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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Flexible silicon photonic architecture for accelerating distributed deep learning

The increasing size and complexity of deep learning (DL) models have led to the wide adoption of distributed training methods in datacenters (DCs) and high-performance computing (HPC) systems. However, communication among distributed computing units (CUs) has emerged as a major bottleneck in the training process. In this study, we propose Flex-SiPAC, a flexible silicon photonic accelerated compute cluster designed to accelerate multi-tenant distributed DL training workloads. Flex-SiPAC takes a co-design approach that combines a silicon photonic hardware platform with a tailored collective algorithm, optimized to leverage the unique physical properties of the architecture. The hardware platform integrates a novel wavelength-reconfigurable transceiver design and a micro-resonator-based wavelength-reconfigurable switch, enabling the system to achieve flexible bandwidth steering in the wavelength domain. The collective algorithm is designed to support reconfigurable topologies, enabling efficient all-reduce communications that are commonly used in DL training. The feasibility of the Flex-SiPAC architecture is demonstrated through two testbed experiments. First, an optical testbed experiment demonstrates the flexible routing of wavelengths by shuffling an array of input wavelengths using a custom-designed spatial-wavelength selective switch. Second, a four-GPU testbed running two DL workloads shows a 23% improvement in job completion time compared to a similarly sized leaf-spine topology. We further evaluate Flex-SiPAC using large-scale simulations, which show that Flex-SiPAC is able to reduce the communication time by 26% to 29% compared to state-of-the-art compute clusters under representative collective operations.

Wu, Zhenguo (ORCID:0000000322847985)↗
DOE OSTI2019

mystic - a brief introduction

The mystic framework enables the solving of difficult optimization problems through three major innovations: (1) plug-and-play component-based optimization algorithms, (2) the ability to dynamically construct and apply generalzed trnasforms, K , where x' = K(x) , and (3) workflows providing asynchronous execution and statefulness. These features, in conjunction with supporting packages pathos , pyina , and klepto , can provide massively-parallel scalable workflows for quickly solving optimization problems in complex nonlinear spaces. mystic can be used to simplify non-convex optimization problems by transforming away nonlinearities through user-built kernel transforms. This tutorial demonstrates using mystic for machine learning with automated dimensional-reduction, using embarrasingly parallel solver ensembles to find an accurate interpolated surrogate for a nonlinear surface, and the determination of worst-case bounds on expectation value of an objective function under uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

MO-D-213-04: The Proximity to the Skin of PTV Affects PTV Coverage and Skin Dose for TomoTherapy

Purpose: The proximity to the skin surface of the PTV for the patients with skin disease could be a concern in terms of the PTV coverage and actual surface dose (SD). IMRT optimization algorithms increase the beam intensity close to the skin in order to compensate for lack of scattering material, leading to enhanced SD but potential hot spots. This study aims to investigate the effect of PTV proximity to the skin on planning and measured SD Methods: All measurements were done for 6 MV X-ray beam of Helical TomoTherapy. An anthropomorphic phantom was scanned in a CT simulator in a routine manner with thermoplastic mask immobilization. PTVs were created with varying distances to the skin of 0 mm -(PTV1), 1 mm- (PTV2), 2 mm-(PTV3) and 3 mm-(PTV4). Also, a 5 mm bolus was used with PTV1 (PTV5). All planning constraints were kept the same in all studies (hard constraint: 95% of the prescription dose covered 95% of the PTV). Gafchromic film (EBT3) was placed under the mask on the phantom surface, and the resulting dose was estimated using RIT software. Results: Optimizing the dose using different PTVs lead to average planned target doses of 10.8, 10.3, 10.2, 10.3 and 10.0 Gy, with maximum doses 12.2, 11.2, 11.1, 11.1 and 10.0 Gy for PTV1, PTV2, PTV3, PTV4 and PTV5, respectively. EBT3 measurements indicated a significant decrease of SD with skin distance by 12.7% (PTV1), 21.9% (PTV2), 24.8% (PTV3) and 28.4% (PTV4) comparing to prescription dose. Placement of a 5 mm bolus on the phantom surface resulted in a SD close to prescribed (+0.5%). Conclusion: This work provides a clear demonstration of the relationship between the skin dose and the PTV to the skin distance. The results indicate the necessity of a bolus even for TomoTherapy when high skin dose is required.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Development and application of marginal likelihood optimization for integral parameter adjustment

