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DOE OSTI2015

Robust Utility Maximization Under Convex Portfolio Constraints

We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption–investment strategy by studying the associated quadratic backward stochastic differential equation. We characterize the optimal control by using the duality method and deriving a dynamic maximum principle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements

Abstract Owing in large part to the advent of integrated biphoton frequency combs, recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si 3 N 4 microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Sample distribution in peak mode isotachophoresis

We present an analytical study of peak mode isotachophoresis (ITP), and provide closed form solutions for sample distribution and electric field, as well as for leading-, trailing-, and counter-ion concentration profiles. Importantly, the solution we present is valid not only for the case of fully ionized species, but also for systems of weak electrolytes which better represent real buffer systems and for multivalent analytes such as proteins and DNA. The model reveals two major scales which govern the electric field and buffer distributions, and an additional length scale governing analyte distribution. Using well-controlled experiments, and numerical simulations, we verify and validate the model and highlight its key merits as well as its limitations. We demonstrate the use of the model for determining the peak concentration of focused sample based on known buffer and analyte properties, and show it differs significantly from commonly used approximations based on the interface width alone. We further apply our model for studying reactions between multiple species having different effective mobilities yet co-focused at a single ITP interface. We find a closed form expression for an effective-on rate which depends on reactants distributions, and derive the conditions for optimizing such reactions. Interestingly, the model reveals that maximum reaction rate is not necessarily obtained when the concentration profiles of the reacting species perfectly overlap. In addition to the exact solutions, we derive throughout several closed form engineering approximations which are based on elementary functions and are simple to implement, yet maintain the interplay between the important scales. Both the exact and approximate solutions provide insight into sample focusing and can be used to design and optimize ITP-based assays.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

Two-dimensional inverse planning and delivery with a preclinical image guided microirradiator

Purpose: Recent advances in preclinical radiotherapy systems have provided the foundation for scaling many of the elements of clinical radiation therapy practice to the dimensions and energy demanded in small animal studies. Such systems support the technical capabilities to accurately deliver highly complex dose distributions, but methods to optimize and deliver such distributions remain in their infancy. This study developed an optimization method based on empirically measured two-dimensional dose kernel measurements to deliver arbitrary planar dose distributions on a recently developed small animal radiotherapy platform.Methods: A two-dimensional dose kernel was measured with repeated radiochromic film measurements for the circular 1 mm diameter fixed collimator of the small animal radiotherapy system at 1 cm depth in a solid water phantom. This kernel was utilized in a sequential quadratic programming optimization framework to determine optimal beam positions and weights to deliver an arbitrary desired dose distribution. The positions and weights were then translated to a set of stage motions to automatically deliver the optimized dose distribution. End-to-end efficacy of the framework was quantified through five repeated deliveries of two dosimetric challenges: (1) a 5 mm radius bullseye distribution, and (2) a “sock” distribution contained within a 9 × 13 mm bounding box incorporating rectangular, semicircular, and exponentially decaying geometric constructs and a rectangular linear dose gradient region. These two challenges were designed to gauge targeting, geometric, and dosimetric fidelity.Results: Optimization of the bullseye and sock distributions required 2.1 and 5.9 min and utilized 50 and 77 individual beams for delivery, respectively. Automated delivery of the resulting optimized distributions, validated using radiochromic film measurements, revealed an average targeting accuracy of 0.32 mm, and a dosimetric delivery error along four line profiles taken through the sock distribution of 3.9%. Mean absolute delivery error across the 0–1 Gy linear dose gradient over 7.5 mm was 0.01 Gy.Conclusions: The work presented here demonstrates the potential for complex dose distributions to be planned and automatically delivered with millimeter scale heterogeneity at submillimeter accuracy. This capability establishes the technical foundation for preclinical validation of biologically guided radiotherapy investigations and development of unique radiobiological experiments.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2026

Enhanced quantum efficiency from optical interference in alkali antimonide photocathodes: Modeling and experimental results

We present measurements of enhanced quantum efficiency (QE) in thin film alkali antimonide photocathodes from optical interference in the cathode-substrate multilayer. Modulations in the spectral response are observed over a range of visible wavelengths and are shown to increase the QE by more than a factor of two at specific wavelengths. We present a model describing the QE modulations based on the three step photoemission process incorporating cases of both constant density of states and density functional theory-derived density of states and show that the calculated results are in good agreement with the measurements. Model predictions demonstrate that QE can be enhanced by more than a factor of 5 by optimization of cathode and substrate layer thicknesses. Additionally, these calculations reveal that optical interference can yield higher quantum efficiencies in thin films compared to thick, optically dense films. We model the QE vs excitation wavelength of multiple alkali antimonide compounds at different thicknesses. We then discuss the advantages of this interference effect for electron accelerators.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Simulating non-native cubic interactions on noisy quantum machines

