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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas

Herein we formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for a broad class of non-ideal pressure-density relations that satisfy a monotonicity property. Further, we develop a Newton-Raphson algorithm for numerical solution of the steady-state problem, which is made possible by a systematic non-dimensionalization of the equations. The developed algorithm has been extensively tested on benchmark instances and shown to converge robustly to a generalized solution. Previous results [1]-[4], indicate that the steady-state network flow equations for an ideal gas are difficult to solve by the Newton-Raphson method because of its extreme sensitivity to the initial guess. In contrast, we find that non-dimensionalization of the steady-state problem is key to robust convergence of the Newton-Raphson method. We identify criteria based on the uniqueness of solutions under which the existence of a non-physical generalized solution found by a non-linear solver implies non-existence of a physical solution, i.e., infeasibility of the problem. Finally, we compare pressure and flow solutions based on ideal and non-ideal equations of state to demonstrate the need to apply the latter in practice. The solver developed in this article is open-source and is made available for both the academic and research communities as well as the industry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A practical approach to determine minimal quantum gate durations using amplitude-bounded quantum controls

Here, we present an iterative scheme to estimate the minimal duration in which a quantum gate can be realized while satisfying hardware constraints on the control pulse amplitudes. The scheme performs a sequence of unconstrained numerical optimal control cycles that each minimize the gate fidelity for a given gate duration alongside an additional penalty term for the control pulse amplitudes. After each cycle, the gate duration is adjusted based on the inverse of the resulting maximum control pulse amplitudes by re-scaling the dynamics to a new duration where control pulses satisfy the amplitude constraints. Those scaled controls then serve as an initial guess for the next unconstrained optimal control cycle, using the adjusted gate duration. We provide multiple numerical examples that each demonstrate fast convergence of the scheme toward a gate duration that is close to the quantum speed limit, given the control pulse amplitude bound. The proposed technique is agnostic to the underlying system and control Hamiltonian models, as well as the target unitary gate operation, making the time-scaling iteration an easy to implement and practically useful scheme for reducing the durations of quantum gate operations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

TH-A-9A-02: BEST IN PHYSICS (THERAPY) - 4D IMRT Planning Using Highly- Parallelizable Particle Swarm Optimization

Purpose: We present a particle swarm optimization (PSO)-based 4D IMRT planning technique designed for dynamic MLC tracking delivery to lung tumors. The key idea is to utilize the temporal dimension as an additional degree of freedom rather than a constraint in order to achieve improved sparing of organs at risk (OARs). Methods: The target and normal structures were manually contoured on each of the ten phases of a 4DCT scan acquired from a lung SBRT patient who exhibited 1.5cm tumor motion despite the use of abdominal compression. Corresponding ten IMRT plans were generated using the Eclipse treatment planning system. These plans served as initial guess solutions for the PSO algorithm. Fluence weights were optimized over the entire solution space i.e., 10 phases × 12 beams × 166 control points. The size of the solution space motivated our choice of PSO, which is a highly parallelizable stochastic global optimization technique that is well-suited for such large problems. A summed fluence map was created using an in-house B-spline deformable image registration. Each plan was compared with a corresponding, internal target volume (ITV)-based IMRT plan. Results: The PSO 4D IMRT plan yielded comparable PTV coverage and significantly higher dose—sparing for parallel and serial OARs compared to the ITV-based plan. The dose-sparing achieved via PSO-4DIMRT was: lung Dmean = 28%; lung V20 = 90%; spinal cord Dmax = 23%; esophagus Dmax = 31%; heart Dmax = 51%; heart Dmean = 64%. Conclusion: Truly 4D IMRT that uses the temporal dimension as an additional degree of freedom can achieve significant dose sparing of serial and parallel OARs. Given the large solution space, PSO represents an attractive, parallelizable tool to achieve globally optimal solutions for such problems. This work was supported through funding from the National Institutes of Health and Varian Medical Systems. Amit Sawant has research funding from Varian Medical Systems, VisionRT Ltd. and Elekta.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Multigrid Reduction in Time for Nonlinear Parabolic Problems: A Case Study

