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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Nondegenerate Noise-Resilient Superconducting Qubit

We propose a superconducting qubit based on engineering the first and second harmonics of the Josephson energy and phase relation 𝐸 𝐽⁢1 ⁢cos 𝜑 and 𝐸 𝐽⁢2 ⁢cos 2⁢𝜑. By constructing a circuit such that 𝐸 𝐽⁢2 is negative and |𝐸 𝐽⁢1 | ≪ |𝐸 𝐽⁢2 |, we create a periodic potential with two nondegenerate minima. The qubit, which we dub “harmonium,” is formed from the lowest-energy states of each minimum. Bit-flip protection of the qubit arises due to the localization of each qubit state to their respective minima, while phase-flip protection can be understood by considering the circuit within the Born-Oppenheimer approximation. We demonstrate with time-domain simulations that single- and two-qubit gates can be performed in approximately 100 ns. Finally, we compute the qubit coherence times using numerical diagonalization of the complete circuit in conjunction with state-of-the-art noise models. We estimate out-of-manifold heating times on the order of milliseconds, which can be treated as erasure errors using conventional dispersive readout. We estimate pure-dephasing times on the order of many tens of milliseconds, and bit-flip times on the order of seconds.

quantum error correction↗
DOE OSTI2020

Backpropagated frame transformation theory: A reformulation

In this work, the energy-dependent frame transformation theory of Gao and Greene [H. Gao and C. H. Greene, Phys. Rev. A 42, 6946 (1990)] is extended to yield a quantitatively accurate description of the dissociative recombination process. Evidence is presented to show that direct application of the original theory leads to inaccurate cross sections. A major revision, based on an interaction-free backpropagation of the Born-Oppenheimer solutions, markedly improves the frame transformation theory, reducing its average error by orders of magnitude. The original theory and its extension are tested on the previously explored two-dimensional (2D) model that is tailored to describe the singlet ungerade states of molecular hydrogen. The 2D model can be solved exactly (within the numerical accuracy) without implementing the Born-Oppenheimer approximation. These exact results then serve as a benchmark for the frame transformation theory developed in this paper.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Molecular bond stabilization in the strong-field dissociation of O 2 +

We theoretically examine the rotational and vibrational dynamics of O 2 + molecular ions exposed to intense, short laser pulses for conditions realized in contemporary pump-probe experiments. We solve the time-dependent Schrödinger equation within the Born-Oppenheimer approximation for an initial distribution of randomly aligned molecular ions. For fixed peak intensities, our numerical results show that total, angle-integrated O 2 + → O( 3 P) + O + ( 4 S 0 ) dissociation yields do not monotonically increase with increasing infrared-probe pulse duration. We find this pulse-duration-dependent stabilization to be consistent with the transient trapping of nuclear probability density in a light-induced (bond-hardening) potential-energy surface and robust against rotational excitation. We analyze this stabilization effect and its underlying bond-hardening mechanism (i) in the time domain, by following the evolution of partial nuclear probability densities associated with the dipole-coupled O 2 + (a 4 Π u ) and O 2 + (f 4 Π g ) cationic states, and (ii) in the frequency domain, by examining rovibrational quantum-beat spectra for the evolution of the partial nuclear probability densities associated with these states. In this work, our analysis reveals the characteristic timescale for the bond-hardening mechanism in O 2 + and explains the onset of bond stabilization for sufficiently long pulse durations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Vibronic States and Their Effect on the Temperature and Strain Dependence of Silicon-Vacancy Qubits in 4$\textit{H}$-SiC

Silicon-vacancy qubits in silicon carbide ( Si C ) are emerging tools in quantum-technology applications due to their excellent optical and spin properties. In this paper, we explore the effect of temperature and strain on these properties by focusing on the two silicon-vacancy qubits, V1 and V2, in 4$\textit{H}$-SiC. We apply density-functional theory beyond the Born-Oppenheimer approximation to describe the temperature-dependent mixing of electronic excited states assisted by phonons. We obtain a polaronic gap of around 5 and 22 meV for the V1 and V2 centers, respectively, which results in a significant difference in the temperature-dependent dephasing and zero-field splitting of the excited states, which explains recent experimental findings. Finally, we also compute how crystal deformations affect the zero-phonon line of these emitters. Our predictions are important ingredients in any quantum applications of these qubits sensitive to these effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Cluster Expansion and Resurgence in the Polyakov Model

