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DOE OSTI2022

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron–electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. In conclusion, the transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Binary Optimal Control of Single-Flux-Quantum Pulse Sequences

We introduce a binary, relaxed gradient, trust-region method for optimizing pulse sequences for single flux quanta (SFQ) control of a quantum computer. The pulse sequences are optimized with the goal of realizing unitary gate transformations. Each pulse has a fixed amplitude and duration. Here we model this process as an binary optimal control problem, constrained by Schrödinger’s equation, where the binary variables indicate whether each pulse is on or off. We introduce a first-order trust-region method, which takes advantage of a relaxed gradient to determine an optimal pulse sequence that minimizes the gate infidelity, while also suppressing leakage to higher energy levels. The proposed algorithm has a computational complexity of O(p log(p)), where p is the number of pulses in the sequence. We present numerical results for the H and X gates, where the optimized pulse sequences give gate fidelity’s better than 99.9%, in ≈ 25 trust-region iterations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Analysis of vibronic coupling in a 4f molecular magnet with FIRMS

Vibronic coupling, the interaction between molecular vibrations and electronic states, is a fundamental effect that profoundly affects chemical processes. In the case of molecular magnetic materials, vibronic, or spin-phonon, coupling leads to magnetic relaxation, which equates to loss of magnetic memory and loss of phase coherence in molecular magnets and qubits, respectively. The study of vibronic coupling is challenging, and most experimental evidence is indirect. Here we employ far-infrared magnetospectroscopy to directly probe vibronic transitions in [Yb(trensal)] (where H 3 trensal = 2,2,2-tris(salicylideneimino)trimethylamine). We find intense signals near electronic states, which we show arise due to an “envelope effect” in the vibronic coupling Hamiltonian, which we calculate fully ab initio to simulate the spectra. We subsequently show that vibronic coupling is strongest for vibrational modes that simultaneously distort the first coordination sphere and break the C 3 symmetry of the molecule. With this knowledge, vibrational modes could be identified and engineered to shift their energy towards or away from particular electronic states to alter their impact. Hence, these findings provide new insights towards developing general guidelines for the control of vibronic coupling in molecules.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Transport coefficients of quasiparticle models within a new relaxation time approximation of the Boltzmann equation

We investigate the transport properties of a kinetic theory model that is tuned to describe the thermodynamic properties of QCD at zero chemical potential using a new formulation of the relaxation time approximation. In contrast to previous approaches, the latter is constructed to preserve the fundamental properties of the collision term of the Boltzmann equation for any energy dependence of the relaxation time. A novel choice of matching conditions is implemented to ensure that the background mean-field depends only on the temperature even when the system is out of equilibrium. We provide a consistent analysis of how the transport coefficients of relativistic Navier-Stokes theory vary with the energy dependence of the relaxation time. We also show that the entropy production of this theory is consistent with the second law of thermodynamics and verify that it is independent of the matching conditions employed. We used this fact to calculate the matching independent combination of transport coefficients.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1993

Preconditioned conjugate-gradient methods for low-speed flow calculations

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations is integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the Lower-Upper Successive Symmetric Over-Relaxation iterative scheme is more efficient than a preconditioner based on Incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional Line Gauss-Seidel Relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Ajmani, Kumud↗

NASA NTRS2003

A Self-Contained Mapping Closure Approximation for Scalar Mixing

Scalar turbulence exhibits interplays of coherent structures and random fluctuations over a broad range of spatial and temporal scales. This feature necessitates a probabilistic description of the scalar dynamics, which can be achieved comprehensively by using probability density functions (PDFs). Therefore, the challenge is to obtain the scalar PDFs (Lundgren 1967; Dopazo 1979). Generally, the evolution of a scalar is governed by three dynamical processes: advection, diffusion and reaction. In a PDF approach (Pope 1985), the advection and reaction can be treated exactly but the effect of molecular diffusion has to be modeled. It has been shown (Pope 1985) that the effect of molecular diffusion can be expressed as conditional dissipation rates or conditional diffusions. The currently used models for the conditional dissipation rates and conditional diffusions (Pope 1991) have resisted deduction from the fundamental equations and are unable to yield satisfactory results for the basic test cases of decaying scalars in isotropic turbulence, although they have achieved some success in a variety of individual cases. The recently developed mapping closure approach (Pope 1991; Chen, Chen & Kraichnan 1989; Kraichnan 1990; Klimenko & Pope 2003) provides a deductive method for conditional dissipation rates and conditional di usions, and the models obtained can successfully describe the shape relaxation of the scalar PDF from an initial double delta distribution to a Gaussian one. However, the mapping closure approach is not able to provide the rate at which the scalar evolves. The evolution rate has to be modeled. Therefore, the mapping closure approach is not closed. In this letter, we will address this problem.

