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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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DOE OSTI2023

Using Multiple Geophysical Methods to Refine a Stratigraphic Conceptual Site Model at a Nuclear Waste Site

At contaminated sites, there is a critical reliance on conceptual site models of which a key component is the geologic framework model (GFM), which is used to build predictive fate and transport modeling in support of remediation goals. Here, we detail an ongoing study at a nuclear waste site (Hanford Site, Washington, USA) where surface geophysical methods were used to complement existing borehole information and to help site new boreholes to update and refine the GFM. Ground-based electrical resistivity tomography (ERT), time-domain electromagnetics (TEM), and seismic data was acquired on the Hanford Site’s Central Plateau, where the presence of a hydraulically transmissive subsurface feature, or paleochannel, was suspected but uncertain based on contaminant concentrations at sparsely located boreholes. To assess and compare ERT, TEM, and seismic geophysical datasets, co-located data was acquired in an area where the existing GFM was more certain. Surrounding the suspected paleochannel, ERT and seismic refraction tomography showed similar subsurface structures consistent with a channelized feature. While TEM interpretation was limited in the suspected paleochannel area due to a thick resistive top layer and high electromagnetic noise, TEM showed greater utility in a different area where these factors were less prevalent. Based on the results of quasi-3D ERT inversions, we propose updates to the GFM, including identifying a paleochannel. Further, we evaluate the utility of geophysical methods and examine lessons learned that will be used as a basis for continued characterization efforts to support site management decisions and implementation efforts.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2018

Integrating geophysical monitoring data into multiphase fluid flow reservoir simulation

Simulation of multiphase flow systems are of critical importance in managing hydrological systems. Flow simulations are affected by a number of factors including structure and flow properties including porosity and permeability as well as the anisotropy and heterogeneity of these properties. In many cases traditional hydrological and reservoir data are highly affected by these parameters, but are not directly sensitive to them. As such modellers often adjust these parameters in an ad hoc manner until solutions numerically converge. Simulation models are generally based on structural data from reflection seismics whose physical flow properties are then populated using geostatistical extrapolation techniques utilizing a sparse number of borehole logs and core analysis. In multiphase systems including enhanced oil recovery and carbon capture and sequestration uncertainties regarding phase-dependent physical properties confounds this challenge further. Geophysical methods provide a means by which to gain an improved understanding of phase distributions in the subsurface. In this paper we will look at applications from active carbon capture and sequestration and enhanced oil recovery applications, as well as synthetic examples. Geophysical data including electromagnetic and gravity are inverted using structural constraints from the reservoir model. Inversions are then mapped into flow properties using calibrated relations such as Archie’s Equation. The coupled models can then be used to both verify and improve on the reservoir flow model which improves it’s predictive power and utility as a management tool.

02 PETROLEUM↗
DOE OSTI2016

Automated Dynamic Demand Response Implementation on a Micro-grid

In this paper, we describe a system for real-time automated Dynamic and Sustainable Demand Response with sparse data consumption prediction implemented on the University of Southern California campus microgrid. Supply side approaches to resolving energy supply-load imbalance do not work at high levels of renewable energy penetration. Dynamic Demand Response (D 2 R) is a widely used demand-side technique to dynamically adjust electricity consumption during peak load periods. Our D 2 R system consists of accurate machine learning based energy consumption forecasting models that work with sparse data coupled with fast and sustainable load curtailment optimization algorithms that provide the ability to dynamically adapt to changing supply-load imbalances in near real-time. Our Sustainable DR (SDR) algorithms attempt to distribute customer curtailment evenly across sub-intervals during a DR event and avoid expensive demand peaks during a few sub-intervals. It also ensures that each customer is penalized fairly in order to achieve the targeted curtailment. We develop near linear-time constant-factor approximation algorithms along with Polynomial Time Approximation Schemes (PTAS) for SDR curtailment that minimizes the curtailment error defined as the difference between the target and achieved curtailment values. Our SDR curtailment problem is formulated as an Integer Linear Program that optimally matches customers to curtailment strategies during a DR event while also explicitly accounting for customer strategy switching overhead as a constraint. We demonstrate the results of our D 2 R system using real data from experiments performed on the USC smartgrid and show that 1) our prediction algorithms can very accurately predict energy consumption even with noisy or missing data and 2) our curtailment algorithms deliver DR with extremely low curtailment errors in the 0.01-0.05 kWh range.