The need for parallelism in the time dimension is being driven by changes in computer architectures, where performance increases are now provided through greater concurrency, not faster clock speeds. This creates a bottleneck for sequential time marching schemes because they lack parallelism in the time dimension. Multigrid reduction in time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficiency is defined as achieving similar performance when compared to an equivalent linear problem. The benchmark nonlinear problem is the p-Laplacian, where p=4 corresponds to a well-known nonlinear diffusion equation and p=2 corresponds to the standard linear diffusion operator, our benchmark linear problem. The key difficulty encountered is that the nonlinear time-step solver becomes progressively more expensive on coarser time levels as the time-step size increases. To overcome such difficulties, multigrid research has historically targeted an accumulated body of experience regarding how to choose an appropriate solver for a specific problem type. To that end, this paper develops a library of MGRIT optimizations and modifications, most important an alternate initial guess for the nonlinear time-step solver and delayed spatial coarsening, that will allow many nonlinear parabolic problems to be solved with parallel scaling behavior comparable to the corresponding linear problem.

parareal↗
DOE OSTI2018

A Nonlinear Algebraic Multigrid Framework for the Power Flow Equations

Multigrid is a highly scalable class of methods most often used for solving large linear systems. In this paper we develop a nonlinear algebraic multigrid framework for the power flow equations, a complex quadratic system of the form ${diag}({v})\overline{Y{v}}={s}$, where $Y$ is approximately a complex scalar rotation of a real graph Laplacian. This is a standard problem that needs to be solved repeatedly during power grid simulations. A key difference between our multigrid framework and typical multigrid approaches is the use of a novel multiplicative coarse-grid correction to enable a dynamic multigrid hierarchy. We also develop a new type of smoother that allows one to coarsen together the different types of nodes that appear in power grid simulations. In developing a specific multigrid method, one must make a number of choices that can significantly affect the method's performance, such as how to construct the restriction and interpolation operators, what smoother to use, and how aggressively to coarsen. In this paper, we make simple but reasonable choices that result in a scalable and robust power flow solver. Experiments demonstrate this scalability and show that it is significantly more robust to poor initial guesses than current state-of-the-art solvers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Iterated Gauss-Seidel GMRES

The GMRES algorithm of Saad and Schultz [SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869] is an iterative method for approximately solving linear systems Ax = b, with initial guess x0 and residual r0 = b Ax0. The algorithm employs the Arnoldi process to generate the Krylov basis vectors (the columns of Vk ). It is well known that this process can be viewed as a QR factorization of the matrix Bk = [r0, AVk] at each iteration. Despite an O (..epsilon..)..kappa.. (Bk ) loss of orthogonality, for unit roundoff ..epsilon..and condition number ..kappa.. , the modified Gram-Schmidt formulation was shown to be backward stable in the seminal paper by Paige et al. [SIAM J. Matrix Anal.Appl., 28 (2006), pp. 264-284]. We present an iterated Gauss-Seidel formulation of the GMRES algorithm (IGS-GMRES) based on the ideas of Ruhe [Linear Algebra Appl., 52 (1983), pp. 591-601] and Swirydowicz et al. [Numer. Linear Algebra Appl., 28 (2020), pp. 1-20]. IGS-GMRES maintains orthogonality to the level O (..epsilon..)..kappa.. (Bk ) or O (..epsilon..), depending on the choice of one or two iterations; for two Gauss-Seidel iterations, the computed Krylov basis vectors remain orthogonal to working accuracy and the smallest singular value of Vk remains close to one. The resulting GMRES method is thus backward stable. We show that IGS-GMRES can be implemented with only a single synchronization point per iteration, making it relevant to large-scale parallel computing environments. We also demonstrate that, unlike MGS-GMRES, in IGS-GMRES the relative Arnoldi residual corresponding to the computed approximate solution no longer stagnates above machine precision even for highly nonnormal systems.

Arnoldi-QR↗
DOE OSTI2022

Accelerated coupled Monte Carlo-Thermal hydraulic calculations using a hybrid GTF-diffusion-based prediction block: first results

Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections' variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint Eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Manufacturability-based optical design optimization for advanced Kirkpatrick–Baez X-ray focusing mirrors

The advanced Kirkpatrick–Baez (AKB) mirror setup is an effective and compelling solution to provide stable X-ray nano-focusing for synchrotron radiation or free-electron laser beamlines. We propose an AKB mirror design optimization approach to mitigate the difficulties associated with mirror fabrication by minimizing the total slope ranges of the four curved mirrors while achieving the expected focusing performance. In the optimization, we have considered geometry constraints to ensure the beam acceptance with the required clear aperture, the diffraction-limited focal size with the adequate numerical aperture, and the desired mirror gaps for adjustment and the necessary working distance for the sample stage. Additionally, practical constraints linked to mirror metrology and fabrication, such as mirror length limits and curvature uncertainty in measurement, are taken into account. Furthermore, progressive objective optimization eliminates the need for any initial guess, fully automating the AKB optimization process. This approach facilitates the development of an elegant Wolter-I or Wolter-III type AKB design solution that satisfies these multiple constraints. In cases where constraints cannot be simultaneously satisfied, the optimization results provide valuable insights into areas where trade-offs need to be considered. Simulations with ray tracing and wavefront propagation validate the optimized AKB design showing high tolerance to the beam incident angle.