He, Guo-Wei↗

NASA NTRS1993

Preconditioned Conjugate Gradient methods for low speed flow calculations

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Ajmani, Kumud↗

DOE OSTI2024

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Boltzmann equation↗

DOE OSTI2024

Toward UV models of kinetic mixing and portal matter. VI. A more complex dark matter sector?

Portal matter (PM), having both Standard Model (SM) and dark sector charges, can induce kinetic mixing between the 𝑈⁢(1) 𝐷 dark photon and the SM gauge fields at the 1-loop level offering an attractive mechanism by which light (≲1 GeV) thermal dark matter (DM) can interact with visible matter and obtain its observed relic density. In doing so, if the DM is fermionic, the CMB and other astrophysical observations inform us that it must be Majorana/pseudo-Dirac in nature to avoid velocity/temperature-independent 𝑠-wave annihilation to SM final states. How does this idea fit into a more UV-complete picture also including the SM interactions? There are some reasons to believe that at least a first step along this path may not lie too far away in energy due to the renormalization group equations running of the dark gauge coupling, which for a significant range of parameters, becomes nonperturbative at/before the ∼10’s of TeV energy range. This implies that 𝑈⁢(1) 𝐷 must become embedded in an asymptotically free, non-Abelian group, 𝐺 𝐷 , before this can occur. The breaking of this larger group then produces the masses for the PM and the additional gauge fields associated with 𝐺 𝐷 then can lead to new interactions between the SM and the dark sector. Following several bottom-up approaches, we have examined a set of distinctive and testable phenomenological features associated with this general setup, based upon a number of simplifying assumptions. Clearly, it behooves us to explore the impact of these specific assumptions on these predictions for the array of possible experimental tests of this class of models. In most past analyses it has been assumed that DM is a vectorlike, complex singlet under the group 𝐺 𝐷 . If this assumption is relaxed, the dark sector must be augmented by additional fermion(s) and the associated scalar fields needed to break the gauge symmetries while generating the needed Majorana-like mass terms for the DM. In this paper, we analyze the simplest extension of this kind wherein the DM lies in a vectorlike doublet of 𝐺 𝐷 , which we take to have the structure 𝑆⁢𝑈⁢(2) 𝐼 ×𝑈⁢(1) 𝑌 𝐼 as in earlier work, leading to new phenomenological implications. We find, for example, that given the current LHC search constraints on the masses of heavy gauge bosons, the production of these new dark states with large rates is unlikely to occur at colliders unless they are produced singly in 𝑔⁡𝑔 fusion or their pair production cross sections are resonantly enhanced. Here, we also find that an additional mechanism arises to generate hierarchal neutrino masses in such a setup.

Extensions of Higgs sector↗

DOE OSTI2021

Distribution function of nuclei from $\mathcal{e}^±$ scattering in the presence of a strong primordial magnetic field

The amplitude of the primordial magnetic field (PMF) is constrained from observational limits on primordial nuclear abundances. Within this constraint, it is possible that nuclear motion is regulated by Coulomb scattering with electrons and positrons (e ± s), while e ± s are affected by a PMF rather than collisions. For example, at a temperature of 10 9 K, thermal nuclei typically experience ~ 10 21 scatterings per second that are dominated by very small angle scattering leading to minuscule changes in the nuclear kinetic energy of order $\mathcal{O}$(1) eV. In this paper the upper limit on the effects of a possible discretization of the e ± momenta by the PMF on the nuclear momentum distribution is estimated under the extreme assumptions that the momentum of the e ± is relaxed before and after Coulomb scattering to Landau levels, and that during Coulomb scattering the PMF is neglected. This assumption explicitly breaks the time reversal invariance of Coulomb scattering, and the Maxwell-Boltzmann distribution is not a trivial steady state solution of the Boltzmann equation under these assumptions. Here we numerically evaluate the collision terms in the Boltzmann equation, and show that the introduction of a special direction in the e ± distribution by the PMF generates no directional dependence of the collisional destruction term of nuclei. Large anisotropies in the nuclear distribution function are then constrained from big bang nucleosynthesis. Ultimately, we conclude that a PMF does not significantly affect the isotropy or big bang nucleosynthesis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Current-conserving relativistic linear response for collisional plasmas