As a milestone for general-purpose computing machines, we demonstrate that quantum processors can be programed to efficiently simulate dynamics that are not native to the hardware. Moreover, on noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates instead of a restricted set of standard gates. We demonstrate the general methodology by solving a cubic interaction problem, which appears in nonlinear optics, gauge theories, as well as plasma and fluid dynamics. To encode the non-native Hamiltonian evolution, we decompose the Hilbert space into a direct sum of invariant subspaces in which the nonlinear problem is mapped to a finite-dimensional Hamiltonian simulation problem. Furthermore, in a three-states example, the resultant unitary evolution is realized by a product of approximately 20 standard gates, using which approximately ten simulation steps can be carried out on state-of-the-art quantum hardware before results are corrupted by decoherence. In comparison, the simulation depth is improved by more than an order of magnitude when the unitary evolution is realized as a single cubic gate, which is compiled directly using optimal control. Alternatively, parametric gates may also be compiled by interpolating control pulses. Modular gates thus obtained provide high-fidelity building blocks for quantum Hamiltonian simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Bootstrap performance profiles in stochastic algorithms assessment

Optimization with stochastic algorithms has become a relevant research field. Due to its stochastic nature, its assessment is not straightforward and involves integrating accuracy and precision. Performance profiles for the mean do not show the trade-off between accuracy and precision, and parametric stochastic profiles require strong distributional assumptions and are limited to the mean performance for a large number of runs. In this work, bootstrap performance profiles are used to compare stochastic algorithms for different statistics. This technique allows the estimation of the sampling distribution of almost any statistic even with small samples. Multiple comparison profiles are presented for more than two algorithms. The advantages and drawbacks of each assessment methodology are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Classical versus quantum models in machine learning: insights from a finance application

Although several models have been proposed towards assisting machine learning (ML) tasks with quantum computers, a direct comparison of the expressive power and efficiency of classical versus quantum models for datasets originating from real-world applications is one of the key milestones towards a quantum ready era. Here, we take a first step towards addressing this challenge by performing a comparison of the widely used classical ML models known as restricted Boltzmann machines (RBMs), against a recently proposed quantum model, now known as quantum circuit Born machines (QCBMs). Both models address the same hard tasks in unsupervised generative modeling, with QCBMs exploiting the probabilistic nature of quantum mechanics and a candidate for near-term quantum computers, as experimentally demonstrated in three different quantum hardware architectures to date. To address the question of the performance of the quantum model on real-world classical data sets, we construct scenarios from a probabilistic version out of the well-known portfolio optimization problem in finance, by using time-series pricing data from asset subsets of the S&P500 stock market index. It is remarkable to find that, under the same number of resources in terms of parameters for both classical and quantum models, the quantum models seem to have superior performance on typical instances when compared with the canonical training of the RBMs. Our simulations are grounded on a hardware efficient realization of the QCBMs on ion-trap quantum computers, by using their native gate sets, and therefore readily implementable in near-term quantum devices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Improved lifetime of a high spin polarization superlattice photocathode

Negative Electron Affinity (NEA) activated surfaces are required to extract highly spin-polarized electron beams from GaAs-based photocathodes, but they suffer extreme sensitivity to poor vacuum conditions that results in rapid degradation of quantum efficiency. We report on a series of unconventional NEA activations on surfaces of bulk GaAs with Cs, Sb, and O 2 using different methods of oxygen exposure for optimizing photocathode performance. Additionally, one order of magnitude improvement in lifetime with respect to the standard Cs–O 2 activation is achieved without significant loss of electron spin polarization and quantum efficiency by codepositing Cs, Sb, and O 2 . A strained GaAs/GaAsP superlattice sample activated with the codeposition method demonstrated similar enhancement in lifetime near the photoemission threshold while maintaining 90% spin polarization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need to develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Quantum field as a quantum cellular automaton: The Dirac free evolution in one dimension