When adjusting nuclear data with integral experiments, care must be taken that spurious adjustments are not made by assimilating poorly characterized integral parameters. If there are unaccounted for biases or poorly estimated uncertainties in the calculated and experimental values for an integral parameter, the Bayesian data assimilation may adjust the nuclear data in a manner that does not reflect the physics of the integral parameter. To identify and lessen the impact of these inconsistent integral parameters, in this study we present a Marginal Likelihood Optimization algorithm. In a data-driven way, the marginalized likelihood is used to modulate hyperparameter terms that decrease the influence of inconsistent integral parameters on the adjustment. The advantage of this approach over other methods in the literature is that it incorporates correlation information and does not remove an integral parameter from the adjustment. Herein, we present and motivate the algorithm, and apply it to an integral data assimilation case study.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Evaluation of a commercial automatic treatment planning system for prostate cancers

Recent developments in Radiation Oncology treatment planning have led to the development of software packages that facilitate automated intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT) planning. Such solutions include site-specific modules, plan library methods, and algorithm-based methods. In this study, the plan quality for prostate cancer generated by the Auto-Planning module of the Pinnacle{sup 3} radiation therapy treatment planning system (v9.10, Fitchburg, WI) is retrospectively evaluated. The Auto-Planning module of Pinnacle{sup 3} uses a progressive optimization algorithm. Twenty-three prostate cancer cases, which had previously been planned and treated without lymph node irradiation, were replanned using the Auto-Planning module. Dose distributions were statistically compared with those of manual planning by the paired t-test at 5% significance level. Auto-Planning was performed without any manual intervention. Planning target volume (PTV) dose and dose to rectum were comparable between Auto-Planning and manual planning. The former, however, significantly reduced the dose to the bladder and femurs. Regression analysis was performed to examine the correlation between volume overlap between bladder and PTV divided by the total bladder volume and resultant V70. The findings showed that manual planning typically exhibits a logistic way for dose constraint, whereas Auto-Planning shows a more linear tendency. By calculating the Akaike information criterion (AIC) to validate the statistical model, a reduction of interoperator variation in Auto-Planning was shown. We showed that, for prostate cancer, the Auto-Planning module provided plans that are better than or comparable with those of manual planning. By comparing our results with those previously reported for head and neck cancer treatment, we recommend the homogeneous plan quality generated by the Auto-Planning module, which exhibits less dependence on anatomic complexity.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2019

Energetic Potential for Demand Response in Detached Single Family Homes in Austin, TX

This study builds a generalized tool to quantify the maximum peak load reduction achievable with residential demand response and distributed energy resources (DERs). The tool is demonstrated by using empirical energy usage data from detached single family households within the service territory of Austin Energy - the local municipal utility in Austin, TX. The demand response optimization algorithm shifts energy usage of four controllable, high-consumption residential devices to off-peak hours: HVAC (heating, ventilation, and air conditioning) systems, electric water heaters, electric vehicles, and pool pumps. In addition, rooftop solar generation on individual residences is considered to reduce net load to the utility, and an energy storage system optimization model performing energy arbitrage further reduces peak demand. Results from the aggregate demand response and battery optimization study indicate that peak demand for the 2017 summer peak in Austin Energy could have been reduced by 26 MW or 2.9%. Here, by considering the combined effect of controllable consumer loads, solar generation, and energy storage systems, this study highlights the potential of strategic demand response and energy arbitrage to reduce peak demand at the distribution level.