Here we investigate the response of a relativistic plasma to electromagnetic fields in the framework of the Boltzmann equation incorporating a collision term in the relaxation rate approximation selected in a form assuring current conservation. We obtain an explicit solution for the linearized perturbation of the Fermi–Dirac equilibrium distribution in terms of the average relaxation rate k. We study the resulting covariant, gauge invariant, and current conserving form of the polarization tensor in the ultrarelativistic and non-relativistic limits. We evaluate the susceptibility in the ultrarelativistic limit and explore their dependence on k. Finally, we study the dispersion relations for the longitudinal and transverse poles of the propagator. We show that for k >2ω p , where ω p is the plasma frequency, the plasma wave modes are overdamped. In the opposite case, k$\ll$ ω p , the propagating plasma modes are weakly damped.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Sneezing and asymptomatic virus transmission

The novel coronavirus disease (COVID-19) spread pattern continues to show that geographical barriers alone cannot contain a virus. Asymptomatic carriers play a critical role in the nature of this virus quickly escalating into a global pandemic. Asymptomatic carriers may transmit the virus unintentionally through sporadic sneezing. A novel Computational Fluid Dynamics (CFD) approach has been proposed with a realistic modeling of a human sneeze achieved by the combination of state-of-the-art experimental and numerical methods. This modeling approach may be suitable for future engineering analyses aimed at reshaping public spaces and common areas, with the main objective to accurately predict the spread of aerosol and droplets that may contain pathogens. This study shows that the biomechanics of a human sneeze, including complex muscle contractions and relaxations, can be accurately modeled by the angular head motion and the dynamic pressure response during sneezing. These have been considered as the human factors and were implemented in the CFD simulation by imposing a momentum source term to the coupled Eulerian–Lagrangian momentum equations. The momentum source was modeled by the measured dynamic pressure response in conjunction with the angular head motion. This approach eliminated the need to create an ad hoc set of inlet boundary conditions. With this proposed technique, it is easier to add multiple fixed and/or moving sources of sneezes in complex computational domains. Additionally, extensive sensitivity analyses based on different environmental conditions were performed, and their impact was described in terms of potential virus spread.

42 ENGINEERING↗

DOE OSTI2025

A spline-based method to obtain spatially dependent viscosity in confined flows

Coupling chemical physics to continuum theories is a critical step to understanding multi-scale phenomena. This paper will connect non-equilibrium molecular dynamics simulations to a continuum-based Navier-Stokes equation that has relaxed the assumption of spatial uniformity in viscosity. Using a form for viscosity based on spline interpolation, viscosity as a function of position is obtained from the least squares fit of the velocity profile measured from molecular simulations of flow in a nanochannel. Viscosity can vary widely, particularly near the channel boundaries, indicating that uniform viscosity is no longer appropriate. Variations of the viscosity near the channel surfaces imply that considering solution and surface chemistry could be necessary to rigorously understand molecular-scale flows in nanochannels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

A passive model for the evolution of subgrid-scale instabilities in turbulent flow regimes

In this work, a zero-dimensional model for the development of turbulent mixing layers driven by Rayleigh–Taylor (RT) or Richtmyer–Meshkov (RM) instabilities is presented, for application in Reynolds-Averaged Navier–Stokes (RANS) simulations. The model approximates the behavior of the turbulent mixing layer at a passively advected tracer particle that sits on the material interface of interest in the simulation, and is used to provide initial conditions for the RANS model once the mixing layer width has developed to a size that may be resolved on the computational mesh. The model relies on approximations to the Besnard–Harlow–Rauenzahn (BHR) RANS closure equations and is thus consistent the turbulent development of the mixing layer, unlike previous models of this type which have focused on the early-time laminar development of RT or RM instabilities. These instabilities will often grow through an initially laminar state before developing into turbulence, and criteria for switching from an existing laminar model to the proposed turbulent model are considered. The proposed model reproduces the mixing layer development of RT and RM instabilities seen in mixed width resolving BHR RANS simulations to a reasonable degree of accuracy, and relaxes the need for the RANS simulation to resolve the mixed width as soon as the mixing layer becomes turbulent, which may be impractical in cases where the mixing layer grows through a wide range of scales.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Machine learning accelerated turbulence modeling of transient flashing jets