In the Polyakov model, a nonperturbative mass gap is formed at leading-order semiclassics by instanton effects. By using the notions of critical points at infinity, cluster expansion, and Lefschetz thimbles, we show that a third-order effect in semiclassics gives an imaginary ambiguous contribution to the mass gap, which is supposed to be real and unambiguous. This is troublesome for the original analysis, and it is difficult to resolve this issue directly in quantum field theory (QFT). However, we find a new compactification of the Polyakov model to quantum mechanics, by using a background ’t Hooft flux. The compactification has the merit of remembering the monopole instantons of the full QFT within Born-Oppenheimer approximation, while the periodic compactification does not. In the quantum mechanical limit, we prove the resurgent cancellation of the ambiguity in three-instanton sector against ambiguity in the Borel resummation of the perturbation theory around one instanton. Assuming that this result holds in QFT, we provide a large-order asymptotics of perturbation theory around perturbative vacuum and instanton.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Improved Precision Scaling for Simulating Coupled Quantum-Classical Dynamics

In this paper, we present a superpolynomial improvement in the precision scaling of quantum simulations for coupled quantum-classical systems. Such systems are found in, e.g., molecular-dynamics simulations within the Born-Oppenheimer approximation. By employing a framework based on the Koopman–von Neumann formulation of classical mechanics, we express the Liouville equation of motion as unitary dynamics and utilize phase kickback from a dynamical quantum simulation to calculate the quantum forces acting on classical particles. This approach allows us to simulate the dynamics of these classical particles without the overheads associated with measuring gradients and solving the equations of motion on a classical computer, resulting in a superpolynomial advantage at the price of increased space complexity. We demonstrate that these simulations can be performed in both microcanonical and canonical ensembles, enabling the estimation of thermodynamic properties from the prepared probability density. Published by the American Physical Society 2024

Simon, Sophia (ORCID:0000000332612338)↗
DOE OSTI2021

Investigation into the transport properties of planetary interiors through inelastic X-ray scattering experiments and quantum molecular dynamics (Final Technical Report)

This was a two-year research project for the period 08/15/2018 - 08/14/2020 conducted at the University of Nevada, Reno using Pronghorn, a newly built high-performance cluster located at the University. The short-term project goal was to provide computational support for the experimental campaigns at LCLS through data analysis of previous and upcoming scheduled experiments, along with performing state-of-the-art atomistic simulations of dense plasmas. The longer-term goal was to create a new computational high energy density physics group located at the University of Nevada, Reno. Guided by results from past and future high-resolution scattering experiments, we aimed to research and develop non-equilibrium and non-adiabatic atomistic simulations of dense plasmas that went beyond the Born-Oppenheimer approximation

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Theory and Simulation of Ultrafast Multidimensional Nonlinear X-ray Spectroscopy of Molecules (Final Report)

Emerging X-ray free electron laser (XFEL) beam sources offer new types of probes of matter with unprecedented spatial and temporal resolutions. These experimental advances must be met by robust theoretical and computational tools that provide predictive modeling capacity of the underlining electronic and structural dynamics. The latter will be essential for the design of sophisticated multi-pulse experiments and for their interpretation. The proposed research effort will focus on developing cutting- edge simulation tools for nonlinear multidimensional X-ray/optical spectroscopies and aims to address key questions in Priority Research Opportunities 1 (Probing and controlling electron motion within a molecule) and 3 (Capturing rare events and intermediate states in the transformation of matter) as mentioned in the BES Roundtable Report “Opportunities for Basic Research at the Frontiers of XFEL Ultrafast Science”. XFEL multidimensional nonlinear techniques, which combine sequences of X-ray and possibly optical pulses, provide a unique experimental toolbox for probing the dynamics of core and valence electronic excitations, as well as material structure. Predictive modeling of these dynamical processes requires the combination of analytical theory for nonlinear interactions of light and matter, robust quantum-chemical methodologies for the accurate description of electronic structure of various materials, and multiscale ab initio electron and nuclear dynamics techniques operating beyond Born-Oppenheimer approximation. These challenges will be addressed with three research thrusts (i) Develop and implement theoretical apparatus for modeling a broad range of multidimensional spectroscopic techniques enabled by present and upcoming XFEL facilities. This thrust also includes the incorporation of a computational module in the DOE supported open-source NWChem computational chemistry package as well as the development of other open-source codes ready for dissemination across a broad user base; (ii) Propose and design new multi-pulse experiments that make use of the capabilities of the incoming LCLS-II facility; (iii) Perform selected applications to specific molecular systems that can be carried out at LCLS-II and demonstrate how these X-ray sources may be used to study nonadiabatic dynamics through conical interactions, electronic correlations in multi-core excitons, and charge transfer/energy transfer processes. The proposed research will be carried out by a multi-disciplinary four-institution research team which combines academia and national laboratories and spans the broad and necessary expertise in theoretical spectroscopy, nonlinear optics, quantum chemistry, molecular non-adiabatic dynamics and code development. The work will be performed in a highly interactive team environment with junior researchers shared between institutions thus cementing cross- disciplinary interactions. The developed simulation tools will be immediately deployed for XFEL facility users, both experimentalists and theorists, via freely distributed codes and databases. Altogether, this project will facilitate establishing XFEL-based multidimensional spectroscopies as a novel diagnostic tool for monitoring electronic and structural dynamics in molecular materials.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Deriving Effective Coupling Strength With Born-Oppenheimer Approx.

