Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Variational methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

Understanding the origin of Tabula Rasa-induced defects in n-type Cz c-Si: The case of nitrogen atmosphere

Phosphorus-doped Czochralski-grown silicon (Cz-Si) has been gaining market share in the large-scale manufacturing of high-efficiency silicon (Si)-based photovoltaic (PV) devices thanks to higher carrier lifetimes than their boron-doped counterpart. However, the fabrication of n-type Cz-Si based solar cells often requires process steps with much higher temperatures and longer times than p-type Silicon. Defect interaction with the high temperatures during such processes tend to be detrimental to the n-type Cz-Si carrier lifetime, therefore limiting the final device efficiency. Short thermal anneals before cell processing, known as Tabula Rasa (TR), have been proposed to mitigate the thermally induced lifetime degradation during n-type Cz-Si solar cell fabrication. This work thoroughly investigates the defects responsible for the lifetime degradation after TR in a N 2 atmosphere treatment. We use temperature-injection-dependent lifetime spectroscopy and the thickness variation method to decouple the effects of TR treatment in the bulk and the surface of the n-type Cz-Si wafers. Using the defect parameter contour mapping (DPCM), we identify the defect energy level (E t ) and the capture cross-section ratio (k) of the most likely process-induced defect, which aligns with previously proposed Si vacancy-associated defects. The DPCM reveals that these vacancy-associated defects have a shallow energy level E t - E v ~0.13 eV and very efficient electron capture cross section k~600. Unexpectedly, the bulk degradation due to vacancy defects in the volume of the wafer, is accompanied by a significant increase in the surface recombination as well. Through evaluating the surface recombination velocity temperature- and injection dependence, we show that after TR, at room temperature and for an injection level of 10 15 cm -3 , in a wafer passivated with a-Si:H(i) the surface recombination dominates the overall lifetime response. Here we hypothesize that the near surface vacancy-associated bulk defects play a role in lowering the electron diffusion current into the a-Si:H(i) from the c-Si(n) reducing the field-effect passivation.

14 SOLAR ENERGY↗

Revealing Variable Dependences in Hexagonal Boron Nitride Synthesis via Machine Learning

Wafer-scale monolayer two-dimensional (2D) materials have been realized by epitaxial chemical vapor deposition (CVD) in recent years. To scale up the synthesis of 2D materials, a systematic analysis of how the growth dynamics depend on the growth parameters is essential to unravel its mechanisms. However, the studies of CVD-grown 2D materials mostly adopted the control variate method and considered each parameter as an independent variable, which is not comprehensive for 2D materials growth optimization. Herein, we synthesized a representative 2D material, monolayer hexagonal boron nitride (hBN), on single-crystalline Cu (111) by epitaxial chemical vapor deposition and varied the growth parameters to regulate the hBN domain sizes. Furthermore, we explored the correlation between two growth parameters and provided the growth windows for large flake sizes by the Gaussian process. Here, this new analysis approach based on machine learning provides a more comprehensive understanding of the growth mechanism for 2D materials.

36 MATERIALS SCIENCE↗

The phase diagram of quantum chromodynamics in one dimension on a quantum computer

The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behaviour of particles in neutron stars to the conditions of the early universe. However, classical simulations of QCD face significant computational barriers, such as the sign problem at finite matter densities. Quantum computing offers a promising solution to overcome these challenges. Here, we take an important step toward exploring the QCD phase diagram with quantum devices by preparing thermal states in one-dimensional non-Abelian gauge theories. We experimentally simulate the thermal states of SU(2) and SU(3) gauge theories at finite densities on a trapped-ion quantum computer using a variational method. This is achieved by introducing two features: Firstly, we add motional ancillae to the existing qubit register to efficiently prepare thermal probability distributions. Secondly, we introduce charge-singlet measurements to enforce colour-neutrality constraints. This work pioneers the quantum simulation of QCD at finite density and temperature for two and three colours, laying the foundation to explore QCD phenomena on quantum platforms.

Quantum information↗

Preparation of metrological states in dipolar-interacting spin systems

Abstract Spin systems are an attractive candidate for quantum-enhanced metrology. Here we develop a variational method to generate metrological states in small dipolar-interacting spin ensembles with limited qubit control. For both regular and disordered spatial spin configurations the generated states enable sensing beyond the standard quantum limit (SQL) and, for small spin numbers, approach the Heisenberg limit (HL). Depending on the circuit depth and the level of readout noise, the resulting states resemble Greenberger-Horne-Zeilinger (GHZ) states or Spin Squeezed States (SSS). Sensing beyond the SQL holds in the presence of finite spin polarization and a non-Markovian noise environment. The developed black-box optimization techniques for small spin numbers ( N ≤ 10) are directly applicable to diamond-based nanoscale field sensing, where the sensor size limits N and conventional squeezing approaches fail.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Accessing the gluon momentum fraction of nucleons through the gradient flow

We calculate the gluon momentum fraction of the nucleon using lattice QCD, with a nonperturbative renormalization technique based on the gradient flow. The gluon momentum fraction is determined on a single Wilson-clover ensemble using 𝑁 𝑓 =2 +1 flavors with pion mass 358 MeV and lattice spacing 0.094 fm. We employ the variational method to reduce excited-state contamination and apply the distillation framework to ensure a large operator basis. To reduce systematic uncertainties, we apply Bayesian model averaging to all fit procedures. We apply matching coefficients to the flow-time dependent lattice results to recover the gluon momentum fraction in the $\overline{MS}$-scheme at 2 GeV. Our final result is ⟨𝑥⟩ 𝑔 ⁢(𝜇 =2 GeV) =0.482⁢(35), where we quote only statistical uncertainties.

