arXiv subjects

Roman V. Krems

Publications and source records attributed to Roman V. Krems.

At least 19 recordsLinked to original sources

arXiv2026

Direct imaging of enantiomer-specific orientation dynamics in unidirectionally rotating chiral molecules

Selectively controlling the dynamics of molecular enantiomers underlies advances across chemistry, biology, and physics, yet direct imaging of enantiomer-specific motion has so far remained elusive. Here, we image ultrafast enantioselective orientation dynamics in isolated chiral molecules. Unidirectional coherent rotation induced by a femtosecond laser-pulse pair generates equal and opposite out-of-plane orientations of the two enantiomers. Applying this scheme to 2-methyloxirane, we follow the rotational wave packets by time-resolved Coulomb explosion imaging with two orthogonally arranged detectors. The measured angular distributions reveal that the unidirectional rotation is identical for both enantiomers, while the out-of-plane orientations are mirror images that persist through both early-time quasi-classical and quantum dynamics regimes, in quantitative agreement with simulations. We demonstrate that full angular distributions provide richer dynamical information, with some qualitatively different distributions yielding similar orientation factors upon integration. Our approach opens a route to real-time observation and control of chiral dynamics in the gas phase.

physics.chem-ph↗

arXiv2026

Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms

We formalize a rigorous connection between barren plateaus (BP) in variational quantum algorithms and exponential concentration of quantum kernels for machine learning. Our results imply that recently proposed strategies to build BP-free quantum circuits can be utilized to construct useful quantum kernels for machine learning. This is illustrated by a numerical example employing a provably BP-free quantum neural network to construct kernel matrices for classification datasets of increasing dimensionality without exponential concentration.

quant-ph↗

arXiv2026

Bayesian Optimization in Chemical Compound Sub-Spaces using Low-Dimensional Molecular Descriptors

Efficient optimization of molecules with targeted properties remains a significant challenge due to the vast size and discrete nature of chemical compound space. Conventional machine-learning-based optimization approaches typically require large datasets to construct accurate surrogate models, limiting their applicability in data-scarce settings. In this study, we present a Bayesian optimization (BO) framework that identifies optimal molecular structures with high precision using fewer than 2,000 training data points within a chemical subspace containing more than 133,000 molecules. The framework employs a low-dimensional and physics-informed molecular descriptor vector that facilitates data-efficient surrogate modelling and optimization. A key innovation of the proposed framework is a reliable inverse mapping scheme that translates optimized points in the descriptor space back into chemically valid molecular structures, thereby bridging continuous optimization and discrete molecular design. We demonstrate the effectiveness of our approach on the QM9 benchmark dataset, where the framework successfully identifies organic molecules with the target entropy and zero-point vibrational energy (ZPVE) values.For entropy optimization, our approach achieves a 100% success rate while requiring fewer than 1,000 molecular evaluations in more than 80% of test cases. For ZPVE, the success rate exceeds 80% for molecules containing more than two heavy atoms. These results highlight the critical role of low-dimensional, interpretable descriptors in enabling data-efficient optimization and robust inverse molecular design, and establish Bayesian optimization as a practical tool for molecular discovery in small-data regimes.

physics.chem-ph↗

arXiv2026

Invariance of quantum scattering rate coefficients to anisotropy of atom-molecule interactions

Quantum scattering calculations for strongly interacting molecular systems are computationally demanding due to the large number of molecular states coupled by the anisotropy of atom - molecule interactions. We demonstrate that thermal rate coefficients for total (elastic + inelastic) atom - molecule scattering are insensitive to the interaction anisotropy of the underlying potential energy surface. In particular, we show that the rate coefficients for Rb-H$_2$ and Rb-N$_2$ scattering at room temperature can be computed to 1% accuracy with anisotropy set to zero, reducing the complexity of coupled channel quantum scattering calculations to numerical solutions of a single differential equation. Our numerical calculations and statistical analysis based on Gaussian process regression elucidate the origin and limitations of the invariance of the total scattering rate coefficients to changes in atom - molecule interaction anisotropy.

physics.chem-ph↗

arXiv2025

Rigorous quantum calculations for atom-molecule chemical reactions in electric fields: from single to multiple partial wave regimes