14 SOLAR ENERGY↗
DOE OSTI2023

Development of Building Design Optimization Methodology: Residential Building Applications

Building design optimization is a highly complex problem, requiring long computational running processes because of the many options that exist when a building is being designed. This paper introduces an integrated approach through which to perform this optimization within an acceptable time frame. The approach includes the methods of variable selection, model simplification, and a sequential optimization process. Using singular value decomposition, a large number of design variables is reduced to a smaller subset that can be solved more quickly through the optimization algorithm. To expedite the variable selection process, a modeling approach that quickly simulates annual energy consumption was developed to replace full annual energy simulations. The developed methodology was applied to two residential buildings in the US, and the results are discussed herein. To assess the accuracy of the integrated optimization methodology, the optimized life cycle costs are compaa variables demonstrating the strongest contributions in the optimization study were identified. The proposed methodology significantly shortened the time requirements for the optimization processes of the two case studies by 74% and 84%; the optimized life cycle costs were within 0.05% and 0.06%, respectively, of the optimum point.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2014

SU-E-T-185: Feasibility Study of Dose Rate Modulated Arc Therapy (DrMAT) for Lung SBRT

Purpose: To show the feasibility of clinical application of DrMAT for SBRT in lung cancer patients. DrMAT is a form of dynamic conformal arc therapy where MLC segments and dose rates are controlled through simple field weight optimization. Methods: To show feasibility a new treatment plan was created based on the CT of SBRT lung cancer patients. Static plans with 33 fields are made, which have 11deg in between each field and are acquired rotating gantry angle from 180deg to 188deg in CCW direction, total 352deg is rotated. MLC maintained static aperture for each field. To optimize 33 individual fields, field weight was adjusted accordingly using weight optimization algorithm. Keeping weights and MU of static plan, static MLC aperture was converted to multiple arc segments. Arc plan could be created with the fields in the intervals of 11deg. Static MLC should be converted to arc segment MLC. Dynamic conformal arc therapy plan consists of 33 arc fields, is converted to one dose rate modulated arc therapy (DrMAT) plan. DrMAT plan consists of 166 control points which becomes a single arc plan that changes the shape of MLC for every 2.2deg. The resulting DrMAT plan is not an inverse plan it is a simple form of dynamic conformal arc plan using field weight obtained from static plan. This is compared and evaluated with the VMAT plan. Results: DrMAT and VMAT plans have been compared based on the RTOG1021. Both DrMAT and VMAT plans satisfy 100% irradiation to 95% of PTV and critical organs did not exceed dose limit suggested in RTOG1021. DrMAT plan is almost similar with VMAT plan in Result. Conclusion: Field weight optimization method did not show better Resultcompared to VMAT optimization. However, considering simplicity, DrMAT satisfies the condition in RTOG1021. Therefore clinical application of DrMAT is feasible.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Geometry Optimization of Cable-Based Actuation for Small-Scale Model Testing of a Floating Marine Turbine: Preprint

This research aims to apply combined wave and tidal current loads to a small-scale floating marine current turbine in a wave tank, where an actuation system applies hydrodynamic and mooring forces on the hardware based on results from a simulation. We use a real-time hybrid test setup with physical wave forcing from the wave tank and simulated current and mooring forces implemented through a tensioned cable array. For this paper, we developed an optimization algorithm that adjusts the hardware geometry of the cable array to achieve more efficient tension allocation across the cables for the loads that need to be actuated. By adjusting the points where the cables are attached to the floating platform and the angles between the platform and the winches, an optimal cable geometry can be found to minimize tension variations in the lines, maintain the desired pretension, and prevent excessive tensions. We present the optimization problem formulation, the actuation system evaluation approach, and optimization results that show effective cable actuation setups that are being considered for implementation in the wave tank tests.

cable-based actuation↗
DOE OSTI2021

Clustering of electromagnetic showers and particle interactions with graph neural networks in liquid argon time projection chambers

Liquid argon time projection chambers (LArTPCs) are a class of detectors that produce high resolution images of charged particles within their sensitive volume. In these images, the clustering of distinct particles into superstructures is of central importance to the current and future neutrino physics program. Electromagnetic (EM) activity typically exhibits spatially detached fragments of varying morphology and orientation that are challenging to efficiently assemble using traditional algorithms. Similarly, particles that are spatially removed from each other in the detector may originate from a common interaction. Graph neural networks (GNNs) were developed in recent years to find correlations between objects embedded in an arbitrary space. The graph particle aggregator (GrapPA) first leverages GNNs to predict the adjacency matrix of EM shower fragments and to identify the origin of showers, i.e., primary fragments. On the PILArNet public LArTPC simulation dataset, the algorithm achieves a shower clustering accuracy characterized by a mean purity of 99.4%, a mean efficiency of 99.6% and a primary identification accuracy of 99.8%. It yields a relative shower energy uncertainty of (4.1 + 1.4 / $\sqrt{\text{E(GeV)})}$% and a shower direction uncertainty of (2.1/ $\sqrt{\text{E(GeV)})}$°. Finally, the optimized algorithm is then applied to the related task of clustering particle instances into interactions and yields a mean purity of 99.8% and a mean efficiency of 99.5% for an interaction density of $\mathcal{O}(1)$ m –3 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Efficient generation of grids and traversal graphs in compositional spaces towards exploration and path planning