We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of homogeneity, parity and time-reversal invariance. The comparison between the automaton and the Dirac evolutions is rigorously set as a discrimination problem between unitary channels. We derive an exact lower bound for the probability of error in the discrimination as an explicit function of the mass, the number and the momentum of the particles, and the duration of the evolution. Computing this bound with experimentally achievable values, we see that in that regime the QCA model cannot be discriminated from the usual Dirac evolution. Finally, we show that the evolution of one-particle states with narrow-band in momentum can be efficiently simulated by a dispersive differential equation for any regime. This analysis allows for a comparison with the dynamics of wave-packets as it is described by the usual Dirac equation. This paper is a first step in exploring the idea that quantum field theory could be grounded on a more fundamental quantum cellular automaton model and that physical dynamics could emerge from quantum information processing. In this framework, the discretization is a central ingredient and not only a tool for performing non-perturbative calculation as in lattice gauge theory. The automaton model, endowed with a precise notion of local observables and a full probabilistic interpretation, could lead to a coherent unification of a hypothetical discrete Planck scale with the usual Fermi scale of high-energy physics. - Highlights: • The free Dirac field in one space dimension as a quantum cellular automaton. • Large scale limit of the automaton and the emergence of the Dirac equation. • Dispersive differential equation for the evolution of smooth states on the automaton. • Optimal discrimination between the automaton evolution and the Dirac equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Influence of single particle orbital sets and configuration selection on multideterminant wavefunctions in quantum Monte Carlo

Multideterminant wavefunctions, while having a long history in quantum chemistry, are increasingly being used in highly accurate quantum Monte Carlo calculations. Since the accuracy of QMC is ultimately limited by the quality of the trial wavefunction, multi-Slater determinants wavefunctions offer an attractive alternative to Slater-Jastrow and more sophisticated wavefunction ansatz for several reasons. They can be efficiently calculated, straightforwardly optimized, and systematically improved by increasing the number of included determinants. In spite of their potential, however, the convergence properties of multi-Slater determinant wavefunctions with respect to orbital set choice and excited determinant selection are poorly understood, which hinders the application of these wavefunctions to large systems and solids. In this paper, by performing QMC calculations on the equilibrium and stretched carbon dimer, we find that convergence of the recovered correlation energy with respect to number of determinants can depend quite strongly on basis set and determinant selection methods, especially where there is strong correlation. We demonstrate that properly chosen orbital sets and determinant selection techniques from quantum chemistry methods can dramatically reduce the required number of determinants (and thus the computational cost) to reach a given accuracy, which we argue shows clear need for an automatic QMC-only method for selecting determinants and generating optimal orbital sets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

The fundamental downscaling limit of field effect transistors

We predict that within next 15 years a fundamental down-scaling limit for CMOS technology and other Field-Effect Transistors (FETs) will be reached. Specifically, we show that at room temperatures all FETs, irrespective of their channel material, will start experiencing unacceptable level of thermally induced errors around 5-nm gate lengths. These findings were confirmed by performing quantum mechanical transport simulations for a variety of 6-, 5-, and 4-nm gate length Si devices, optimized to satisfy high-performance logic specifications by ITRS. Different channel materials and wafer/channel orientations have also been studied; it is found that altering channel-source-drain materials achieves only insignificant increase in switching energy, which overall cannot sufficiently delay the approaching downscaling limit. Alternative possibilities are discussed to continue the increase of logic element densities for room temperature operation below the said limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Study of self-compliance behaviors and internal filament characteristics in intrinsic SiO{sub x}-based resistive switching memory

Self-compliance characteristics and reliability optimization are investigated in intrinsic unipolar silicon oxide (SiO{sub x})-based resistive switching (RS) memory using TiW/SiO{sub x}/TiW device structures. The program window (difference between SET voltage and RESET voltage) is dependent on external series resistance, demonstrating that the SET process is due to a voltage-triggered mechanism. The program window has been optimized for program/erase disturbance immunity and reliability for circuit-level applications. The SET and RESET transitions have also been characterized using a dynamic conductivity method, which distinguishes the self-compliance behavior due to an internal series resistance effect (filament) in SiO{sub x}-based RS memory. By using a conceptual “filament/resistive gap (GAP)” model of the conductive filament and a proton exchange model with appropriate assumptions, the internal filament resistance and GAP resistance can be estimated for high- and low-resistance states (HRS and LRS), and are found to be independent of external series resistance. Our experimental results not only provide insights into potential reliability issues but also help to clarify the switching mechanisms and device operating characteristics of SiO{sub x}-based RS memory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

