Mathematics and physics at the quantum-classical interface
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general physics↗
SEARCH · Engineering Papers
Results for “quantum mechanics and quantum computing”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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HZE reactions and data-base development
The primary cosmic rays are dispersed over a large range of linear energy transfer (LET) values and their distribution over LET is a determinant of biological response. This LET distribution is modified by radiation shielding thickness and shield material composition. The current uncertainties in nuclear cross sections will not allow the composition of the shield material to be distinguished in order to minimize biological risk. An overview of the development of quantum mechanical models of heavy ion reactions will be given and computational results compared with experiments. A second approach is the development of phenomenological models from semi-classical considerations. These models provide the current data base in high charge and energy (HZE) shielding studies. They will be compared with available experimental data. The background material for this lecture will be available as a review document of over 30 years of research at Langley but will include new results obtained over the last year.
Townsend, Lawrence W.↗
Ultra-bright Quantum Light Source Using Entangled Two-Mode State
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Modeling Chemo-Mechanics with Electrolyte Infiltration to Quantify Degradation of Cathode Particles
One of the main goals in modeling lithium-ion batteries is to improve/predict longevity and resilience of new chemistries. To that end, this talk investigates the formation of stress-induced fracture within polycrystalline cathode particles and the impact on capacity loss. Physically based cathode aging dynamics is simulated in a 3D, continuum-level chemo-mechanical model. The model captures anisotropic Li diffusion within a single polycrystalline particle comprised of hundreds to thousands of randomly oriented grains. A recent addition to this model includes electrolyte infiltration, which occurs when the electrolyte seeps into surface cracks within the particle. The model predicts that particle fracture is primarily due to non-ideal grain interactions with slight dependence on high-rate charge demands. Essentially, when neighboring grains are misaligned, they expand a different rates relative to one another leading to high stresses and ultimately the formation of intraparticle cracks. The model predicts that small particles with large grains develop significantly less damage than larger particles with small grains. Finally, the model predicts most of the chemo-mechanical damage accumulates in the first charge after formation. This chemo-mechanical "damage saturation" effect indicates that initial particle fracture occurs within the first few cycles, while long-term cathode degradation is not solely chemo-mechanically induced. The principle contribution of this research is the use of an anisotropic chemo-mechanical model to test how particle geometry affect capacity fade, which predicts that particle size has a stronger effect on capacity fade than grain size and ultimately that small particles with large grains have the least capacity fade.
cathode↗
Suitability of Altair FEKO's Computational Electromagnetic Techniques for Tree Model Scattering and Penetration at Ku-band
Foliage penetration (FOPEN) radar at lower frequencies (VHF, UHF) is a well-studied area with many contributions. However, there is growing interest in using higher Ku-band frequencies (12-18 GHz) for FOPEN. Specifically, the reduced wavelength sizes provide some key saliencies for developing more optimized detection solutions. The disadvantage is that exploiting Ku-band for FOPEN is complicated because higher frequencies have pronounced scattering effects due to their smaller wavelengths. A methodology h as been developed to model and simulate FOPEN problems that characterize the phenomenology of Ku-band electromagnetic ( EM ) wave transmissions through moderate foliage. The details of this research (i.e. the realistic tree models, simulation setup and results) are documented in multiple reports. The main focus of this report is to describe the preliminary validation and verification of Altair FEKO, the computational EM (CEM) software used for this research, as well as present a simplified symmetrical tree model and an introductory CAD tree model.
