arXiv subjects

R. V. Krems

Publications and source records attributed to R. V. Krems.

At least 19 recordsLinked to original sources

arXiv2026

Roadmap on Quantum Sensors for Vacuum Metrology

We describe how laser-cooled and trapped alkali-metal atoms have been used as pressure sensors in the high- and ultra-high-vacuum regimes operating with relative uncertainties of just over a percent at pressures from a few nPa and up to a few tens of $μ$Pa. These sensors can serve as primary standards of pressure as the determination of pressure requires only knowledge of collision cross sections between atoms and molecules, eliminating the need for calibration with other devices. The collision cross sections can be measured independently or computed with rigorous quantum methods at percent relative accuracies. We argue that this technology has advanced sufficiently to provide an alternative to the existing, expensive pressure standard in the ultra-high vacuum regime, the orifice flow standard. Experiments with trapped atoms can be used to calibrate cheaper pressure sensors (such as devices based on ionization gauges). However, the technology has not yet matured enough to be of use in other research fields because of the complexity and cost of the experiments. We propose a roadmap for this new pressure standard for vacuum metrology.

physics.atom-ph↗

arXiv2026

Advantage of discrete variable representation in variational quantum eigensolvers for vibrational energy calculations

While quantum computing algorithms have been widely applied for electronic structure calculations, applications to molecular dynamics remain scarce. Complex and varied landscapes of molecular potential energy surfaces give rise to vibrational states with a wide range of properties, making it difficult to construct a general representation of ro-vibrational states by a quantum computer with a limited number of qubits and gates. Another challenge is the exponential growth of the computation complexity - for example, the number of terms required to expand a general Hamiltonian in Pauli strings increases exponentially with the number of qubits. Here, we show that discrete variable representation (DVR) can be leveraged to represent molecular Hamiltonians by the polynomial (in the number of qubits) number of quantum circuits. We then demonstrate that DVR Hamiltonians lead to very efficient quantum ansatze for vibrational states. For this purpose, we develop a compositional quantum ansatz search that adapts gate sequences in variational quantum eigensolvers (VQE) to a specific molecular state. We apply VQE to compute the vibrational energy levels of Cr$_2$ in seven electronic states as well as of van der Waals complexes Ar-HCl and Mg-NH. Our numerical results show that accuracy of 1~cm$^{-1}$ can be achieved by very shallow quantum circuits with 2 to 9 entangling gates.

quant-ph↗

arXiv2024

General classification of qubit encodings in ultracold diatomic molecules

Owing to their rich internal structure and significant long-range interactions, ultracold molecules have been widely explored as carriers of quantum information. Several different schemes for encoding qubits into molecular states, both bare and field-dressed, have been proposed. At the same time, the rich internal structure of molecules leaves many unexplored possibilities for qubit encodings. We show that all molecular qubit encodings can be classified into four classes by the type of the effective interaction between the qubits. In the case of polar molecules, the four classes are determined by the relative magnitudes of matrix elements of the dipole moment operator in the single molecule basis. We exemplify our classification scheme by considering a new type of encoding of the effective spin-1/2 system into non-adjacent rotational states (e.g., $N=0$ and $N=2$) of polar and non-polar molecules with the same nuclear spin projection. Our classification scheme is designed to inform the optimal choice of molecular qubit encoding for quantum information storage and processing applications, as well as for dynamical generation of many-body entangled states and for quantum annealing.

quant-ph↗

arXiv2023

Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules

The generalization accuracy of machine learning models of potential energy surfaces (PES) and force fields (FF) for large polyatomic molecules can be generally improved either by increasing the number of training points or by improving the models. In order to build accurate models based on expensive high-level ab initio calculations, much of recent work has focused on the latter. In particular, it has been shown that gradient domain machine learning (GDML) models produce accurate results for high-dimensional molecular systems with a small number of ab initio calculations. The present work extends GDML to models with composite kernels built to maximize inference from a small number of molecular geometries. We illustrate that GDML models can be improved by increasing the complexity of underlying kernels through a greedy search algorithm using Bayesian information criterion as the model selection metric. We show that this requires including anisotropy into kernel functions and produces models with significantly smaller generalization errors. The results are presented for ethanol, uracil, malonaldehyde and aspirin. For aspirin, the model with composite kernels trained by forces at 1000 randomly sampled molecular geometries produces a global 57-dimensional PES with the mean absolute accuracy 0.177 kcal/mol (61.9 cm$^{-1}$) and FFs with the mean absolute error 0.457 kcal/mol Å$^{-1}$.