We present an efficient method for rigorous quantum calculations of cross sections for atom-molecule reactive scattering in the presence of a dc electric field. The wavefunction of the reaction complex is expanded in an overcomplete set of arrangement-dependent Fock-Delves hyperspherical basis functions and the interactions of the reactants and products with electric fields are accounted for in the total angular momentum representation. A significant computational challenge affecting our previously developed approach [Phys. Rev. Lett. $\mathbf{115}$, 023201 (2015)] is addressed by an efficient asymptotic frame transformation between the hyperspherical and Jacobi coordinates in the presence of an external field. Using accurate {\it ab initio} potential energy surfaces, we calculate total and state-resolved cross sections for the chemical reactions LiF$(v=1,j=0)$ + H $\to$ Li + HF($v'=0,j'$) and F + HD$(v=0,j=0)$ $\to$ HF + D, DF + H as functions of collision energy and electric field strength. The field dependence of the cross sections for the LiF + H chemical reaction exhibits resonance structure mediated by tunneling-driven interactions between reactants and products. No significant field effects are found for the F + HD $\to$ HF + D, DF + H chemical reaction at 1 Kelvin, even for state-resolved transitions and with field magnitudes reaching 200 kV/cm. Our calculations illustrate the essential role of basis set convergence for the proper interpretation of external field effects on chemical reaction dynamics. While reduced-basis calculations for the F + HD reaction indicate significant effects of electric fields on product state distributions, these effects vanish when the number of total angular momentum basis states is increased.

physics.chem-ph↗

arXiv2025

Neural network ensemble for computing cross sections for rotational transitions in H$_{2}$O + H$_{2}$O collisions

Water (H$_2$O) is one of the most abundant molecules in the universe and is found in a wide variety of astrophysical environments. Rotational transitions in H$_2$O + H$_2$O collisions are important in modeling environments rich in water molecules but they are computationally intractable using quantum mechanical methods. Here, we present a machine learning (ML) tool using an ensemble of neural networks (NNs) to predict cross sections to construct a database of rate coefficients for rotationally inelastic transitions in collisions of complex molecules such as water. The proposed methodology utilizes data computed with a mixed quantum-classical theory (MQCT). We illustrate that efficient ML models using NN can be built to accurately interpolate in the space of 12 quantum numbers for rotational transitions in two asymmetric top molecules, spanning both initial and final states. We examine various architectures of data corresponding to each collision energy, symmetry of water molecule, and excitation/de-excitation rotational transitions, and optimize the training/validation data sets. Using only about 10\% of the computed data for training, the NNs predict cross sections of state-to-state rotational transitions of H$_{2}$O + H$_{2}$O collision with average relative root mean square error of 0.409. Thermally averaged cross sections, computed using the predicted state-to-state cross sections ($\sim$90\%) and the data used for training and validation ($\sim$10\%) were compared against those obtained entirely from MQCT calculations. The agreement is found to be excellent with an average percent deviation of about $\sim$13.5\%. The methodology is robust, and thus, applicable to other complex molecular systems.

physics.chem-ph↗

arXiv2025

Echoes in a parametrically perturbed Kerr-nonlinear oscillator

We study classical and quantum echoes in a Kerr oscillator driven by a frequency-controlling pulsed perturbation. We consider dynamical response to the perturbation for a single coherent state and for Schrödinger cat states constructed as both balanced and imbalanced superpositions of two coherent states. For individual coherent states, we demonstrate that a weak parametric drive yields a long-lived sequence of classical echoes. Cat states are found to exhibit distinct quantum echoes that are sensitive to the initial relative phase and weights of the coherent states in superposition. We examine the effect of dissipation on quantum echoes and quantum revivals of cat states. We demonstrate that, even when dissipation suppresses quantum revivals, quantum echoes can be recovered by properly tuning the timing and strength of the perturbation. These results may be useful for characterizing and mitigating errors of cat qubits.