42 ENGINEERING↗
Estimation of distributions via multilevel Monte Carlo with stratified sampling
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the joint cumulative distribution function (CDF) of a vector-valued quantity of interest in problems with random input parameters and initial conditions. Our approach combines MLMC with stratified sampling of the input sample space by replacing standard Monte Carlo at each level with stratified Monte Carlo initialized with proportionally allocated samples. We show that the resulting stratified MLMC (sMLMC) algorithm is more efficient than its standard MLMC counterpart due to the additional variance reduction provided by the stratification of the random parameter's domain, especially at the coarsest levels. Additional computational cost savings are obtained by smoothing the indicator function with a Gaussian kernel, which proves to be an efficient and robust alternative to recently developed polynomial-based techniques.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum Computing by Coherent Cooling
Interesting problems in quantum computation take the form of finding low-energy states of (pseudo)spin systems with engineered Hamiltonians that encode the problem data. Motivated by the practical possibility of producing very low-temperature spin systems, we propose and exemplify the possibility to compute by coupling the computational spins to a quantum coherent bath that serves as a heat sink. The quantum tunneling effect provides additional cooling channels to accelerate the cooling process. Here, we demonstrate both analytically and numerically that this strategy can achieve a quantum advantage in the unstructured search problem.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Sequential ensemble transform for Bayesian inverse problems
In this work, we present the Sequential Ensemble Transform (SET) method, an approach for generating approximate samples from a Bayesian posterior distribution. The method explores the posterior distribution by solving a sequence of discrete optimal transport problems to produce a series of transport plans which map prior samples to posterior samples. We prove that the sequence of Dirac mixture distributions produced by the SET method converges weakly to the true posterior as the sample size approaches infinity. Furthermore, our numerical results indicate that, when compared to standard Sequential Monte Carlo (SMC) methods, the SET approach is more robust to the choice of Markov mutation kernels and requires less computational efforts to reach a similar accuracy when used to explore complex posterior distributions. Finally, we describe adaptive schemes that allow to completely automate the use of the SET method.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Central vortex steady states and dynamics of Bose–Einstein condensates interacting with a microwave field
Here we study central vortex steady states and dynamics of a two-dimensional (2D), two-component, Gross–Pitaevskii equation (CGPE) system for two pseudo-spinor Bose Einstein condensates (BECs) interacting with an electromagnetic field (microwave) analytically and numerically. For the central vortex steady state at any given winding number S, we prove its existence in a reduced, single component detuning limit when contact-interaction strength β < β b , and nonexistence when β > β b , respectively, where β b is a threshold value, whose value is given in Theorem 3.1 in the paper. We extend the existence and nonexistence result to the general two pseudo-spinor case and prove that a central vortex steady state exists for any given S if β ≤ β b while it does not exist when β > 2β b . We then derive dynamical equations for some observables (expectations of the matter wave function) such as the center-of-mass, position of dispersion, the linear and angular momentum of the two pseudo-spinor CGPEs. Finally, numerical computations are brought in to validate and extend the existence of vortex steady state results to β b ≤ β < 2β b for the two pseudo-spinor case and to explore transient dynamics of the observables.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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↗
$\mathrm{Perturbo}$: A software package for ab initio electron–phonon interactions, charge transport and ultrafast dynamics
We report Perturbo is a software package for first-principles calculations of charge transport and ultrafast carrier dynamics in materials. The current version focuses on electron–phonon interactions and can compute phonon-limited transport properties such as the conductivity, carrier mobility and Seebeck coefficient. It can also simulate the ultrafast nonequilibrium electron dynamics in the presence of electron–phonon scattering. Perturbo uses results from density functional theory and density functional perturbation theory calculations as input, and employs Wannier interpolation to reduce the computational cost. It supports norm-conserving and ultrasoft pseudopotentials, spin–orbit coupling, and polar electron–phonon interactions for bulk and 2D materials. Hybrid MPI plus OpenMP parallelization is implemented to enable efficient calculations on large systems (up to at least 50 atoms) using high-performance computing. Taken together, Perturbo provides efficient and broadly applicable ab initio tools to investigate electron–phonon interactions and carrier dynamics quantitatively in metals, semiconductors, insulators, and 2D materials.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Learning a General Model of Single Phase Flow in Complex 3D Porous Media
Modeling effective transport properties of 3D porous media, such as permeability, at multiple scales is challenging as a result of the combined complexity of the pore structures and fluid physics—in particular, confinement effects which vary across the nanoscale to the microscale. While numerical simulation is possible, the computational cost is prohibitive for realistic domains, which are large and complex. Although machine learning (ML) models have been proposed to circumvent simulation, none so far has simultaneously accounted for heterogeneous 3D structures, fluid confinement effects, and multiple simulation resolutions. By utilizing numerous computer science techniques to improve the scalability of training, we have for the first time developed a general flow model that accounts for the pore-structure and corresponding physical phenomena at scales from Angstrom to the micrometer. Using synthetic computational domains for training, our ML model exhibits strong performance (R 2 = 0.9) when tested on extremely diverse real domains at multiple scales.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Classical combinatorial optimization scaling for random Ising models on 2D heavy-hex graphs
Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum algorithms such as the quantum approximate optimization algorithm. In this study, a specific class of near term quantum computing hardware defined combinatorial optimization problems, Ising models on heavy-hex graphs both with and without geometrically local cubic terms, are examined for their classical computational hardness via empirical computation time scaling quantification. Specifically the time-to-solution (TTS) metric using the classical heuristic simulated annealing is measured for finding optimal variable assignments (ground states), as well as the time required for the optimization software Gurobi to find an optimal variable assignment. Because of the sparsity of these Ising models, the classical algorithms are able to find optimal solutions efficiently even for large instances (i.e. 100 000 spin variables). The Ising models both with and without geometrically local cubic terms exhibit average-case linear-time or weakly quadratic scaling when solved exactly using Gurobi, and the Ising models with no cubic terms show evidence of exponential-time TTS scaling when sampled using simulated annealing. These findings point to the necessity of developing and testing more complex, namely more densely connected, optimization problems in order for quantum computing to ever have a practical advantage over classical computing. Our results are another illustration that different classical algorithms can indeed have exponentially different running times, thus making the identification of the best practical classical technique important in any quantum computing vs. classical computing comparison.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Efficient approach to kinetic simulation in the inner magnetically insulated transmission line on Z
This project explores the idea of performing kinetic numerical simulations in the Z inner magnetically insulated transmission line (inner MITL) by reduced physics models such as a guiding center drift kinetic approximation for particles and electrostatic and magnetostatic approximation for the fields. The basic problem explored herein is the generation, formation, and evolution of vortices by electron space charge limited (SCL) emission. The results indicate that for relevant to Z values of peak current and pulse length, these approximations are excellent, while also providing tens to hundreds of times reduction in the computational load. The benefits could be enormous: Implementation of these reduced physics models in present particle-in-cell (PIC) codes could enable them to be routinely used for experimental design while still capturing essential non-thermal (kinetic) physics.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
IBM Open Science Price - SWAP Gate Challenge
On November 30, 2020, IBM announced an open science price competition aimed at improving the fidelity of a SWAP gate on their 7 qubit Quantum system named ”Casablanca”. The details of the SWAP gate problem was outlined in a Jupyter notebook, which utilizes the IBM developed open source package Qiskit. The participants were allowed to work in teams with up to five people and restricted to only use open source software in solving the problem. Their results were due on April 16, 2021. Our approach to solving the SWAP gate challenge is based on the quantum optimal control techniques implemented in our open source packages Juqbox.jl and Quandary. The results from the optimal control approach is only as good as the accuracy in the description of the quantum system dynamics, characterized by a Hamiltonian model that was provided by IBM. Based on the calibrated control pulses IBM provide for the standard gate set, we developed a reverse engineering approach to calibrate our computational model. Techniques were developed to translate between Qiskit’s pulse representation and the B-spline formulation used in Juqbox and Quandary. The fidelity of the optimized pulse sequences were estimated using Qiskit’s randomized bench marking techniques.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DMFTwDFT: An open-source code combining Dynamical Mean Field Theory with various density functional theory packages
We report Dynamical Mean Field Theory (DMFT) is a successful method to compute the electronic structure of strongly correlated materials, especially when it is combined with density functional theory (DFT). Here, we present an open-source computational package (and a library) combining DMFT with various DFT codes interfaced through the Wannier90 package. The correlated subspace is expanded as a linear combination of Wannier functions introduced in the DMFT approach as local orbitals. In particular, we provide a library mode for computing the DMFT density matrix. This library can be linked and then internally called from any DFT package, assuming that a set of localized orbitals can be generated in the correlated subspace. The existence of this library allows developers of other DFT codes to interface with our package and achieve the charge-self-consistency within DFT+DMFT loops. To test and check our implementation, we computed the density of states and the band structure of well-known solid-state correlated materials, namely LaNiO, SrVO, and NiO. The obtained results are compared to those obtained from other DFT+DMFT implementations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains
In this work, we propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modeling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved domains with piecewise smooth curved boundaries that may present corners. The solution method we present is based on the hybridizable discontinuous Galerkin method and sidesteps the need for geometry-conforming triangulations thanks to a transfer technique that allows to approximate the solution using only a polygonal subset as computational domain. Moreover, the solver features automatic mesh refinement driven by a residual-based a posteriori error estimator. As the mesh is locally refined, the computational domain is automatically updated in order to always maintain the distance between the actual boundary and the computational boundary of the order of the local mesh diameter. Numerical evidence is presented of the suitability of the estimator as an approximate error measure for physically relevant equilibria with pressure pedestals, internal transport barriers, and current holes on realistic geometries.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Readout rebalancing for near-term quantum computers
Readout errors are a significant source of noise for near-term intermediate-scale quantum computers. Mismeasuring a qubit as |1) when it should be |0) occurs much less often than mismeasuring a qubit as |0) when it should have been |1). We make the simple observation that one can improve the readout fidelity of quantum computers by applying targeted X gates prior to performing a measurement. These X gates are placed so that the expected number of qubits in the |1) state is minimized. Classical postprocessing can undo the effect of the X gates so that the expectation value of any observable is unchanged. This protocol is designed to have no effect when readout errors are symmetric. We show that the statistical uncertainty following readout error corrections is smaller when using readout rebalancing. The statistical advantage is circuit and computer dependent and is demonstrated for the W state, a Grover search, and for a Gaussian state. The benefit in statistical precision is most pronounced (and nearly a factor of 2 in some cases) when states with many qubits in the excited state have high probability.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