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DOE OSTI2020

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↗

DOE OSTI2020

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↗

DOE OSTI2021

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↗

DOE OSTI2022

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↗

DOE OSTI2017

Vestigial nematicity from spin and/or charge order in the cuprates

Nematic order has manifested itself in a variety of materials in the cuprate family. We propose an effective field theory of a layered system with incommensurate, intertwined spin- and charge-density wave (SDW and CDW) orders, each of which consists of two components related by C4 rotations. Using a variational method (which is exact in a large N limit), we study the development of nematicity from partially melting those density waves by either increasing temperature or adding quenched disorder. As temperature decreases we first find a transition to a nematic phase, but depending on the range of parameters (e.g. doping concentration) the strongest fluctuations associated with this phase reflect either proximate SDW or CDW order. We also discuss the changes in parameters that can account for the differences in the SDW-CDW interplay between the (214) family and the other hole-doped cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

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↗

DOE OSTI2022

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↗

DOE OSTI2020

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↗

DOE OSTI2015

SU-E-T-147: Beam Specific Planning Target Volumes Incorporating 4DCT for Pencil Beam Scanning Proton Therapy of Thoracic Tumors

Purpose: The purpose of this study is to determine whether organ sparing and target coverage can be simultaneously maintained for pencil beam scanning (PBS) proton therapy treatment of thoracic tumors in the presence of motion, stopping power uncertainties and patient setup variations. Methods: Ten consecutive patients that were previously treated with proton therapy to 66.6/1.8 Gy (RBE) using double scattering (DS) were replanned with PBS. Minimum and maximum intensity images from 4DCT were used to introduce flexible smearing in the determination of the beam specific PTV (BSPTV). Datasets from eight 4DCT phases, using ±3% uncertainty in stopping power, and ±3 mm uncertainty in patient setup in each direction were used to create 8*12*10=960 PBS plans for the evaluation of ten patients. Plans were normalized to provide identical coverage between DS and PBS. Results: The average lung V20, V5, and mean doses were reduced from 29.0%, 35.0%, and 16.4 Gy with DS to 24.6%, 30.6%, and 14.1 Gy with PBS, respectively. The average heart V30 and V45 were reduced from 10.4% and 7.5% in DS to 8.1% and 5.4% for PBS, respectively. Furthermore, the maximum spinal cord, esophagus and heart dose were decreased from 37.1 Gy, 71.7 Gy and 69.2 Gy with DS to 31.3 Gy, 67.9 Gy and 64.6 Gy with PBS. The conformity index (CI), homogeneity index (HI), and global maximal dose were improved from 3.2, 0.08, 77.4 Gy with DS to 2.8, 0.04 and 72.1 Gy with PBS. All differences are statistically significant, with p values <0.05, with the exception of the heart V45 (p= 0.146). Conclusion: PBS with BSPTV achieves better organ sparing and improves target coverage using a repainting method for the treatment of thoracic tumors. Incorporating motion-related uncertainties is essential This work was supported by the US Army Medical Research and Materiel Command under Contract Agreement No. DAMD17-W81XWH-07-2-0121 and W81XWH-09-2-0174.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Detection of Sodium in Highly Pure Graphite via High-Resolution Electrothermal Atomic Absorption Spectrometry with a Continuous Spectrum Source

This study is dedicated to elucidating the analytical abilities of electrothermal atomic absorption spectrometry with a continuous spectrum source (ETAAS-CSS) to detect the presence of sodium in highly pure graphite powder. In order to plot the calibration dependence for sodium detection, a special technique based on argon dilution of the atomic vapor obtained by introducing the aqueous reference solution in the atomizer is applied. The conditions for thermal pretreatment of highly pure graphite powder and atomization of sodium are established, and the sodium detection threshold is evaluated via ETAAS-CSS (2.6 × 10{sup –4} ng) as well. The validity of the results is confirmed via the sample variation method.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Bayesian Abel Inversion in Quantitative X-Ray Radiography