physics.chem-ph↗

arXiv2022

Quantum annealing with pairs of $^2Σ$ molecules as qubits

The rotational and fine structure of open-shell molecules in a $Σ$ electronic state gives rise to crossings between Zeeman states of different parity. These crossings become avoided in the presence of an electric field. We propose an algorithm that encodes Ising models into qubits defined by pairs of $^2Σ$ molecules sharing an excitation near these avoided crossings. This can be used to realize a transverse field Ising model tunable by an external electric or magnetic field, suitable for quantum annealing applications. We perform dynamical calculations for several examples with one- and two-dimensional connectivities. Our results demonstrate that the probability of obtaining valid annealing solutions is high and can be optimized by varying the annealing times.

quant-ph↗

arXiv2021

Quantum transfer through small networks coupled to phonons: effects of topology vs phonons

Particle or energy transfer through quantum networks is determined by network topology and couplings to environments. This study examines the combined effect of topology and external couplings on the efficiency of directional quantum transfer through quantum networks. We consider a microscopic model of qubit networks coupled to external vibrations by Holstein and Peierls couplings. By treating the positions of the network sites and the site-dependent phonon frequencies as independent variables, we determine the Hamiltonian parameters corresponding to minimum transfer time by Bayesian optimization. The results show that Holstein couplings may accelerate transfer through sub-optimal network configurations but cannot accelerate quantum dynamics beyond the limit of the transfer time in an optimal phonon-free configuration. By contrast, Peierls couplings distort the optimal networks to accelerate quantum transfer through configurations with less than six sites. However, the speed-up offered by Peierls couplings decreases with the network size and disappears for networks with more than seven sites. For networks with seven sites or more, Peierls couplings distort the optimal network configurations and change the mechanism of quantum transfer but do not affect the lower limit of the transfer time. The machine-learning approach demonstrated here can be applied to determine quantum speed limits in other applications.

quant-ph↗

arXiv2020

Bayesian optimization for inverse problems in time-dependent quantum dynamics

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 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 reduce 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 SO$_2$ and chiral 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 to within 1% accuracy. 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.

physics.comp-ph↗

arXiv2020

Machine-learning-corrected quantum dynamics calculations

Quantum scattering calculations for all but low-dimensional systems at low energies must rely on approximations. All approximations introduce errors. The impact of these errors is often difficult to assess because they depend on the Hamiltonian parameters and the particular observable under study. Here, we illustrate a general, system and approximation-independent, approach to improve the accuracy of quantum dynamics approximations. The method is based on a Bayesian machine learning (BML) algorithm that is trained by a small number of rigorous results and a large number of approximate calculations, resulting in ML models that accurately capture the dependence of the dynamics results on the quantum dynamics parameters. Most importantly, the present work demonstrates that the BML models can generalize quantum results to different dynamical processes. Thus, a ML model trained by a combination of approximate and rigorous results for a certain inelastic transition can make accurate predictions for different transitions without rigorous calculations. This opens the possibility of improving the accuracy of approximate calculations for quantum transitions that are out of reach of rigorous scattering calculations.