Lattice QCD↗

Quantum state reduction: Generalized bipartitions from algebras of observables

Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with the partial-trace map by tracing out part of the quantum state, but in many natural situations this reduction may not be achievable. We investigate the general problem of identifying how the quantum state is reduced given a restriction on the observables. For example, in an experimental setting, the set of observables that can actually be measured is usually modest (compared to the set of all possible observables) and their resolution is limited. In such situations, the appropriate state-reduction map can be defined via a generalized bipartition, which is associated with the structure of irreducible representations of the algebra generated by the restricted set of observables. One of our main technical results is a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras. In our work, we demonstrate the viability of this approach with two examples of limited-resolution observables. The definition of quantum state reductions can also be extended beyond algebras of observables. To accomplish this task we introduce a more flexible notion of bipartition, the partial bipartition, which describes coarse grainings preserving information about a limited set (not necessarily algebra) of observables. We describe a variational method to choose the coarse grainings most compatible with a specified Hamiltonian, which exhibit emergent classicality in the reduced state space. We apply this construction to the concrete example of the one-dimensional Ising model. Our results have relevance for quantum information, bulk reconstruction in holography, and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Validity of the static-exchange approximation for inner-shell photoionization of polyatomic molecules

The simple single-channel static-exchange approximation completely ignores correlation between the continuum and molecular ion electrons. In molecular systems with symmetry equivalent atoms, the single-channel approximation can seriously fail in core ionization when using delocalized orbitals to represent the core hole states. We present cross sections and molecular frame photoelectron angular distributions with both localized and delocalized core orbitals in CF 4 F (1 s ) ionization. We show that only a full coupled-channel calculation can recover an accurate description of the physics of inner-shell photoionization when using delocalized orbitals, whereas nearly the same result can be obtained from independent single-channel static-exchange calculations when localized core orbitals are used. A grid-based variational method described here makes such single-channel calculations possible on larger systems without local-exchange approximations. Illustrative calculations on the core ionization of SF 6 are presented to illustrate the power of the grid-based method.

74 ATOMIC AND MOLECULAR PHYSICS↗

Superconductivity in the bilayer Hubbard model: Two Fermi surfaces are better than one

Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping t⊥, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Lifshitz transition and even when it becomes incipient. Here we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust s± pairing correlations in the large t⊥ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased Tc. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Composite excitonic states in doped semiconductors

We present a theoretical model of composite excitonic states in doped semiconductors. Many-body interactions between a photoexcited electron-hole pair and the electron gas are integrated into a computationally tractable few-body problem, solved by the variational method. We focus on electron-doped monolayer (ML)-MoSe 2 and ML-WSe 2 due to the contrasting character of their conduction bands. In both cases, the core of the composite is a tightly bound trion (two electrons and a valence-band hole) surrounded by a region depleted of electrons. The composite in ML-WSe 2 further includes a satellite electron with different quantum numbers. The theory is general and can be applied to semiconductors with various energy-band properties, allowing one to calculate their excitonic states and to quantify the interaction with the Fermi sea.

36 MATERIALS SCIENCE↗

Quantum Computing for Neutrino-Nucleus Scattering

Neutrino-nucleus cross section uncertainties are expected to be a dominant systematic in future accelerator neutrino experiments. The cross sections are determined by the linear response of the nucleus to the weak interactions of the neutrino, and are dominated by energy and distance scales of the order of the separation between nucleons in the nucleus. These response functions are potentially an important early physics application of quantum computers. Here we present an analysis of the resources required and their expected scaling for scattering cross section calculations. The current estimates of Trotter steps needed to achieve an energy resolution of 10 MeV and the number of CNOT gates for analyzing Ar40 highlights the need for significant improvements in algorithms. We also examine simple small-scale neutrino-nucleus models on modern quantum hardware. In this paper, we use variational methods to obtain the ground state of a three nucleon system (the triton) and then implement the relevant time evolution. To tame the errors in present-day NISQ devices, we explore the use of different error-mitigation techniques to increase the fidelity of the calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Finite-volume pionless effective field theory for few-nucleon systems with differentiable programming

Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wave functions optimized using differentiable programming and via solution of a generalized eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wave functions, yielding comparably accurate representations of the ground-state wave functions with an order of magnitude fewer terms. The efficiency of representation allows such calculations to be extended to larger systems than in previous work. Further, the method is demonstrated through calculations of the binding energies of nuclei with atomic number A ϵ {2,3,4} in finite volume, matched to lattice QCD calculations at quark masses corresponding to m π = 806 MeV, and infinite-volume effective field theory calculations of A ϵ {2,3,4,5,6} systems based on this matching.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Automated label flows for excited states of correlation functions in lattice gauge theory