36 MATERIALS SCIENCE↗
DOE OSTI2012

Automated exploration of the mechanism of elementary reactions

Optimization of new transportation fuels and engine technologies requires the characterization of the combustion chemistry of a wide range of fuel classes. Theoretical studies of elementary reactions — the building blocks of complex reaction mechanisms — are essential to accurately predict important combustion processes such as autoignition of biofuels. The current bottleneck for these calculations is a user-intensive exploration of the underlying potential energy surface (PES), which relies on the “chemical intuition” of the scientist to propose initial guesses for the relevant chemical configurations. For newly emerging fuels, this approach cripples the rate of progress because of the system size and complexity. The KinBot program package aims to accelerate the detailed chemical kinetic description of combustion, and enables large-scale systematic studies on the sub-mechanism level.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The cause of outliers in electromagnetic pulse (EMP) locations

We present methods to calculate the location of EMP pulses when observed by 5 or more satellites. Simulations show that, even with a good initial guess and fitting a location to all of the data, there are sometime outlier results whose locations are much worse than most cases. By comparing simulations using different ionospheric transfer functions (ITFs), it appears that the outliers are caused by not including the additional path length due to refraction rather than being caused by not including higher order terms in the Appleton-Hartree equation. We suggest ways that the outliers can be corrected. These correction methods require one to use an electron density profile along the line of sight from the event to the satellite rather than using the total electron content (TEC) to characterize the ionosphere.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2016

Multigrid Reduction in Time for Nonlinear Parabolic Problems

The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Assessment of Model-Based Schemes for Accelerating Optimization by RAVEN

Nuclear-Renewable Hybrid Energy Systems (N-R HES) combine different energy technologies in a synergistic way with the objective of achieving a more economical energy production. In this report the particular hybrid system dealt with includes a PWR nuclear reactor, the associated Rankine-based energy conversion cycle (Balance of Plant, BOP), an Industrial Process (IP) for hydrogen production, a gas turbine (Second Energy Source, SES), and a battery (Energy Storage, ES). The RAVEN-based HYBRID framework is used to find the optimal installed capacity and the optimal economical dispatch of each component of the N-R HES. HYBRID solves the coupled capacity planning-economic and dispatch optimization problem with the objective of minimizing the Levelized Cost of Electricity (LCOE). In the optimization of the power dispatch strategy, the HYBRID framework takes into account the time-dependent dynamics of each subsystem by including a Dymola object-oriented model of the process dynamics. To ease the computational burden of the optimization process, an initial guess for the dispatch optimization problem is provided by a preconditioner. The solution guess is calculated by means of a least-marginal cost approach which applies the same criterion behind the screening curve method. Though this algorithm allows evaluating an economically adapted generation mix for a target load duration curve within a few seconds, it neglects the constraints due to the single component dynamics, and it is not able to adequately represent the ES. An improved treatment of the pre-conditioner problem was addressed by introducing a Monte Carlo based optimization algorithm. The new approach takes into account limits on power rates for the system subcomponents, which was not previously done. Additionally, this new Monte-Carlo based preconditioner addresses the problem with the ES component through improved modeling of that component. The new algorithm has been implemented in the HYBRID framework and tested to assess its performance. The results obtained with the new Monte Carlobased preconditioner were benchmarked against those obtained through the reference deterministic approach. The comparison shows that the Monte-Carlo based approach provides improved solution accuracy to the power dispatch optimization problem. Also in this report, the treatment of the penalty function on LCOE is discussed, and an improved penalty function for missed demand is suggested and tested.