Kuppannagari, Sanmukh R.↗
DOE OSTI2018

Distinguishing one from many using super-resolution compressive sensing

We present that distinguishing whether a signal corresponds to a single source or a limited number of highly overlapping point spread functions (PSFs) is a ubiquitous problem across all imaging scales, whether detecting receptor-ligand interactions in cells or detecting binary stars. Super-resolution imaging based upon compressed sensing exploits the relative sparseness of the point sources to successfully resolve sources which may be separated by much less than the Rayleigh criterion. However, as a solution to an underdetermined system of linear equations, compressive sensing requires the imposition of constraints which may not always be valid. One typical constraint is that the PSF is known. However, the PSF of the actual optical system may reflect aberrations not present in the theoretical ideal optical system. Even when the optics are well characterized, the actual PSF may reflect factors such as non-uniform emission of the point source (e.g. fluorophore dipole emission). As such, the actual PSF may differ from the PSF used as a constraint. Similarly, multiple different regularization constraints have been suggested including the l 1 -norm, l 0 -norm, and generalized Gaussian Markov random fields (GGMRFs), each of which imposes a different constraint. Other important factors include the signal-to-noise ratio of the point sources and whether the point sources vary in intensity. In this work, we explore how these factors influence super-resolution image recovery robustness, determining the sensitivity and specificity. In conclusion, we determine an approach that is more robust to the types of PSF errors present in actual optical systems.

42 ENGINEERING↗
DOE OSTI2018

A comparison of preconditioned Krylov subspace methods for large‐scale nonsymmetric linear systems

Summary Preconditioned Krylov subspace (KSP) methods are widely used for solving large‐scale sparse linear systems arising from numerical solutions of partial differential equations (PDEs). These linear systems are often nonsymmetric due to the nature of the PDEs, boundary or jump conditions, or discretization methods. While implementations of preconditioned KSP methods are usually readily available, it is unclear to users which methods are the best for different classes of problems. In this work, we present a comparison of some KSP methods, including GMRES, TFQMR, BiCGSTAB, and QMRCGSTAB, coupled with three classes of preconditioners, namely, Gauss–Seidel, incomplete LU factorization (including ILUT, ILUTP, and multilevel ILU), and algebraic multigrid (including BoomerAMG and ML). Theoretically, we compare the mathematical formulations and operation counts of these methods. Empirically, we compare the convergence and serial performance for a range of benchmark problems from numerical PDEs in two and three dimensions with up to millions of unknowns and also assess the asymptotic complexity of the methods as the number of unknowns increases. Our results show that GMRES tends to deliver better performance when coupled with an effective multigrid preconditioner, but it is less competitive with an ineffective preconditioner due to restarts. BoomerAMG with a proper choice of coarsening and interpolation techniques typically converges faster than ML, but both may fail for ill‐conditioned or saddle‐point problems, whereas multilevel ILU tends to succeed. We also show that right preconditioning is more desirable. This study helps establish some practical guidelines for choosing preconditioned KSP methods and motivates the development of more effective preconditioners.

Ghai, Aditi↗
DOE OSTI2021

Learning an Algebriac Multrigrid Interpolation Operator Using a Modified GraphNet Architecture

This work, building on previous efforts, develops a suite of new graph neural network machine learning architectures that generate data-driven prolongators for use in Algebraic Multigrid (AMG). Algebraic Multigrid is a powerful and common technique for solving large, sparse linear systems. Its effectiveness is problem dependent and heavily depends on the choice of the prolongation operator, which interpolates the coarse mesh results onto a finer mesh. Previous work has used recent developments in graph neural networks to learn a prolongation operator from a given coefficient matrix. In this paper, we expand on previous work by exploring architectural enhancements of graph neural networks. A new method for generating a training set is developed which more closely aligns to the test set. Asymptotic error reduction factors are compared on a test suite of 3-dimensional Poisson problems with varying degrees of element stretching. Results show modest improvements in asymptotic error factor over both commonly chosen baselines and learning methods from previous work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Mechanical Test Frame for Property Evaluations at Cryogenic Temperature

On-board storage of hydrogen fuel has been designated as a limiting factor in the advancement of fuel cell technologies in the automotive industry. The use of cryo-compressed Type III pressure vessels presents one option to overcome this barrier. These multi-material vessels will be expected to perform at high pressure and extreme low temperatures, which creates a complex engineering design challenge. Many materials exhibit highly temperature-dependent properties, which must be considered for the efficient design of cryo-compressed pressure vessels. Complicating this issue, mechanical property data at cryogenic temperatures is sparse. This technical paper provides a description of a test apparatus commissioned specifically to help address this shortcoming. A mechanical test frame was retrofitted with a continuous flow cryostat capable to evaluate various mechanical properties throughout a broad temperature range of 25 °C to -269 °C with a load limit of 10 kN. An investigation of the thermomechanical properties of an epoxy resin was carried out as a demonstration.