We report modeling the sudden depressurization of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including ligaments and droplets, due to both mechanical and thermodynamic effects. As the simulation comprises increasingly numerous phenomena, the computational cost begins to increase. One way to moderate the additional cost is to use machine learning surrogacy for specific elements of the calculation. This study presents a machine learning-assisted computational fluid dynamics approach for simulating the atomization of flashing liquids accounting for distinct stages, from primary atomization to secondary breakup to small droplets using the Σ - Y model coupled with the homogeneous relaxation model. Notably, the models for thermodynamic non-equilibrium (HRM) and Σ - Y are coupled, for the first time, with a deep neural network that simulates the turbulence quantities, which are then used in the prediction of superheated liquid jet atomization. The data-driven component of this method is used for turbulence modeling, avoiding the solution of the two-equation turbulence model typically used for Reynolds-averaged Navier-Stokes simulations for these problems. Both the accuracy and speed of the hybrid approach are evaluated, demonstrating adequate accuracy and at least 25% faster computational fluid dynamics simulations than the traditional approach. This acceleration suggests that perhaps additional components of the calculation could be replaced for even further benefit. Published under an exclusive license by AIP Publishing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Quantum dynamics of a nucleon in the Fermi accelerator

Highlights: • In nuclear physics, the Fermi accelerator is a coherent open quantum system. • There is not a true equilibrium for a nucleon‘s mean-energy in the Fermi accelerator. • Occupation of higher energy eigen-states remains even after the mean-energy plateaus. • This work paves the way for work on quantum tunnelling in the Fermi accelerator. The quantum dynamics of a particle in a one-dimensional box with an oscillating wall (the Fermi accelerator) is investigated. The model is applied to the motion of a single nucleon in the mean-field potential of a heavy atomic nucleus whose surface vibrates. By directly solving the time-dependent Schrödinger equation, both the state of the particle and its mean-energy are studied. The effects of the frequency of the wall oscillation on the nucleon’s energy are addressed. Its energy oscillates in phase with the moving wall for all frequencies, showing no chaotic behaviour. There is a large initial peak of the nucleon’s energy as the particle adjusts to the sudden change in the size of the box and a varying relaxation time as it plateaus towards lower energy and a partial equilibrium. Small oscillations in energy continue, since there cannot be a true equilibrium while the wall is moving. The quantum coherence between the different parts of the nucleon’s wave-function in real space is very much preserved. This research lays the foundation for future investigations into quantum tunnelling in the Fermi accelerator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Non-conformal attractor in boost-invariant plasmas

We study the dissipative evolution of (0+1)-dimensionally expanding media with Bjorken symmetry using the Boltzmann equation for massive particles in relaxation-time approximation. Breaking conformal symmetry by a mass induces a non-zero bulk viscous pressure in the medium. It is shown that even a small mass (in units of the local temperature) drastically modifies the well-known attractor for the shear Reynolds number previously observed in massless systems. For generic nonzero particle mass, neither the shear nor the bulk viscous pressure relax quickly to a non-equilibrium attractor; they approach the hydrodynamic limit only late, at small values of the inverse Reynolds numbers. Only the longitudinal pressure, which is a combination of thermal, shear and bulk viscous pressures, continues to show early approach to a far-off-equilibrium attractor, driven by the rapid longitudinal expansion at early times. Second-order dissipative hydrodynamics based on a gradient expansion around locally isotropic thermal equilibrium fails to reproduce this attractor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Molecular-level insights into structure and dynamics in ionic liquids and polymer gel electrolytes

We report designing new electrolytes requires a better understanding of the correlation between their transport properties and their molecular structure. In this work, we present a detailed study of ionic liquids and polymer gel electrolytes probing their structure and dynamics by nuclear magnetic resonance (NMR) spectroscopy. In particular, ammonium- and phosphonium-based ionic liquids (ILs) are combined with different LiTFSI concentrations, and then with different ratios of poly(methylmethacrylate) polymer. The temperature dependence of self-diffusion coefficients of mobile species, D Li+ , D TFSI- and D P4441+ or D N4441+ , measured by pulsed field gradient (PFG) NMR spectroscopy obeys the Arrhenius equation. Diffusivity of [P4441][TFSI] ILs is found to be greater than those of the [N4441][TFSI] ILs in both liquid and gel electrolytes. Solid state NMR experiments including 13 C and 19 F MAS, 13 C{ 19 F}, 13 C{ 1 H} CPMAS probe the local structure and molecular-level interactions between ions and polymer in gel electrolytes, particularly for samples with higher PMMA content (≥25 wt%). Finally, the fast field cycling relaxometry has been used to unveil the rotational and translational dynamics of P4441 + or N4441 + and TFSI - by measuring 1 H and 19 F R 1 relaxation rate profiles at different temperatures. A comprehensive NMR analysis including relaxation studies at low magnetic field provides decisive new insights regarding the formation of ionic clusters and the interaction of ions with the polymer chain in the case of the gel electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