≳ 1 K. The classical threshold law is derived and numerically confirmed for the Newtonian three-body recombination rate. Finally, a relationship is found between the quantum and classical three-body hard hypersphere elastic cross sections which is analogous to the well-known shadow scattering in two-body collisions.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Far-infrared collision-induced absorption in rare gas mixtures: Quantum and semi-classical calculations

We compare calculations of the translational collision-induced spectra and their integrated intensities of both He–Ar and Ne–Ar collisional complexes, using the quantum mechanical and a semiclassical formalism. Advanced potential energy and induced dipole functions are used for the calculations. The quantum method used is as described previously [L. Frommhold, Collision-induced Absorption in Gases (Cambridge University Press, 1993 and 2006)]. The semiclassical method is based on repeated classical atom-atom scattering calculations to simulate an ensemble average; subsequent Fourier transform then renders the binary absorption coefficient as a function of frequency. The problem of classical calculations is the violation of the principle of detailed balance, which may be introduced only artificially in classical calculations. Nevertheless, it is shown that the use of classical trajectories permits a fairly accurate reproduction of the experimental spectra, comparable to the quantum mechanical results at not too low temperatures and for collisional pairs of not too small reduced mass. Inexpensive classical calculations may thus be promising to compute spectra also of molecular pairs, or even of polyatomic collisional pairs with anisotropic intermolecular interactions, for which the quantum approach is still inefficient or impractical.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Ice and water droplets on graphite: A comparison of quantum and classical simulations

Ice and water droplets on graphite have been studied by quantum path integral and classical molecular dynamics simulations. The point-charge q-TIP4P/F potential was used to model the interaction between flexible water molecules, while the water-graphite interaction was described by a Lennard-Jones potential previously used to reproduce the macroscopic contact angle of water droplets on graphite. Several energetic and structural properties of water droplets with sizes between 10{sup 2} and 10{sup 3} molecules were analyzed in a temperature interval of 50–350 K. The vibrational density of states of crystalline and amorphous ice drops was correlated to the one of ice Ih to assess the influence of the droplet interface and molecular disorder on the vibrational properties. The average distance of covalent OH bonds is found 0.01 Å larger in the quantum limit than in the classical one. The OO distances are elongated by 0.03 Å in the quantum simulations at 50 K. Bond distance fluctuations are large as a consequence of the zero-point vibrations. The analysis of the H-bond network shows that the liquid droplet is more structured in the classical limit than in the quantum case. The average kinetic and potential energy of the ice and water droplets on graphite has been compared with the values of ice Ih and liquid water as a function of temperature. The droplet kinetic energy shows a temperature dependence similar to the one of liquid water, without apparent discontinuity at temperatures where the droplet is solid. However, the droplet potential energy becomes significantly larger than the one of ice or water at the same temperature. In the quantum limit, the ice droplet is more expanded than in a classical description. Liquid droplets display identical density profiles and liquid-vapor interfaces in the quantum and classical limits. The value of the contact angle is not influenced by quantum effects. Contact angles of droplets decrease as the size of the water droplet increases which implies a positive sign of the line tension of the droplet.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Classical-quantum scattering

We analyze the framework recently proposed by Oppenheim et al (2023 Nat. Commun. 14; 2023 Phys. Rev. X 13 041040; arXiv:2302.07283 [gr-qc]; 2023 J. High Energy Phys. JHEP08(2023)163) to model relativistic quantum fields coupled to relativistic, classical, stochastic fields (in particular, as a model of quantum matter coupled to ‘classical gravity’). Perhaps surprisingly, we find that we can define and calculate scattering probabilities which are Lorentz-covariant and conserve total probability, at least at tree level. As a concrete example, we analyze 2→2 scattering of quantum matter mediated by a classical Yukawa field. Mapping this to a gravitational coupling in the non-relativistic limit, and assuming that we can treat large objects as point masses, we find that the simplest possible ‘classical-quantum’ gravity theory constructed this way gives predictions for 2→2 gravitational scattering which are inconsistent with simple observations of, e.g. spacecraft undergoing slingshot maneuvers. We comment on lessons learned for attempts to couple quantum matter to ‘non-quantum’ gravity, or more generally, for attempts to couple relativistic quantum and classical systems.

Carney, Daniel↗