physics.chem-ph↗

arXiv2019

Bayesian machine learning for quantum molecular dynamics

This article discusses applications of Bayesian machine learning for quantum molecular dynamics. One particular formulation of quantum dynamics advocated here is in the form of a machine learning simulator of the Schrödinger equation. If combined with the Bayesian statistics, such a simulator allows one to obtain not only the quantum predictions but also the error bars of the dynamical results associated with uncertainties of inputs (such as the potential energy surface or non-adiabatic couplings) into the nuclear Schrödinger equation. Instead of viewing atoms as undergoing dynamics on a given potential energy surface, Bayesian machine learning allows one to formulate the problem as the Schrödinger equation with a non-parametric distribution of potential energy surfaces that becomes conditioned by the desired dynamical properties (such as the experimental measurements). Machine learning models of the Schrödinger equation solutions can identify the sensitivity of the dynamical properties to different parts of the potential surface, the collision energy, angular momentum, external field parameters and basis sets used for the calculations. This can be used to inform the design of efficient quantum dynamics calculations. Machine learning models can also be used to correlate rigorous results with approximate calculations, providing accurate interpolation of exact results. Finally, there is evidence that it is possible to build Bayesian machine learning models capable of physically extrapolating the solutions of the Schrödinger equation. This is particularly valuable as such models could complement common discovery tools to explore physical properties at Hamiltonian parameters not accessible by rigorous quantum calculations or experiments, and potentially be used to accelerate the numerical integration of the nuclear Schrödinger equation.

physics.chem-ph↗

arXiv2018

Bayesian optimization for the inverse scattering problem in quantum reaction dynamics

We propose a machine-learning approach based on Bayesian optimization to build global potential energy surfaces (PES) for reactive molecular systems using feedback from quantum scattering calculations. The method is designed to correct for the uncertainties of quantum chemistry calculations and yield potentials that reproduce accurately the reaction probabilities in a wide range of energies. These surfaces are obtained automatically and do not require manual fitting of the {\it ab initio} energies with analytical functions. The PES are built from a small number of {\it ab initio} points by an iterative process that incrementally samples the most relevant parts of the configuration space. Using the dynamical results of previous authors as targets, we show that such feedback loops produce accurate global PES with 30 {\it ab initio} energies for the three-dimensional H + H$_2$ $\rightarrow$ H$_2$ + H reaction and 290 {\it ab initio} energies for the six-dimensional OH + H$_2$ $\rightarrow$ H$_2$O + H reaction. These surfaces are obtained from 360 scattering calculations for H$_3$ and 600 scattering calculations for OH$_3$. We also introduce a method that quickly converges to an accurate PES without the {\it a priori} knowledge of the dynamical results. By construction, our method illustrates the lowest number of potential energy points (i.e. the minimum information) required for the non-parametric construction of global PES for quantum reactive scattering calculations.

physics.chem-ph↗

arXiv2018

Quantum walks assisted by particle number fluctuations

We study the spreading of a quantum particle placed in a single site of a lattice or binary tree with the Hamiltonian permitting particle number changes. We show that the particle number-changing interactions accelerate the spreading beyond the ballistic expansion limit by inducing off-resonant Rabi oscillations between states of different numbers of particles. We consider the effect of perturbative number-changing couplings on Anderson localization in one-dimensional disordered lattices and show that they lead to decrease of localization. The effect of these couplings is shown to be larger at larger disorder strength, which is a consequence of the disorder-induced broadening of the particle dispersion bands.

quant-ph↗

arXiv2018

Phonon-mediated repulsion, sharp transitions and (quasi)self-trapping in the extended Peierls-Hubbard model

We study two identical fermions, or two hard-core bosons, in an infinite chain and coupled to phonons by interactions that modulate their hopping as described by the Peierls/Su-Schrieffer-Heeger (SSH) model. We show that exchange of phonons generates effective nearest-neighbor repulsion between particles and also gives rise to interactions that move the pair as a whole. The two-polaron phase diagram exhibits two sharp transitions, leading to light dimers at strong coupling and the flattening of the dimer dispersion at some critical values of the parameters. This dimer (quasi)self-trapping occurs at coupling strengths where single polarons are mobile. This illustrates that, depending on the strength of the phonon-mediated interactions, the coupling to phonons may completely suppress or strongly enhance quantum transport of correlated particles.

cond-mat.str-el↗

arXiv2016

Lattice models with long-range and number-non-conserving interactions with Zeeman excitations of ultracold magnetic atoms