Maronati, Giovanni↗
DOE OSTI2021

Non-Diffusive Volume Advection with A High Order Interface Reconstruction Method

We show that non-diffusive volume advection in two-dimensions is achieved with several benchmark problems using a newly developed high-order volume of fluids (VOF) interface reconstruction method. (1) A new VOF interface reconstruction method using circular/corner facets (linear facets are a degenerate case of arcs). We create a circular interface facet in each mixed zone by matching neighbor volume with a hybrid Newton’s-bisection method and the local solution is final. In the general case, the new VOF interface reconstruction has 3rd order accuracy and can be easily made seamless. The new method addresses intrinsic issues with Young’s method such as gaps between interface facets in the case of a curved interface, and inability to define curvature nor identify corners. (2) A non-diffusive volume advection scheme. In an ALE advection step, a well-defined interface can be carried over through a Lagrange step and used to compute volume distribution into a relaxed mesh. Then, an interface reconstruction step is performed to redefine the interface in the relaxed mesh. We must point out that the interface carried over is also a solution of interface reconstruction because all the volume fractions in the relaxed mesh are naturally matched. We provide an interface tracking method compatible with our reconstruction scheme, where it is granted to use the prior info as an initial guess to capture sub-mesh resolution features. As a result, we are able to treat multiple facets inside a single mixed cell and obtain highly accurate, non-diffusive solution for advection problems with rather coarse meshes. We show our solutions for two-dimensional incompressible flows with two materials with a) the X + O diagonal translation; b) the Zalesak rotational test; and c) the single vortex spiral test.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Terrain-Influenced Winds and Fire-Fire Interactions in Wildland Fire Simulations [Dissertation]

Ensemble-based approaches to prescribed fire planning cannot be supported by computational fluid dynamics based models like FIRETEC and the Wildland-Urban Interface Fire Dynamics Simulator (WFDS) because they are too computationally expensive and cannot leverage large eddy simulation approaches like CAWFE and WRF-SFIRE because they have too coarse of resolution. QUIC-Fire was developed to fill this gap but it cannot currently address complex terrain, that is typical for instance in the Western United States. This dissertation describes a variety of improvements made to QUIC-Fire and its various incorporated algorithms in an effort to make it a viable tool in simulating wildland and prescribed fires on terrain. The modifications made to QUIC-Fire are described in three chapters. The first chapter describes the extension of the diagnostic wind model QUIC-URB, the wind engine of QUIC-Fire, to a terrain-following coordinate system. The terraininfluenced winds it generates are analyzed and compared. In particular, this chapter presents the mathematical derivation of the wind solver leading to a linear system of equations that are solved through the successive over-relaxation method. The model is validated against a standard test used in previous works (the Askervein Hill) and against a new dataset from measurements in the Socorro Mountains, New Mexico. The terrain-following implementation captures the correct phenomenology for the isolated Askervein Hill, with a wind speed up at the top of the hill. The model agrees well with measurements on the upwind side of the peak, but overestimates speed-up on the downwind side of the hill. This is due to the inability of the model to generate flow separation and wake-eddy dynamics. On a common laptop, the divergence-free wind field is obtained in 6 s, making the solver appealing for coupled fire-atmosphere simulations. The Socorro Mountain is highly complex, with many cliff faces, peaks, and valleys. Although the model captures the magnitude and direction of inlet and outlet areas of the domain, it performs rather poorly in the valley region and in the regions near the steep cliffs. Hence, the model shows good agreement with data in areas of open sloped terrain but lacks in areas where flow separation and thermally driven effects may be present (neither effect is addressed in this work). In the second chapter the implementation of the terrain-following version of QUIC-URB into QUIC-Fire, and the necessary changes needed to include terrain are described. No changes to the underlying fire spread algorithm are made other than what is required to correctly account for the inclusion of terrain. Previously published FIRETEC results that use five different topographies that share the same centerline profile are compared to simulation results from the modified QUIC-Fire that use the same topographies and fuels. QUIC-Fire results show overall similar behaviors in terms of how the topographies affect fire shapes and trends in spread rates. Due to the terrain-following version of QUIC-URB being unable to generate flow separations at the crest of hills, fire spread rates in these regions across all topographies are over-predicted when compared to FIRETEC. Lateral fire growth shows similar trends with FIRETEC between topographies but does not capture the increase in spread due to a diagonal interface between grassland and forested fuel region of the domain. These results suggest that there are three algorithms within QUIC-Fire that could use improvement: how flame tilt angle is accounted for, the incorporation of non-local drag effects, and the inclusion of the wake-eddy parameterizations that are used in QUIC-URB. Lastly, the third chapter describes a modification to the initial guess used for the calculation of the QUIC-URB mass-conserved wind solution during fire simulations. The modification is aimed at improving fire-fire interactions in QUIC-Fire simulations. The modification consists of using the solution from the previous timestep as the starting point for the calculation of the solution for the next timestep. Fire-fire interactions is greatly improved by the change but a new source of error is introduced. Due to how plumes are modelled in QUIC-Fire the new solution contains errors where gaps in the plume structure are present. However, these errors are mostly limited to the upper atmosphere, where they do not affect fire behavior at the surface, and their magnitude isn’t significant enough to discount the amount of new fire phenomenology now captured in QUIC-Fire with the change.

