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At least 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An introduction to financial option pricing on a qudit-based quantum computer

The financial sector is anticipated to be one of the first industries to benefit from the increased computational power of quantum computers, in areas such as portfolio optimisation and risk management to financial derivative pricing. Financial mathematics, and derivative pricing in particular, are not areas quantum physicists are traditionally trained in despite the fact that they often have the raw technical skills needed to understand such topics. On the other hand, most quantum algorithms have largely focused on qubits, which are comprised of two discrete states, as the information carriers. However, discrete higher-dimensional qudits, in addition to possibly possessing increased noise robustness and allowing for novel error correction protocols in certain hardware implementations, also have logarithmically greater information storage and processing capacity. In the current NISQ era of quantum computing, a wide array of hardware paradigms are still being studied and any potential advantage a platform offers is worth exploring. Here we introduce the basic concepts behind financial derivatives for the unfamiliar enthusiast as well as outline in great detail the quantum algorithm routines needed to price a European option, the simplest derivative. This is done within the context of a quantum computer comprised of qudits and employing the natural higher-dimensional analogue of a qubit-based pricing algorithm with its various subroutines. From these pieces, one should relatively easily be able to tailor the scheme to more complex, realistic financial derivatives. Finally, the entire stack is numerically simulated with the results demonstrating how the qudit-based scheme's payoff quickly approaches that of both a similarly-resourced classical computer as well as the true payoff, within error, for a modest increase in qudit dimension.

Bornman, Nicholas↗
DOE OSTI2020

Decomposition Algorithms for Solving NP-hard Problems on a Quantum Annealer

NP-hard problems such as the maximum clique or minimum vertex cover problems, two of Karp’s 21 NP-hard problems, have several applications in computational chemistry, biochemistry and computer network security. Adiabatic quantum annealers can search for the optimum value of such NP-hard optimization problems, given the problem can be embedded on their hardware. However, this is often not possible due to certain limitations of the hardware connectivity structure of the annealer. This paper studies a general framework for a decomposition algorithm for NP-hard graph problems aiming to identify an optimal set of vertices. Our generic algorithm allows us to recursively divide an instance until the generated subproblems can be embedded on the quantum annealer hardware and subsequently solved. Furthermore, the framework is applied to the maximum clique and minimum vertex cover problems, and we propose several pruning and reduction techniques to speed up the recursive decomposition. The performance of both algorithms is assessed in a detailed simulation study.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

High frequency impedance characteristics of a tunable microplasma device

Computational studies on high frequency impedance characteristics of a microplasma device are reported. While microplasma is ignited using a primary excitation signal, frequency response of plasma impedance is determined by a secondary high frequency probe signal with significantly lower voltage amplitude such that it does not influence the plasma parameters. Here, the computational model utilizing the drift–diffusion approximation is first validated by comparing with experimental data for microplasmas ignited at pressures ranging from 1 to 5 Torr. In spite of quantitative discrepancies, good overall agreement is obtained between the measured frequency response of impedance of the discharge. Comparisons are also presented for various plasma parameters including mean electron number density, sheath thickness, mean electron temperature, and collision frequency that were inferred from the impedance measurements. The computational model is then used to perform simulations of near-atmospheric pressure microplasmas with the probe signal frequency ranging from 3 to 20 GHz. The simulations demonstrate the presence of a resonance frequency at which the impedance vanishes. More importantly, it is shown that this resonant frequency can be tuned effectively by suitably modifying the operating parameters (gap size, pressure, and excitation voltage). The simulated impedance characteristics are used to determine the effective plasma inductance and capacitance using a non-linear fitting approach, thereby showing the dependence of these electrical parameters on the plasma operating conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Surface-Controlled TiO 2 Nanocrystals with Catalytically Active Single-Site Co Incorporation for the Oxygen Evolution Reaction

The design of advanced electrocatalysts is often hindered by uncertainties in identifying and controlling the active surfaces and catalytic centers within heterogeneous materials. Here we present the synthesis of single-site Co catalysts, substitutionally doped into surface-controlled TiO 2 anatase nanocrystals, aimed at enhancing the oxygen evolution reaction (OER). Grand canonical quantum mechanics calculations reveal that the kinetics of the OER, following an adsorbate evolution mechanism, is markedly influenced by the coordination environment of Co. The simulations suggest significantly higher turnover frequencies when Co is doped into the (001) surface of TiO 2 compared to the (101) surface. Consistent with the computational findings, experimental results show that Co-doped TiO 2 (Co-TiO 2 ) nanoplates with selectively exposed {001} surfaces exhibit enhanced current densities and turnover frequencies compared to Co-TiO 2 nanobipyramids with {101} surfaces. This study highlights the synergy between theoretical calculations and precision synthesis in the development of more effective catalysts.