Abstract Diverse disciplines across science and engineering deal with problems related to compositions, which exist in non-Euclidean simplex spaces, rendering many standard tools inaccurate or inefficient. This work explores such spaces conceptually in the context of materials discovery, quantifies their computational feasibility, and implements several essential methods specific to simplex spaces through a new high-performance open-source library . Most significantly, we derive and implement an algorithm for constructing a novel n-dimensional simplex graph data structure, containing all discretized compositions and possible neighbor-to-neighbor transitions. Critically, no distance or neighborhood calculations are performed, instead leveraging pure combinatorics and order in procedurally generated simplex grids, keeping the algorithm $${\mathcal{O}}(N)$$ O ( N ) , with minimal memory, enabling rapid construction of graphs with billions of transitions in seconds. Additionally, we demonstrate how such graph representations can be combined to homogeneously express complex path-planning problems, while facilitating efficient deployment of existing high-performance gradient descent, graph traversal, and other optimization algorithms.

Krajewski, Adam M. (ORCID:0000000222660099)↗
DOE OSTI2024

Effective optimization of atomic decoration in giant and superstructurally ordered crystals with machine learning

Crystals with complicated geometry are often observed with mixed chemical occupancy among Wyckoff sites, presenting a unique challenge for accurate atomic modeling. Similar systems possessing exact occupancy on all the sites can exhibit superstructural ordering, dramatically inflating the unit cell size. In this work, a crystal graph convolutional neural network (CGCNN) is used to predict optimal atomic decorations on fixed crystalline geometries. This is achieved with a site permutation search (SPS) optimization algorithm based on Monte Carlo moves combined with simulated annealing and basin-hopping techniques. Our approach relies on the evidence that, for a given chemical composition, a CGCNN estimates the correct energetic ordering of different atomic decorations, as predicted by electronic structure calculations. This provides a suitable energy landscape that can be optimized according to site occupation, allowing the prediction of chemical decoration in crystals exhibiting mixed or disordered occupancy, or superstructural ordering. Verification of the procedure is carried out on several known compounds, including the superstructurally ordered clathrate compound Rb8Ga27Sb16 and vacancy-ordered perovskite Cs2SnI6, neither of which was previously seen during the neural network training. In addition, the critical temperature of an order–disorder phase transition in solid solution CuZn is probed with our SPS routines by sampling site configuration trajectories in the canonical ensemble. This strategy provides an accurate method for determining favorable decoration in complex crystals and analyzing site occupation at unprecedented speed and scale.

Chemistry↗
DOE OSTI2025

Plant Reload Optimization (prlo)

The PRLO framework is built on a modular and extensible architecture that tightly couples advanced evolutionary optimization algorithms with nuclear fuel depletion solvers (i.e., nuclear physics neutronics code). It supports exploring complex, high-dimensional design spaces constrained by user-specified operational, safety, and economic constraints. Objectives such as minimizing fresh fuel enrichment, flattening radial and axial power distributions, and maximizing discharge burnup are evaluated. PRLO’s equilibrium cycle optimization capability enables the identification of core configurations that maintain fuel cycle sustainability over extended planning horizons. Its integration with the RAVEN platform facilitates optimization of loading patterns or fuel shuffling schemes across multiple cycles. The interface with SIMULATE, a licensed industry-standard nodal code developed by Studsvik, ensures accurate neutronic and thermal-hydraulic feedback for reactor core design. PRLO’s automated workflow engine supports iterative design refinement, enabling utilities to streamline core design processes and meet evolving performance and regulatory targets.