quant-ph↗

arXiv2025

Molecular representations of quantum circuits for quantum machine learning

We establish an isomorphism between quantum circuits and a subspace of polyatomic molecules, which suggests that molecules can be used as descriptors of quantum circuits for quantum machine learning. Our numerical results show that the performance of quantum circuits for quantum support vector machines can be characterized by dimensionality-reduced molecular fingerprints as well as by the size of the largest and smallest Gershgorin circles derived from the Coulomb matrices of the corresponding molecules. This can be used to restrict the search space for the compositional optimization of quantum circuits. We show that a high accuracy of a quantum algorithm can be achieved with high probability by sampling from a specific set of molecules. This work implies that quantum ansatz optimization can benefit from advances in cheminformatics and suggests an approach to identify key elements that enhance the accuracy of a quantum algorithm by mapping quantum circuits onto molecules and exploring correlations between physical properties of molecules and circuit performance.

quant-ph↗

arXiv2025

Lattice stitching by eigenvector continuation for Holstein polaron

Simulations of lattice particle - phonon systems are fundamentally restricted by the exponential growth of the number of quantum states with the lattice size. Here, we demonstrate an algorithm that constructs the lowest eigenvalue and eigenvector for the Holstein model in extended lattices from eigenvalue problems for small, independent lattice segments. This leads to exponential reduction of the computational Hilbert space and allows applications of variational quantum algorithms to particle - phonon interactions in large lattices. We illustrate that the ground state of the Holstein polaron in the entire range of electron - phonon coupling, from weak to strong, and the lowest phonon frequency ($ω/t = 0.1$) considered by numerical calculations to date can be obtained from a sequence of up to four-site problems. When combined with quantum algorithms, the present approach leads to a dramatic reduction of required quantum resources. We show that the ground state of the Holstein polaron in a lattice with 100 sites and 32 site phonons can be computed by a variational quantum eigensolver with 11 qubits.

quant-ph↗

arXiv2024

Boundaries of universality of thermal collisions for atom-atom scattering

Thermal rate coefficients for some atomic collisions have been observed to be remarkably independent of the details of interatomic interactions at short range. This makes these rate coefficients universal functions of the long-range interaction parameters and masses, which was previously exploited to develop a self-defining atomic sensor for ambient pressure. Here, we employ rigorous quantum scattering calculations to examine the response of thermally averaged rate coefficients for atom-atom collisions to changes in the interaction potentials. We perform a comprehensive analysis of the universality, and the boundaries thereof, by treating the quantum scattering observables as probabilistic predictions determined by a distribution of interaction potentials. We show that there is a characteristic change of the resulting distributions of rate coefficients, separating light, few-electron atoms and heavy, polarizable atoms. We produce diagrams that illustrate the boundaries of the thermal collision universality at different temperatures and provide guidance for future experiments seeking to exploit the universality.

physics.atom-ph↗

arXiv2024

Benchmarking of quantum fidelity kernels for Gaussian process regression

Quantum computing algorithms have been shown to produce performant quantum kernels for machine-learning classification problems. Here, we examine the performance of quantum kernels for regression problems of practical interest. For an unbiased benchmarking of quantum kernels, it is necessary to construct the most optimal functional form of the classical kernels and the most optimal quantum kernels for each given data set. We develop an algorithm that uses an analog of the Bayesian information criterion to optimize the sequence of quantum gates used to estimate quantum kernels for Gaussian process models. The algorithm increases the complexity of the quantum circuits incrementally, while improving the performance of the resulting kernels, and is shown to yield much higher model accuracy with fewer quantum gates than a fixed quantum circuit ansatz. We demonstrate that quantum kernels thus obtained can be used to build accurate models of global potential energy surfaces (PES) for polyatomic molecules. The average interpolation error of the six-dimensional PES obtained with a random distribution of 2000 energy points is 16 cm$^{-1}$ for H$_3$O$^+$, 15 cm$^{-1}$ for H$_2$CO and 88 cm$^{-1}$ for HNO$_2$. We show that a compositional optimization of classical kernels for Gaussian process regression converges to the same errors. This indicates that quantum kernels can achieve the same, though not better, expressivity as classical kernels for regression problems.

quant-ph↗

arXiv2023

Extrapolation of polaron properties to low phonon frequencies by Bayesian machine learning