Mechanical characterization, cryogenic pressure ve↗
DOE OSTI2025

Non-intrusive reduced-order modeling for dynamical systems with spatially localized features

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately 8$\times$ compared to the numerical simulation.

42 ENGINEERING↗
DOE OSTI2022

Subcell limiting strategies for discontinuous Galerkin spectral element methods

Here, we present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations that allow for convex blending with the high-order variant with the goal of guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre–Gauss–Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex blending factors, which can be either based on heuristic troubled-cell indicators, or using ideas from flux-corrected transport methods. By carefully designing the metric terms of the subcell FV method, the resulting methods can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy. We further show that it is possible to choose the four ingredients to recover existing methods such as a provably entropy dissipative subcell shock-capturing approach or a sparse invariant domain preserving approach. We test the versatility of the presented strategies and mix and match the four ingredients to solve challenging simulation setups, such as the KPP problem (a hyperbolic conservation law with non-convex flux function), turbulent and hypersonic Euler simulations, and MHD problems featuring shocks and turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Model-measurement consistency and limits of bioaerosol abundance over the continental United States

Abstract. Due to low concentrations and chemical complexity, in situ observations of bioaerosol are geographically and temporally sparse, and this limits the accuracy of current emissions inventories. In this study, we apply a new methodology, including corrections for misidentification of mineral dust, to measurements of single particles over four airborne sampling campaigns to derive vertical profiles of bioaerosol over the continental United States. The new methodology is based on single-particle mass spectrometry (SPMS); it can extend historic datasets to include measurements of bioaerosol, it allows comparisons to other techniques, and it generally agrees with a global aerosol model. In the locations sampled, bioaerosols were at least a factor of 10 less abundant than mineral dust. Below 2 km, bioaerosol concentrations were measured between 6×103 and 2×104 m−3. Between 2 and 8 km, bioaerosol concentrations were between 0 and 2×104 m−3, and above 8 km, bioaerosol concentrations were between 0 and 1×103 m−3. Between 30 % and 80 % of single bioaerosol particles detected were internally mixed with dust. A direct comparison of the SPMS methodology with a co-located wideband integrated bioaerosol sensor (WIB) fluorescence sensor on a mountaintop site showed agreement to within a factor of 3 over the common size range.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Performance optimization, modeling and analysis of sparse matrix-matrix products on multi-core and many-core processors

Sparse matrix-matrix multiplication (SpGEMM) is a computational primitive that is widely used in areas ranging from traditional numerical applications to recent big data analysis and machine learning. Although many SpGEMM algorithms have been proposed, hardware specific optimizations for multi- and many-core processors are lacking and a detailed analysis of their performance under various use cases and matrices is not available. In this work, we firstly identify and mitigate multiple bottlenecks with memory management and thread scheduling on Intel Xeon Phi (Knights Landing or KNL). Specifically targeting many-core processors, we develop a hash-table-based algorithm and optimize a heap-based shared-memory SpGEMM algorithm. We examine their performance together with other publicly available codes. Different from the literature, our evaluation also includes use cases that are representative of real graph algorithms, such as multi-source breadth-first search or triangle counting. Our hash-table and heap-based algorithms are showing significant speedups from libraries in the majority of the cases while different algorithms dominate the other scenarios with different matrix size, sparsity, compression factor and operation type. We wrap up in-depth evaluation results and make a recipe to give the best SpGEMM algorithm for target scenario. We build the performance model for hash-table and heap-based algorithms, which supports the recipe. A critical finding is that hash-table-based SpGEMM gets a significant performance boost if the nonzeros are not required to be sorted within each row of the output matrix. Finally, we integrate our implementations into a large-scale protein clustering code named HipMCL, accelerating its SpGEMM kernel by up to 10X and achieving an overall performance boost for the whole HipMCL application by 2.6X.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A universal preconditioner for simulating condensed phase materials

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

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

Reducing Communication Costs for Sparse Matrix Multiplication within Algebraic Multigrid