TU-F-18C-02: Increasing Amorphous Selenium Thickness in Direct Conversion Flat-Panel Imagers for Contrast-Enhanced Dual-Energy Breast Imaging

Purpose: Contrast-enhanced (CE) breast imaging using iodinated contrast agents requires imaging with x-ray spectra at energies greater than those used in mammography. Optimizing amorphous selenium (a-Se) flat panel imagers (FPI) for this higher energy range may increase lesion conspicuity. Methods: We compare imaging performance of a conventional FPI with 200 μm a-Se conversion layer to a prototype FPI with 300 μm a-Se layer. Both detectors are evaluated in a Siemens MAMMOMAT Inspiration prototype digital breast tomosynthesis (DBT) system using low-energy (W/Rh 28 kVp) and high-energy (W/Cu 49 kVp) x-ray spectra. Detectability of iodinated lesions in dual-energy images is evaluated using an iodine contrast phantom. Effects of beam obliquity are investigated in projection and reconstructed images using different reconstruction methods. The ideal observer signal-to-noise ratio is used as a figure-of-merit to predict the optimal a-Se thickness for CE lesion detectability without compromising conventional full-field digital mammography (FFDM) and DBT performance. Results: Increasing a-Se thickness from 200 μm to 300 μm preserves imaging performance at typical mammographic energies (e.g. W/Rh 28 kVp), and improves the detective quantum efficiency (DQE) for high energy (W/Cu 49 kVp) by 30%. While the more penetrating high-energy x-ray photons increase geometric blur due to beam obliquity in the FPI with thicker a-Se layer, the effect on lesion detectability in FBP reconstructions is negligible due to the reconstruction filters employed. Ideal observer SNR for CE objects shows improvements in in-plane detectability with increasing a-Se thicknesses, though small lesion detectability begins to degrade in oblique projections for a-Se thickness above 500 μm. Conclusion: Increasing a-Se thickness in direct conversion FPI from 200 μm to 300 μm improves lesion detectability in CE breast imaging with virtually no cost to conventional FFDM and DBT. This work was partially supported by a research grant from Siemens Healthcare.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

The FMO-DFTB Method

Although the fragment molecular orbital (FMO) method enables electronic structure calculations with near-linear scaling behavior with respect to system size, the computational cost of ab initio methods typically employed in conjunction with FMO is still prohibitive for routine calculations of very large systems or long timescale molecular dynamics simulations. We, therefore, combined the FMO and density-functional tight-binding (DFTB) method, which is one of the emerging semi-empirical quantum chemical methods, and have demonstrated that FMO-DFTB is capable of performing geometry optimizations for systems containing up to one million atoms using limited computational resources. In this chapter, we will review the basics of the DFTB method first before introducing FMO-DFTB, focusing on the relationship with density functional theory and other FMO methodologies. We also demonstrate the latest scalings of FMO-DFTB2 and DFTB3 using three-dimensional water clusters, showing that the most favorable scaling is O(N1.16). Applications of FMO-DFTB to various systems are briefly summarized, and an outlook to future applications is provided.

Nishimoto, Yoshio↗
DOE OSTI2015

Inconsistent Investment and Consumption Problems

In a traditional Black–Scholes market we develop a verification theorem for a general class of investment and consumption problems where the standard dynamic programming principle does not hold. The theorem is an extension of the standard Hamilton–Jacobi–Bellman equation in the form of a system of non-linear differential equations. We derive the optimal investment and consumption strategy for a mean-variance investor without pre-commitment endowed with labor income. In the case of constant risk aversion it turns out that the optimal amount of money to invest in stocks is independent of wealth. The optimal consumption strategy is given as a deterministic bang-bang strategy. In order to have a more realistic model we allow the risk aversion to be time and state dependent. Of special interest is the case were the risk aversion is inversely proportional to present wealth plus the financial value of future labor income net of consumption. Using the verification theorem we give a detailed analysis of this problem. It turns out that the optimal amount of money to invest in stocks is given by a linear function of wealth plus the financial value of future labor income net of consumption. The optimal consumption strategy is again given as a deterministic bang-bang strategy. We also calculate, for a general time and state dependent risk aversion function, the optimal investment and consumption strategy for a mean-standard deviation investor without pre-commitment. In that case, it turns out that it is optimal to take no risk at all.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