25 ENERGY STORAGE↗
DOE OSTI2022

Teaching Quantum Computing to High School Students

Quantum computing is a growing field at the intersection of physics and computer science. The goal of this article is to highlight a successfully trialled quantum computing course for high school students between the ages of 15 and 18 years old. This course was designed to bridge the gap between popular science articles and advanced undergraduate textbooks. Conceptual ideas in the text are reinforced with active learning techniques, such as interactive problem sets and simulation-based labs at various levels. The course is freely available for use and download under the Creative Commons “Attribution-NonCommercial-ShareAlike 4.0 International” license.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The Quantum Alternating Operator Ansatz for Satisfiability Problems

Here, we comparatively study, through large-scale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial optimization problems. Our survey includes over 100 different mixing unitaries, and we combine each mixer with both the standard phase separator unitary representing the objective function and a thresholded version. Our numerical tests for randomly chosen instances of the unconstrained optimization problems Max 2-SAT and Max 3-SAT reveal that the traditional transverse-field mixer with the standard phase separator performs best for problem sizes of 8 through 14 variables, while the recently introduced Grover mixer with thresholding wins at problems of size 6. This result (i) corrects earlier work suggesting that the Grover mixer is a superior mixer based only on results from problems of size 6, thus illustrating the need to push numerical simulation to larger problem sizes to more accurately predict performance; and (ii) it suggests that more complicated mixers and phase separators may not improve QAOA performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Symmetry dilemmas in quantum computing for chemistry: A comprehensive analysis

Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically generate long and deep quantum circuits; gate-efficient universal operator pools generally break symmetries; and gate-efficient, fully symmetry-adapted operator pools may not be universal. In this work, we analyze such symmetry dilemmas both theoretically and numerically. On the theory side, we prove that the popular, gate-efficient operator pool consisting of singlet spin-adapted singles and perfect-pairing doubles is not universal when spatial symmetry is enforced. To demonstrate the strengths and weaknesses of the three types of pools, we perform numerical simulations using an adaptive algorithm paired with operator pools that are (i) fully symmetry-adapted and universal, (ii) fully symmetry-adapted and non-universal, and (iii) breaking a single symmetry and universal. Our numerical simulations encompass three physically relevant scenarios in which the target state is (i) the global ground state, (ii) the ground state crossed by a state differing in multiple symmetry properties, and (iii) the ground state crossed by a state differing in a single symmetry property. Our results show when symmetry-breaking but universal pools can be used safely, when enforcing at least one distinguishing symmetry suffices, and when a particular symmetry must be rigorously preserved to avoid variational collapse. Together, the formal and numerical analyses provide a practical guide for designing and benchmarking symmetry-adapted operator pools that balance universality, resource requirements, and robust state targeting in quantum simulations for chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Integrated Quantum-Classical Protocol for the Realistic Description of Solvated Multinuclear Mixed-Valence Transition-Metal Complexes and Their Solvatochromic Properties

Linear cyanide-bridged polymetallic complexes, which undergo photoinduced metal-to-metal charge transfer, represent prototypical systems for studying long-range electron-transfer reactions and understanding the role played by specific solute–solvent interactions in modulating the excited-state dynamics. Here, to tackle this problem, while achieving a statistically meaningful description of the solvent and of its relaxation, one needs a computational approach capable of handling large polynuclear transition-metal complexes, both in their ground and excited states, as well as the ability to follow their dynamics in several environments up to nanosecond time scales. Here, we present a mixed quantum classical approach, which combines large-scale molecular dynamics (MD) simulations based on an accurate quantum mechanically derived force field (QMD-FF) and self-consistent QMD polarized point charges, with IR and UV–vis spectral calculations to model the solvation dynamics and optical properties of a cyano-bridged trinuclear mixed-valence compound (trans-[(NC) 5 Fe III (μ-CN)Ru II (pyridine) 4 (μ-NC)Fe III (CN) 5 ] 4– ). We demonstrate the reliability of the QMD-FF/MD approach in sampling the solute conformational space and capturing the local solute–solvent interactions by comparing the results with higher-level quantum mechanics/molecular mechanics (QM/MM) MD reference data. The IR spectra calculated along the classical MD trajectories in different solvents correctly predict the red shift of the CN stretching band in the aprotic medium (acetonitrile) and the subtle differences measured in water and methanol, respectively. By explicitly including the solvent molecules around the cyanide ligands and calculating the thermal averaged absorption spectra using time-dependent density functional theory calculations within the Tamm–Dancoff approximation, the experimental solvatochromic shift is quantitatively reproduced going from water to methanol, while it is overestimated for acetonitrile. This discrepancy can likely be traced back to the lack of important dispersion interactions between the solvent cyano groups and the pyridine substituents in our micro solvation model. The proposed protocol is applied to the ground state in water, methanol, and acetonitrile and can be flexibly generalized to study excited-state nonequilibrium solvation dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Goorjian, Peter M.↗
NASA NTRS1994