A common image formation process in high-energy X-ray radiography is to have a pulsed power source that emits X-rays through a scene, a scintillator that absorbs X-rays and uoresces in the visible spectrum in response to the absorbed photons, and a CCD camera that images the visible light emitted from the scintillator. The intensity image is related to areal density, and, for an object that is radially symmetric about a central axis, the Abel transform then gives the object's volumetric density. Two of the primary drawbacks to classical variational methods for Abel inversion are their sensitivity to the type and scale of regularization chosen and the lack of natural methods for quantifying the uncertainties associated with the reconstructions. In this work we cast the Abel inversion problem within a statistical framework in order to compute volumetric object densities from X-ray radiographs and to quantify uncertainties in the reconstruction. A hierarchical Bayesian model is developed with a likelihood based on a Gaussian noise model and with priors placed on the unknown density pro le, the data precision matrix, and two scale parameters. This allows the data to drive the localization of features in the reconstruction and results in a joint posterior distribution for the unknown density pro le, the prior parameters, and the spatial structure of the precision matrix. Results of the density reconstructions and pointwise uncertainty estimates are presented for both synthetic signals and real data from a U.S. Department of Energy X-ray imaging facility.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2019

On stochastic effects and primordial black-hole formation

The effect of large quantum fluctuations on primordial black-hole formation for inflationary models with a quasi-inflection point is investigated. By using techniques of stochastic inflation in combination with replica field theory and the Feynman–Jensen variational method, it is non-perturbatively demonstrated that the abundance of primordial black holes is amplified by several orders of magnitude as compared to the classical computation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

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 ↗

DOE OSTI2024

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↗

DOE OSTI2018

3-D Semantic Information Inference from Airborne Video. Final Report

We developed a full 3D modeling pipeline focusing on an important application scenario: city-scale 3D reconstruction from aerial imagery. We propose an approach to solve camera pose estimation and dense reconstruction from Wide Area Aerial Surveillance (WAAS) videos captured by an airborne platform. Our approach solves them in an online fashion: it incrementally updates a sparse 3D map and estimates the camera pose as each new frame arrives; depth maps of selected key frames are computed using a variational method and integrated to produce a full 3D model via volumetric reconstruction. In practice, aerial imagery is usually captured using a multicamera system. We propose an approach for camera pose estimation of multi-camera aerial imagery which is parallelized on multiple GPUs for efficiency. The approach is also extended for progressive 3D model acquisition with a hand-held camera. We also developed an offline approach since online approach is not a necessity and accuracy has higher priority over efficiency in many scenarios. We presented MeshRecon, a mesh-based offline system composed of three modules: a dense point cloud is generated using multi-resolution plane sweep method; an initial mesh model is extracted from the point cloud via global optimization considering visibility information of all images; the mesh model is then iteratively refined to capture structural details by optimizing the photometric consistency and spatial regularization. The major processes are parallelized on GPU for efficiency. For the aerial imagery case, we evaluate our system on several real-world multicamera aerial imagery datasets, each covering an urban scenario of several square kilometers. Quantitative result shows that the reconstructed geometric 3D model is highly accurate with error smaller than 1 meter over the entire city. Besides aerial imagery, we also evaluate its performance on general geometric 3D model acquisition of real-world objects. Result shows that the system is robust and flexible for various types of objects at different scales in both indoor and outdoor environments. Based on city 3D models reconstructed at different times, we present a system for city-scale geometry change detection by performing comparisons at the 3D geometry level. Our system is able to detect geometry changes at different scales, ranging from a building cluster to small-scale vegetation changes, with high accuracy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Excited-state spectrum, and the low-energy degrees of freedom of QCD

A major challenge in the study of the structure of hadrons is eliminating the systematic uncertainty due to the presence of excited states whilst avoiding the exponential degradation of the signal-to-noise ratio that arises as the source and sink hadrons are placed at increasing temporal separations. In this talk, I describe how the use of ?distillation? combined with a basis of non-local operators and the variational method facilitates the construction of an ?optimal? interpolating operator for the ground state, and hence the hadronic matrix elements to be computed at shorter separations. I apply the method to the calculation of the moments of the quark distribution amplitude in the pion, using isotropic clover lattices.

Richards, David↗

DOE OSTI2017

Hadron charges and role of excited states

I describe the role of eliminating excited states in precision calculations of nucleon structure in lattice QCD through the use of the variational method. I then describe how lattice calculations may delineate the different contributions to the mass of excited states, and hence contribute to our understanding of the origin of mass.

Richards, David↗