We consider the sequence of sparse matrix-matrix multiplications performed during the setup phase of algebraic multigrid. In particular, we show that the most commonly used parallel algorithm is often not the most communication-efficient one for all of the matrix-matrix multiplications involved. By using an alternative algorithm, we show that the communication costs are reduced (in theory and practice), and we demonstrate the performance benefit for both model (structured) and more realistic unstructured problems on large-scale distributed-memory parallel systems. Our theoretical analysis shows that we can reduce communication by a factor of up to 5.4 for a model problem, and we observe in our empirical evaluation communication reductions of factors up to 4.7 for structured problems and 3.7 for unstructured problems. These reductions in communication translate to run-time speedups of up to factors of 2.3 and 2.5, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Characterizing spatiotemporal information loss in sparse-sampling-based dynamic MRI for monitoring respiration-induced tumor motion in radiotherapy

Purpose: Sparse-sampling and reconstruction techniques represent an attractive strategy to achieve faster image acquisition speeds, while maintaining adequate spatial resolution and signal-to-noise ratio in rapid magnetic resonance imaging (MRI). The authors investigate the use of one such sequence, broad-use linear acquisition speed-up technique (k-t BLAST) in monitoring tumor motion for thoracic and abdominal radiotherapy and examine the potential trade-off between increased sparsification (to increase imaging speed) and the potential loss of “true” information due to greater reliance on a priori information. Methods: Lung tumor motion trajectories in the superior–inferior direction, previously recorded from ten lung cancer patients, were replayed using a motion phantom module driven by an MRI-compatible motion platform. Eppendorf test tubes filled with water which serve as fiducial markers were placed in the phantom. The modeled rigid and deformable motions were collected in a coronal image slice using balanced fast field echo in conjunction with k-t BLAST. Root mean square (RMS) error was used as a metric of spatial accuracy as measured trajectories were compared to input data. The loss of spatial information was characterized for progressively increasing acceleration factor from 1 to 16; the resultant sampling frequency was increased approximately from 2.5 to 19 Hz when the principal direction of the motion was set along frequency encoding direction. In addition to the phantom study, respiration-induced tumor motions were captured from two patients (kidney tumor and lung tumor) at 13 Hz over 49 s to demonstrate the impact of high speed motion monitoring over multiple breathing cycles. For each subject, the authors compared the tumor centroid trajectory as well as the deformable motion during free breathing. Results: In the rigid and deformable phantom studies, the RMS error of target tracking at the acquisition speed of 19 Hz was approximately 0.3–0.4 mm, which was smaller than the reconstructed pixel resolution of 0.67 mm. In the patient study, the dynamic 2D MRI enabled the monitoring of cycle-to-cycle respiratory variability present in the tumor position. It was seen that the range of centroid motion as well as the area covered due to target motion during each individual respiratory cycle was underestimated compared to the entire motion range observed over multiple breathing cycles. Conclusions: The authors’ initial results demonstrate that sparse-sampling- and reconstruction-based dynamic MRI can be used to achieve adequate image acquisition speeds without significant information loss for the task of radiotherapy guidance. Such monitoring can yield spatial and temporal information superior to conventional offline and online motion capture methods used in thoracic and abdominal radiotherapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model

Simulating the Hubbard model is of great interest to a wide range of applications within condensed matter physics, however its solution on classical computers remains challenging in dimensions larger than one. The relative simplicity of this model, embodied by the sparseness of the Hamiltonian matrix, allows for its efficient implementation on quantum computers, and for its approximate solution using variational algorithms such as the variational quantum eigensolver. While these algorithms have been shown to reproduce the qualitative features of the Hubbard model, their quantitative accuracy in terms of producing true ground state energies and other properties, and the dependence of this accuracy on the system size and interaction strength, the choice of variational ansatz, and the degree of spatial inhomogeneity in the model, remains unknown. Here we present a rigorous classical benchmarking study, demonstrating the potential impact of these factors on the accuracy of the variational solution of the Hubbard model on quantum hardware, for systems with up to 32 qubits. We find that even when using the most accurate wavefunction ansätze for the Hubbard model, the error in its ground state energy and wavefunction plateaus for larger lattices, while stronger electronic correlations magnify this issue. Concurrently, spatially inhomogeneous parameters and the presence of off-site Coulomb interactions only have a small effect on the accuracy of the computed ground state energies. Our study highlights the capabilities and limitations of current approaches for solving the Hubbard model on quantum hardware, and we discuss potential future avenues of research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