Numerical Simulations of Light Bullets, Using the Full Vector, Time Dependent, Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Goorjian, Peter M.↗
NASA NTRS1995

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Goorjian, Peter M.↗
NASA NTRS1994

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Goorjian, Peter M.↗
NASA NTRS1999

Quantum Model of Emerging Grammars

A special class of quantum recurrent nets simulating Markov chains with absorbing states is introduced. The absorbing states are exploited for pattern recognition: each class of patterns, each combination of patterns acquires its own meaning.

Quantum computing Markov chains↗
DOE OSTI2024

A parametrically programmable delay line for microwave photons

Delay lines that store quantum information are crucial for advancing quantum repeaters and hardware efficient quantum computers. Traditionally, they are realized as extended systems that support wave propagation but provide limited control over the propagating fields. Here, we introduce a parametrically addressed delay line for microwave photons that provides a high level of control over the stored pulses. By parametrically driving a three-wave mixing circuit element that is weakly hybridized with an ensemble of resonators, we engineer a spectral response that simulates that of a physical delay line, while providing fast control over the delay line’s properties. We demonstrate this novel degree of control by choosing which photon echo to emit, translating pulses in time, and even swapping two pulses, all with pulse energies on the order of a single photon. We also measure the noise added from our parametric interactions and find it is much less than one photon.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

1 / ω electric-field noise in surface ion traps from correlated adsorbate dynamics

Ion traps are promising architectures for implementing quantum computers, but they suffer from excessive “anomalous” ion motional heating that limit their overall coherence and practicality for scalable quantum computing. The exact microscopic origins of anomalous heating remain an open question, but experiments point to adsorbates on trap electrodes as one likely source. Many different models of anomalous heating have been proposed, but these models have yet to pinpoint the atomistic origin of the experimentally observed 1/ω electric-field noise scaling seen in ion traps at frequencies between 0.1–10 MHz. In this work, we show that a model based on previously proposed surface-induced dipole fluctuations on adsorbates, but which also incorporates interparticle interaction dynamics through molecular dynamics simulations of up to multiple monolayers of adsorbates, gives rise to 1/ω frequency scaling at the MHz frequencies typically employed in ion traps. Overall, these results demonstrate that moderate-to-high densities of adsorbates can give rise to a set of activated motions that produce the 1/ω noise observed in ion traps and that collective adsorbate motions produce the observed noise spectra that a noninteracting model does not capture.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Decoherence in Molecular Electron Spin Qubits: Insights from Quantum Many-Body Simulations

Quantum states are described by wave functions whose phases cannot be directly measured, but which play a vital role in quantum effects such as interference and entanglement. The loss of the relative phase information, termed decoherence, arises from the interactions between a quantum system and its environment. Decoherence is perhaps the biggest obstacle on the path to reliable quantum computing. Here we show that decoherence occurs even in an isolated molecule although not all phase information is lost via a theoretical study of a central electron spin qubit interacting with nearby nuclear spins in prototypical magnetic molecules. The residual coherence, which is molecule-dependent, provides a microscopic rationalization for the nuclear spin diffusion barrier proposed to explain experiments. The contribution of nearby molecules to the decoherence has a non-trivial dependence on separation, peaking at intermediate distances. Molecules that are far away only affect the long-time behavior. Because the residual coherence is simple to calculate and correlates well with the coherence time, it can be used as a descriptor for coherence in magnetic molecules. This work will help establish design principles for enhancing coherence in molecular spin qubits and serve to motivate further theoretical work

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

SIERRA/Aero Theory Manual - Version 5.8

SIERRA/Aero is a compressible fluid dynamics program intended to solve a wide variety compressible fluid flows including transonic and hypersonic problems. This document describes the commands for assembling a fluid model for analysis with this module, henceforth referred to simply as Aero for brevity. Aero is an application developed using the SIERRA Toolkit (STK). The intent of STK is to provide a set of tools for handling common tasks that programmers encounter when developing a code for numerical simulation. For example, components of STK provide field allocation and management, and parallel input/output of field and mesh data. These services also allow the development of coupled mechanics analysis software for a massively parallel computing environment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