Tunable couplers have been important in the development of superconducting quantum computers. The ability to maintain zero coupling between qubits during operation, a feature of high-fidelity quantum gates, has been shown to be possible with the use of tunable couplers. As an example, Sete et al., 2021 showed this was possible with a tunable coupler between transmons: the qubit-coupler and qubit-qubit couplings create a net effective coupling strength between the qubits that can be tuned to zero. However, the derivation of the effective coupling strength between the qubits is quite complex. We propose a simpler method of obtaining this effective coupling with the Born-Oppenheimer approximation.

Wichmann, Conrad↗
DOE OSTI2025

New Methods for Predicting Non-Born-Oppenheimer Chemistry

Current methods for modeling non-adiabatic molecular dynamics face fundamental limitations when treating geometric phase effects: quantum mechanical phenomena where nuclear wavepackets acquire phase shifts when encircling conical intersections. Existing approaches either neglect these effects entirely or rely on potential energy surfaces arising from the Born-Oppenheimer approximation, which introduce artificial singularities and can overestimate geometric phase contributions. This project developed a new theoretical framework based on exact factorization (XF) methods to overcome these limitations. We derived mathematical formulations for hybrid quantum-classical XF dynamics that selectively treat critical nuclear degrees of freedom quantum mechanically while propagating others classically. This approach addresses the computational intractability that has previously limited exact methods to toy systems. Key innovations include a new approach to systematically identifying nuclear coordinates requiring quantum treatment, as well as novel implementation strategies that interface with existing quantum chemistry codes. The project also developed a proof-of-concept code for treating Jahn-Teller systems and creation of educational materials on non-adiabatic dynamics geared at the graduate level. The theoretical framework developed will enable future systematically improvable calculations of nuclear quantum effects in realistic molecular systems, filling a critical gap in non-adiabatic dynamics methods. This foundation supports future development of predictive tools for designing energy-relevant photochemical processes where quantum coherence effects may be exploited to control reaction outcomes.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2020

Deep Minima in the Triply Differential Cross Section for Ionization of Atomic Hydrogen by Electron and Positron Impact

We investigate ionization of atomic hydrogen by electron- and positron-impact. We apply the Coulomb–Born (CB1) approximation, various modified CB1 approximations, the three body distorted wave (3DW) approximation, and the time-dependent close-coupling (TDCC) method to electron-impact ionization of hydrogen. For electron-impact ionization of hydrogen for an incident energy of approximately 76.45 eV, we obtain a deep minimum in the CB1 triply differential cross section (TDCS). However, the TDCC for 74.45 eV and the 3DW for 74.46 eV gave a dip in the TDCS. For positron-hydrogen ionization (breakup) we apply the CB1 approximation and a modified CB1 approximation. We obtain a deep minimum in the TDCS and a zero in the CB1 transition matrix element for an incident energy of 100 eV with a gun angle of 56.13 °. Corresponding to a zero in the CB1 transition matrix element, there is a vortex in the velocity field associated with this element. For both electron- and positron-impact ionization of hydrogen the velocity field rotates in the same direction, which is anticlockwise. All calculations are performed for a doubly symmetric geometry; the electron-impact ionization is in-plane and the positron-impact ionization is out-of-plane.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Photoionization from the Ground and Excited Vibrational States of H$^+_2$ and Its Deuterated Isotopologues

Photoionization cross sections and rate coefficients have been calculated for all bound vibrational levels of the 1sσ g state of H$^+_2$, HD+, and D$^+_2$. The Born–Oppenheimer approximation is employed in our calculation of vibrationally resolved photoionization cross sections. Vibrationally resolved and local thermal equilibrium photoionization rate coefficients are presented for photon temperatures less than 50,000 K and are found to be several orders of magnitude larger than previous results in the literature. Analytic fits for the vibrationally resolved and local thermal equilibrium photoionization rate coefficients are provided. Near-threshold oscillations in the vibrationally resolved photoionization are observed. A benchmark set of photoionization cross sections are presented. Fixed-nuclei photoionization cross sections are calculated using two-center true continuum wave functions and are verified by comparison with previous calculations and are found to be in excellent agreement in all cases. Data files for our set of benchmark cross sections, rate coefficients, and fitting parameters for H$^+_2$, HD + , and D$^+_2$ are available on Zenodo under an open-source Creative Commons Attribution license at doi:10.5281/zenodo.8304061.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Quantum science with arrays of metastable helium-3 atoms