The Improved Simple Corner Balance Method and Efforts to Enhance its Computational Performance

The diamond difference (DD) spatial discretization has long been a work horse of the neutron transport community. For nearly as long as DD has been used in neutron transport, it has been observed that DD produces undamped, non-physical angular fluxes in spatially under resolved problems and can fail in the thick diffusion limit. A long list of alternative spatial discretizations, all with better physics properties: accuracy, robustness, and/or preservation of the thick diffusion limit, have been proposed as alternatives to DD. Unfortunately, these alternative spatial discretizations also require significantly more floating point operations (FLOPs) per unknown compared to DD. Historically, neutron transport problems of interest have been able to be resolved sufficiently that DD is accurate enough and FLOPs have been the computational performance bottleneck controlling time to solution. Thus, in practice DD has been and remains a preferred spatial discretization for neutron transport simulations. Trends in computing architecture are leading to a new paradigm where data movement, not FLOPs will control time to solution. This presents an opportunity to improve neutron transport physics by reconsidering more FLOP intensive spatial discretization than DD without incurring a time to solution penalty. In this work, we consider the improved simple corner balance (ISCB) spatial discretization, a unique alternative to DD that has the same memory footprint as DD, and detail efforts to improve its computational performance. The ISCB spatial discretization is a more FLOP intensive spatial discretization than DD with the same memory footprint as DD. Though designed to maximize FLOP intensity, third party libraries such as LAPACK are not tuned for the unique, frequent, small linear algebra needs of neutron transport problems. While hand coding a sparse Gauss elimination is likely to be faster than a dense matrix solve (CM vs. HGE), were LAPACK suitable for small linear algebra problems, we would not have seen a performance increase with decreased numbers of LAPACK calls for the Schur complement solve (SC4 vs. SC1). Significant effort has reduced the relative compute time of ISCB to DD, but on current computer architectures DD is still faster than ISCB. Future work comparing the overall efficiency of ISCB to DD may reveal that while ISCB is slower than DD on current computers, ISCB is more accurate than DD by a factor greater than the compute time slowdown. As new computer architectures become available, we will test our hypothesis that neutron transport simulations will be bandwidth limited, ideally rendering the additional FLOPs required by ISCB to be 'free' [in terms of time to solution]. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2018

Pion and kaon structure functions at an electron-ion collider

Pions and kaons are, along with protons and neutrons, the main building blocks of nuclear matter. They are connected to the Goldstone modes of dynamical chiral symmetry breaking, the mechanism thought to generate all hadron mass in the visible universe. The distribution of the fundamental constituents, the quarks and gluons, is expected to be different in pions, kaons, and nucleons. However, experimental data are sparse. As a result, there has been persistent doubt about the behaviour of the pion's valence quark structure function at large Bjorken-$x$ and virtually nothing is known about the contribution of gluons. The Electron-Ion Collider (EIC) with an acceptance optimized for forward physics could provide access to structure functions over a larger kinematic region. This would allow for measurements testing if the origin of mass is encoded in the differences of gluons in pions, kaons, and nucleons, and measurements that could serve as a test of assumptions used in the extraction of structure functions and the pion and kaon form factors. Furthermore, measurements at an EIC would also allow to explore the effect of gluons at high x.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Quantum Search Approaches to Sampling-Based Motion Planning

In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse environments, we formulate the Quantum Full Path Search Algorithm (q-FPS), which creates a superposition of full random path solutions, manipulates probability amplitudes with Quantum Amplitude Amplification (QAA), and quantum measures a single obstacle free full path solution. For dense unstructured environments, we formulate the Quantum Rapidly Exploring Random Tree algorithm, q-RRT, that creates quantum superpositions of possible parent-child connections, manipulates probability amplitudes with QAA, and quantum measures a single reachable state, which is added to a tree. As performance depends on the number of oracle calls and the probability of measuring good quantum states, we quantify how these errors factor into the probabilistic completeness properties of the algorithm. We then numerically estimate the expected number of database solutions to provide an approximation of the optimal number of oracle calls in the algorithm. We compare the q-RRT algorithm with a classical implementation and verify quadratic run-time speedup in the largest connected component of a 2D dense random lattice. We conclude by evaluating a proposed approach to limit the expected number of database solutions and thus limit the optimal number of oracle calls to a given number.

97 MATHEMATICS AND COMPUTING↗