Feasibility of accurate quantum calculations is often restricted by the dimensionality of the truncated Hilbert space required for the numerical computations. The present work demonstrates Bayesian machine learning (ML) models that use quantum properties in an effectively lower-dimensional Hilbert space to make predictions for the Hamiltonian parameters that require a larger basis set as applied to a classical problem in quantum statistical mechanics, the polaron problem. We consider two polaron models: the Su-Schrieffer-Heeger (SSH) model and the mixed SSH-Holstein model. We demonstrate ML models that can extrapolate polaron properties in the phonon frequency. We consider the sharp transition in the ground-state momentum of the SSH polaron and examine the evolution of this transition from the anti-adiabatic regime to the adiabatic regime. We also demonstrate Bayesian models that use the posterior distributions of highly approximate quantum calculations as the prior distribution for models of more accurate quantum results. This drastically reduces the number of fully converged quantum calculations required to map out the polaron dispersion relations for the full range of Hamiltonian parameters of interest.

quant-ph↗

arXiv2023

Efficient interpolation of molecular properties across chemical compound space with low-dimensional descriptors

We demonstrate accurate data-starved models of molecular properties for interpolation in chemical compound spaces with low-dimensional descriptors. Our starting point is based on three-dimensional, universal, physical descriptors derived from the properties of the distributions of the eigenvalues of Coulomb matrices. To account for the shape and composition of molecules, we combine these descriptors with six-dimensional features informed by the Gershgorin circle theorem. We use the nine-dimensional descriptors thus obtained for Gaussian process regression based on kernels with variable functional form, leading to extremely efficient, low-dimensional interpolation models. The resulting models trained with 100 molecules are able to predict the product of entropy and temperature ($S \times T$) and zero point vibrational energy (ZPVE) with the absolute error under 1 kcal mol$^{-1}$ for $> 78$ \% and under 1.3 kcal mol$^{-1}$ for $> 92$ \% of molecules in the test data. The test data comprises 20,000 molecules with complexity varying from three atoms to 29 atoms and the ranges of $S \times T$ and ZPVE covering 36 kcal mol$^{-1}$ and 161 kcal mol$^{-1}$, respectively. We also illustrate that the descriptors based on the Gershgorin circle theorem yield more accurate models of molecular entropy than those based on graph neural networks that explicitly account for the atomic connectivity of molecules.

physics.chem-ph↗

arXiv2023

Neural network Gaussian processes as efficient models of potential energy surfaces for polyatomic molecules

Kernel models of potential energy surfaces (PES) for polyatomic molecules are often restricted by a specific choice of the kernel function. This can be avoided by optimizing the complexity of the kernel function. For regression problems with very expensive data, the functional form of the model kernels can be optimized in the Gaussian process (GP) setting through compositional function search guided by the Bayesian information criterion. However, the compositional kernel search is computationally demanding and relies on greedy strategies, which may yield sub-optimal kernels. An alternative strategy of increasing complexity of GP kernels treats a GP as a Bayesian neural network (NN) with a variable number of hidden layers, which yields NNGP models. Here, we present a direct comparison of GP models with composite kernels and NNGP models for applications aiming at the construction of global PES for polyatomic molecules. We show that NNGP models of PES can be trained much more efficiently and yield better generalization accuracy without relying on any specific form of the kernel function. We illustrate that NNGP models trained by distributions of energy points at low energies produce accurate predictions of PES at high energies. We also illustrate that NNGP models can extrapolate in the input variable space by building the free energy surface of the Heisenberg model trained in the paramagnetic phase and validated in the ferromagnetic phase. By construction, composite kernels yield more accurate models than kernels with a fixed functional form. Therefore, by illustrating that NNGP models outperform GP models with composite kernels, our work suggests that NNGP models should be a preferred choice of kernel models for PES.

physics.chem-ph↗

arXiv2023

Compositional optimization of quantum circuits for quantum kernels of support vector machines

While quantum machine learning (ML) has been proposed to be one of the most promising applications of quantum computing, how to build quantum ML models that outperform classical ML remains a major open question. Here, we demonstrate a Bayesian algorithm for constructing quantum kernels for support vector machines that adapts quantum gate sequences to data. The algorithm increases the complexity of quantum circuits incrementally by appending quantum gates selected with Bayesian information criterion as circuit selection metric and Bayesian optimization of the parameters of the locally optimal quantum circuits identified. The goal is to build quantum kernels for SVM that can solve classification problems with as little training data as possible. The performance of the resulting quantum models for the classification problems considered here significantly exceeds that of optimized classical models with conventional kernels.