The motion of atoms in programmable optical tweezer arrays offers many new opportunities for neutral atom quantum science. These include inter- and intra-site atom motion for resource-efficient implementations of fermionic and bosonic modes, respectively, as well as tweezer transport for efficient compilation of arbitrary circuits. However, the exploitation of atomic motion for all three purposes and others is limited by the inertia of the atoms. We present a comprehensive architectural blueprint for the use of fermionic metastable helium-3 (He) atoms -- the lightest trappable atomic species -- in programmable optical tweezer arrays. This includes a concrete analysis of atomic structure considerations as well as Rydberg-mediated interactions. We show that inter-tweezer hopping of He atoms can be faster than previous demonstrations with lithium-6. We also demonstrate a new toolbox for encoding and manipulating qubits directly in the tweezer trap potential, uniquely enabled by the light mass of He. Finally, we provide several examples of new opportunities for fermionic quantum simulation and computation that leverage the transport and inter-tweezer hopping of He atom arrays. These tools present new methods to improve the resource efficiency of neutral atom quantum science that may also enable quantum simulations of lattice gauge theories and quantum chemistry outside the Born-Oppenheimer approximation

Li, Zheyuan↗
DOE OSTI2024

Deriving Effective Coupling Strength With Born-Oppenheimer Approx.

The development of high-fidelity quantum gates is paramount to the scalability of quantum pro- cessors. Tunable couplers have played a key role in the realization of these low error rate quantum gates in superconducting circuits. However, the derivation of the effective coupling strength between the qubits is usually enabled by a Schrieffer-Wolff transformation, which is complex and requires prior-knowledge of the proper generator for the transformation. We propose a simpler method of obtaining this effective coupling using an approach similar to the Born-Oppenheimer approximation.

Wichmann, Conrad↗
DOE OSTI2020

Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation

It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Capturing Deuteration Effects in a Molecular Mechanics Force Field: Deuterated THF and the THF–Water Miscibility Gap

Deuteration is a common chemical modification used in conjunction with experiments such as neutron scattering, NMR, and Fourier-transform infrared for the study of molecular systems. Under the Born–Oppenheimer (BO) approximation, while the underlying potential energy surface remains unchanged by isotopic substitutions, isotopic substitution still alters intramolecular vibrations, which in turn may alter intermolecular interactions. Molecular mechanics (MM) force fields used in classical molecular dynamics simulations are assumed to represent local approximations of the BO potential energy surfaces, and hence, MD simulations using simple isotopic mass substitutions should capture BO-compatible isotope effects. However, standard MM force-field parameterizations do not directly fit to the local harmonic quantum mechanical (QM) Hessian that describes the BO surface, but rather to QM normal-modes and/or mass-dependent internal-coordinate derived distortion energies. In this study, using tetrahydrofuran (THF)–water mixtures as our model system, we show that not only does a simple mass-substitution approach fail to capture an experimentally characterized deuteration effect (the loss of the closed-loop miscibility gap associated with the complete deuteration of THF) but also it is necessary to generate new MM force-field parameters that correctly describe isotopic dependent vibrations to capture the experimental deuteration effect. We show that the origin of this failure is a result of using mass-dependent features to fit the THF MM force field, which unintentionally biases the bonded terms of the force field to represent only the isotopologue used during the original force-field parameterization. In addition, we make use of our isotopologue-corrected force field for D 8 THF to examine the molecular origins of the isotope-dependent loss of the THF–water miscibility gap.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

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

Exotic hidden-heavy hadrons and where to find them

The Born-Oppenheimer potentials for QCD with light quarks include adjoint-hadron potentials that are repulsive at short distances and heavy-hadron-pair potentials that approach thresholds at large distances. The adjoint-hadron potentials must connect smoothly to the heavy-hadron-pair potentials at intermediate distances. We identify exotic hidden-heavy hadrons as bound states and resonances in adjoint-hadron potentials that cross below a heavy-hadron-pair threshold before approaching it. This explains why many exotic hidden-charm and hidden-bottom hadrons have energies near heavy-hadron-pair thresholds. The remarkable properties of some exotic hidden-heavy mesons can be explained by fine tunings of adjoint-meson energies in QCD.

Born-Oppenheimer approximation↗