Extracting excited states from lattice gauge theory correlation functions can be achieved through $χ^2$ minimization fits or algebraic approaches such as the variational method and Prony's method. Performing any kind of error analysis often leads to overlapping confidence regions of model parameters, even when the spectrum is not particularly dense. To correctly estimate errors, one must beware of mislabeling the states. In this work, we provide an algorithm that we call automated label flows which consistently and systematically identifies a deterministic labeling of states. This is a black-box approach in the sense that it gives a sensible set of labels without user guidance. Further, as an example, we pair one black box method with another, analyzing a lattice correlation function from real data using automated label flows in the context of Prony's method.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

CV4Quantum

CV4Quantum is a statistical technique for reducing the sampling overhead in probabilistic error cancellation, which is an error mitigation technique used in quantum computing. CV4Quantum is based on the control variates method, which is a Monte Carlo variance reduction technique. This repository contains the code and data associated with a demonstration of CV4Quantum using simulation experiments.

Shyamsundar, Prasanth [Fermi National Accelerator ↗

Evaluation of Physical Microphysical Property Retrieval Algorithms During the 2020 IMPACTS Field Campaign

The NASA Investigation of Microphysics and Precipitation for Atlantic Coast Threatening Snowstorms (IMPACTS) field campaign provides high-quality, high-altitude aircraft lidar (532 nm), radar (W-band) and in-cloud microphysical aircraft data taken during wintertime storm events impacting the United States. This study evaluates two mass-dimensional relationships (Brown and Francis (1995, BF95); Heymsfield (2014, H14) and two lidar-radar microphysical retrieval algorithms (Cloudsat and CALIPSO Ice Cloud Property Product (2C-ICE); VarPy (a variational method derived from the satellite lidar-radar data community)) to estimate aircraft-retrieved volume extinction coefficient (σ), ice water content (IWC), and effective radius (r e ) during the 2020 IMPACTS deployment. BF95 and H14 have a close 1:1 correlation (R 2 = 0.98) with in-situ observations of σ. However, only BF95 displays a linear, consistent, and almost temperature-independent low bias for IWC and r e , which likely arises from the environmental conditions used to determine each. Unlike the field-campaign-derived BF95 and H14 relationships, VarPy and 2C-ICE directly ingest the aircraft-based lidar and radar data to simulate σ, IWC, and r e . For all three microphysical parameters, VarPy and 2C-ICE retrieval errors became notably more pronounced around the dendritic growth zone (-15°C to -10°C) and near freezing (≥-5°C), which suggests that both algorithms experience difficulty addressing riming and aggregation processes and with larger particles (dendrites and plates) due in part to their simplified ice particle assumptions. However, the mean-melt diameter ice-particle assumption did yield more accurate IWC estimates, which led to slightly better overall results for VarPy.

54 ENVIRONMENTAL SCIENCES↗

Fifty ways to build a deuteron: a variational calculation of two-nucleon systems

A variational study of two-nucleon systems with lattice quantum chromodynamics is performed using a wide range of interpolating operators: dibaryon operators built from products of momentum-projected nucleons, hexaquark operators built from six spatially localized quarks, and quasi-local operators inspired by two-nucleon bound-state wavefunctions in nuclear effective field theories. Correlation-function matrices involving products of these operators are constructed by computing timeslice-to-all quark propagators with sparsening techniques. Comparisons between results obtained using the same gauge-field ensemble but different interpolating-operator sets demonstrate that interpolating-operator dependence can lead to significant effects on the two-nucleon energy spectra obtained using both variational and non-variational methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers

The transport of conserved quantities like spin and charge is fundamental to characterizing the behavior of quantum many-body systems. Numerically simulating such dynamics is generically challenging, which motivates the consideration of quantum computing strategies. However, the relatively high gate errors and limited coherence times of today's quantum computers pose their own challenge, highlighting the need to be frugal with quantum resources. In this work we report simulations on quantum hardware of infinite-temperature energy transport in the mixed-field Ising chain, a paradigmatic many-body system that can exhibit a range of transport behaviors at intermediate times. We consider a chain with L = 12 sites and find results broadly consistent with those from ideal circuit simulators over 90 Trotter steps, containing up to 990 entangling gates. To obtain these results, we use two key problem-tailored insights. First, we identify a convenient basis – the Pauli Y basis – in which to sample the infinite-temperature trace and provide theoretical and numerical justifications for its efficiency relative to, e.g., the computational basis. Second, in addition to a variety of problem-agnostic error mitigation strategies, we employ a renormalization strategy that compensates for global nonconservation of energy due to device noise. We discuss the applicability of the proposed sampling approach beyond the mixed-field Ising chain and formulate a variational method to search for a sampling basis with small sample-to-sample fluctuations for an arbitrary Hamiltonian. This opens the door to applying these techniques in more general models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

Shen, Yizhi↗