quant-ph↗

arXiv2023

Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines

Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that variational quantum classifiers and support vector machines with quantum kernels can solve a classification problem based on the $k$-Forrelation problem, which is known to be PromiseBQP-complete. Because the PromiseBQP complexity class includes all Bounded-Error Quantum Polynomial-Time (BQP) decision problems, our results imply that there exists a feature map and a quantum kernel that make variational quantum classifiers and quantum kernel support vector machines efficient solvers for any BQP problem. Hence, this work implies that their feature map and quantum kernel, respectively, can be designed to have a quantum advantage for any classification problem that cannot be classically solved in polynomial time but contrariwise by a quantum computer.

quant-ph↗

arXiv2022

Cross-calibration of atomic pressure sensors and deviation from quantum diffractive collision universality for light particles

The total room-temperature, velocity-averaged cross section for atom-atom and atom-molecule collisions is well approximated by a universal function depending only on the magnitude of the leading order dispersion coefficient, $C_6$. This feature of the total cross section together with the universal function for the energy distribution transferred by glancing angle collisions ($P_{\rm{QDU}6}$) can be used to empirically determine the total collision cross section and realize a self-calibrating, vacuum pressure standard. This was previously validated for Rb+N$_2$ and Rb+Rb collisions. However, the post-collision energy distribution is expected to deviate from $P_{\rm{QDU}6}$ in the limit of small $C_6$ and small reduced mass. Here we observe this deviation experimentally by performing a direct cross-species loss rate comparison between Rb+H$_2$ and Li+H$_2$ and using the \textit{ab initio} value of $\langle σ_{\rm{tot}} \, v \rangle_{\rm{Li+H}_2}$. We find a velocity averaged total collision cross section ratio, $R = \langle σ_{\rm{tot}} \, v \rangle_{\rm{Li+H}_2} : \langle σ_{\rm{tot}} \, v \rangle_{\rm{Rb+H}_2} = 0.83(5)$. Based on an \textit{ab initio} computation of $\langle σ_{\rm{tot}} \, v \rangle_{\rm{Li+H}_2} = 3.13(6)\times 10^{-15}$ m$^3$/s, we deduce $\langle σ_{\rm{tot}} \, v \rangle_{\rm{Rb+H}_2} = 3.8(2) \times 10^{-15}$ m$^3$/s, in agreement with a Rb+H$_2$ \textit{ab initio} value of $\langle σ_{\mathrm{tot}} v \rangle_{\mathrm{Rb+H_2}} = 3.57 \times 10^{-15} \mathrm{m}^3/\mathrm{s}$.By contrast, fitting the Rb+H$_2$ loss rate as a function of trap depth to the universal function we find $\langle σ_{\rm{tot}} \, v \rangle_{\rm{Rb+H}_2} = 5.52(9) \times 10^{-15}$ m$^3$/s. Finally, this work demonstrates how to perform a cross-calibration of sensor atoms to extend and enhance the cold atom based pressure sensor.

physics.atom-ph↗

arXiv2022

Gradient-based reconstruction of molecular Hamiltonians and density matrices from time-dependent quantum observables

We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters $α$. The system is prepared in a general quantum state by an evolution operator that depends on a set of unknown parameters $P$. After the preparation, the system evolves in time, and it is characterized by a time-dependent observable ${\cal O}(t)$. We show that it is possible to obtain closed-form expressions for the gradients of the distance between ${\cal O}(t)$ and a calculated observable with respect to $α$, $P$ and all elements of the system density matrix, whether for pure or mixed states. These gradients can be used in projected gradient descent to infer $α$, $P$ and the relevant density matrix from dynamical observables. We combine this approach with random phase wave function approximation to obtain closed-form expressions for gradients that can be used to infer population distributions from averaged time-dependent observables in problems with a large number of quantum states participating in dynamics. The approach is illustrated by determining the temperature of molecular gas (initially, in thermal equilibrium at room temperature) from the laser-induced time-dependent molecular alignment.

quant-ph↗