58 GEOSCIENCES↗
DOE OSTI2024

Continued performance improvement and integration of MOOSE's thermal-hydraulics capabilities (M3 Milestone Report)

This work introduces performance, robustness and workflow improvements to Multiphysics Object-Oriented Simulation Environment (MOOSE)-based thermal-hydraulics solvers. It presents work related to the acceleration of segregated fluid dynamics algorithms, which show approximately a factor of 10 speedup compared to the preceding implementation. Additionally, we discuss approaches to use advanced, Schurr complement-based, field split preconditioners for monolithic solution algorithms relying on the finite volume method. The presence of the Rhie-Chow interpolation makes the utilization of this preconditioner challenging, but the results indicate that for a moderately large problem a factor of 3.4 speedup can be achieved in conjunction with a factor of 3.5 reduction in memory usage. Furthermore, we introduce several pseudo-time stepping approaches to MOOSE for the robust convergence to steady-state solutions when steady-state solves don't converge due to the initial guesses being too far from the solution in Newton's method. Every MOOSE-based application has access this algorithm and can benefit from its use. Moreover, several new avenues have been presented for importing meshes from commercial software which make meshing easier. Lastly, the Component system within the Thermal-Hydraulics Module (THM) of MOOSE is abstracted by separating geometry- and physics-related properties.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Spectrum Unfolding with the MC-15

The Multiplicity Counter 15 tube detector or MC-15 is an optimized detector designed for use in the field. It is composed of 15 3 He tubes embedded in high density polyethylene (HDPE). Recent work has explored expanding the use of the MC-15 beyond multiplicity counting to neutron dosimetry applications. Knowledge of the neutron energy spectrum information is required to use a detector as a neutron dosimeter. The MC-15 tube layout is shown in Figure 1. The unique layout makes it possible to use the detector for neutron spectroscopy via spectrum unfolding. Spectrum unfolding requires (1) energy dependence of the detector response, (2) a detector response matrix that precisely quantifies the response to mono-energetic neutrons, (3) an initial guess spectrum, (4) an unfolding algorithm, and (5) measured data (counts in the case of the MC-15). An energy dependent detector response matrix (DRM) can be constructed by considering either each of the three rows of 3 He tubes as a distinct detector or each individual tube as a distinct detector. The HDPE separating the 3 He in the MC-15 provides the distinct energy dependent response for the rows and individual tubes. In this report we detail the development of detector response matrices for the MC-15 and the application of the Los Alamos Unfolding Code (LUC) to both simulated and measured data. Three MC-15 orientations were studied: (1) standard orientation with the MC-15 front facing the source, (2) standard orientation with Cd sheet, (3) 90° orientation with the side of the MC-15 facing the source.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Simulating Effective QED on Quantum Computers

In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated in polynomial time under reasonable assumptions while properly treating all four components of the wavefunction of the fermionic field. In particular, we provide a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. We find that the number of T -gates needed to perform such simulations on a 3 D lattice of n s sites scales at worst as O ( n s 3 / ϵ ) 1 + o ( 1 ) in the thermodynamic limit for position basis simulations and O ( n s 4 + 2 / 3 / ϵ ) 1 + o ( 1 ) in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of O ~ ( n s 2 + 2 / 3 / ϵ ) for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of O ~ ( n s 5 + 2 / 3 / ϵ ) . We further provide concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than 10 13 non-Clifford operations and also provide a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED which can provide a reasonable initial guess for the ground state. Finally, we estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

On the energy landscape of symmetric quantum signal processing

Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given polynomial f , the parameters (called phase factors) can be obtained by solving an optimization problem. However, the cost function is non-convex, and has a very complex energy landscape with numerous global and local minima. It is therefore surprising that the solution can be robustly obtained in practice, starting from a fixed initial guess Φ 0 that contains no information of the input polynomial. To investigate this phenomenon, we first explicitly characterize all the global minima of the cost function. We then prove that one particular global minimum (called the maximal solution) belongs to a neighborhood of Φ 0 , on which the cost function is strongly convex under the condition ‖ f ‖ ∞ = O ( d − 1 ) with d = d e g ( f ) . Our result provides a partial explanation of the aforementioned success of optimization algorithms.

Wang, Jiasu↗