We show that Zeeman excitations of ultracold Dy atoms trapped in an optical lattice can be used to engineer extended Hubbard models with tunable inter-site and particle number-non-conserving interactions. We show that the ratio of the hopping amplitude and inter-site interactions in these lattice models can be tuned in a wide range by transferring the atoms to different Zeeman states. We propose to use the resulting controllable models for the study of the effects of direct particle interactions and particle number-non-conserving terms on Anderson localization.

physics.atom-ph↗

arXiv2016

Effects of long-range hopping and interactions on quantum walk in ordered and disordered lattices

We study the effects of long-range hopping and long-range inter-particle interactions on quantum walk of hard-core bosons in ideal and disordered one-dimensional lattices. We find that the range of hopping has a much more significant effect on the particle correlation dynamics than the range of interactions. We illustrate that long-range hopping makes the correlation diagrams asymmetric with respect to the sign of the interaction and examine the relative role of repulsive and attractive interactions on the dynamics of scattering by isolated impurities and Anderson localization in dis- ordered lattices. We show that weakly repulsive interactions increase the probability of tunnelling through isolated impurities and decrease the localization.

quant-ph↗

arXiv2012

Efficient method for quantum calculations of molecule - molecule scattering properties in a magnetic field

We show that the cross sections for molecule - molecule collisions in the presence of an external field can be computed efficiently using a total angular momentum basis, defined either in the body-fixed frame or in the space-fixed coordinate system. This method allows for computations with much larger basis sets than previously possible. We present calculations for 15NH - 15NH collisions in a magnetic field. Our results support the conclusion of the previous study that the evaporative cooling of rotationally ground 15NH molecules in a magnetic trap has a prospect of success.

physics.atom-ph↗

arXiv2010

RF-field-induced Feshbach resonances

A rigorous quantum theory of atomic collisions in the presence of radio frequency (rf) magnetic fields is developed and applied to elucidate the effects of combined dc and rf magnetic fields on elastic scattering in ultracold collisions of Rb atoms. We show that rf fields can be used to induce Feshbach resonances, which can be tuned by varying the amplitude and frequency of the rf field. The rf-induced Feshbach resonances occur also in collisions of atoms in low-field-seeking states at moderate rf field strengths easily available in atom chip experiments, which opens up the world of tunable interactions to magnetically trappable atomic quantum gases.

physics.atom-ph↗

arXiv2010

Collisional decoherence of internal state superpositions in a trapped ultracold gas

We analyze collisional decoherence of atoms or molecules prepared in a coherent superposition of nondegenerate internal states at ultralow temperatures and placed in an ultracold buffer gas. Our analysis is applicable for an arbitrary bath particle/tracer particle mass ratio. Both elastic and inelastic collisions contribute to decoherence. We obtain an expression relating the observable decoherence rate to pairwise scattering properties, specifically the low-temperature scattering amplitudes. We consider the dependence on the bath particle/tracer particle mass ratio for the case of light bath and heavy tracer particles. The expressions obtained may be useful in low-temperature applications where accurate estimates of decoherence rates are needed. The results suggest a method for determining the scattering lengths of atoms and molecules in different internal states by measuring decoherence-induced damping of coherent oscillations.

quant-ph↗

arXiv2009

Reactive Collisions of Ultracold Molecules Confined in quasi-2D Geometry

We present a formalism for rigorous calculations of cross sections for inelastic and reactive collisions of ultracold atoms and molecules confined by laser fields in quasi-2D geometry. Our results show that the elastic-to-inelastic ratios of collision cross sections are enhanced in the presence of a laser confinement and that the threshold energy dependence of the collision cross sections can be tuned by varying the confinement strength and external magnetic fields. The enhancement of the elastic-to-inelastic ratios is inversely proportional to $\sqrt{ε/\hbar ω_0}$, where $ε$ is the kinetic energy and $ω_0$ is the oscillation frequency of the trapped particles in the confinement potential.

physics.atom-ph↗