Kim, Junyung [Idaho National Laboratory] (00090005↗
DOE OSTI2023

Approximate Boltzmann distributions in quantum approximate optimization

Approaches to compute or estimate the output probability distributions from the quantum approximate optimization algorithm (QAOA) are needed to assess the likelihood it will obtain a quantum computational advantage. We analyze output from QAOA circuits solving 7200 random MaxCut instances, with $n$ = 14–23 qubits and depth parameter $p$ ≤ 12 and find that the average basis state probabilities follow approximate Boltzmann distributions: The average probabilities scale exponentially with their energy (cut value), with a peak at the optimal solution. Furthermore, we describe the rate of exponential scaling or effective temperature in terms of a series with a leading-order term $T$ ~ $C$ min /$n$ $\sqrt{p}$, with $C$ min the optimal solution energy. Using this scaling, we generate approximate output distributions with up to 38 qubits and find these give accurate accounts of important performance metrics in cases we can simulate exactly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

WE-G-16A-01: Evolution of Radiation Treatment Planning

Welcome and Introduction - Lawrence N. Rothenberg This symposium is one a continuing series of presentations at AAPM Annual Meetings on the historical aspects of medical physics, radiology, and radiation oncology that have been organized by the AAPM History Committee. Information on previous presentations including “Early Developments in Teletherapy” (Indianapolis 2013), “Historical Aspects of Cross-Sectional Imaging” (Charlotte 2012), “Historical Aspects of Brachytherapy” (Vancouver 2011), “50 Years of Women in Medical Physics” (Houston 2008), and “Roentgen's Early Investigations” (Minneapolis 2007) can be found in the Education Section of the AAPM Website. The Austin 2014 History Symposium will be on “Evolution of Radiation Treatment Planning.” Overview - Radhe Mohan Treatment planning is one of the most critical components in the chain of radiation therapy of cancers. Treatment plans of today contain a wide variety of sophisticated information conveying the potential clinical effectiveness of the designed treatment to practitioners. Examples of such information include dose distributions superimposed on three- or even four-dimensional anatomic images; dose volume histograms, dose, dose-volume and dose-response indices for anatomic structures of interest; etc. These data are used for evaluating treatment plans and for making treatment decisions. The current state-of-the-art has evolved from the 1940s era when the dose to the tumor and normal tissues was estimated approximately by manual means. However, the symposium will cover the history of the field from the late-1950's, when computers were first introduced for treatment planning, to the present state involving the use of high performance computing and advanced multi-dimensional anatomic, functional and biological imaging, focusing only on external beam treatment planning. The symposium will start with a general overview of the treatment planning process including imaging, structure delineation, assignment of dose requirements, consideration of uncertainties, selection of beam configurations and shaping of beams, and calculations, optimization and evaluation of dose distributions. This will be followed by three presentations covering the evolution of treatment planning, which parallels the evolution of computers, availability of advanced volumetric imaging and the development of novel technologies such as dynamic multi-leaf collimators and online image guidance. This evolution will be divided over three distinct periods - prior to 1970's, the 2D era; from 1980 to the mid-1990's, the 3D era; and from the mid 1990's to today, the IMRT era. When the World was Flat: The Two-Dimensional Radiation Therapy Era” - Jacob Van Dyk In the 2D era, anatomy was defined with the aid of solder wires, special contouring devices and projection x-rays. Dose distributions were calculated manually from single field, flat surface isodoses on transparencies. Precalculated atlases of generic dose distributions were produced by the International Atomic Energy Agency. Massive time-shared main frames and mini-computers were used to compute doses at individual points or dose distributions in a single plane. Beam shapes were generally rectangular, with wedges, missing tissue compensators and occasional blocks to shield critical structures. Dose calculations were measurement-based or they used primary and scatter calculations based on scatter-air ratio methodologies. Dose distributions were displayed on line printers as alpha-numeric character maps or isodose patterns made with pen plotters. More than Pretty Pictures: 3D Treatment Planning and Conformal Therapy - Benedick A. Fraass The introduction of computed tomography allowed the delineation of anatomy three-dimensionally and, supported partly by contracts from the National Cancer Institute, made possible the introduction and clinical use of 3D treatment planning, leading to development and use of 3D conformal therapy in the 1980's. 3D computer graphics and 3D anatomical structure definitions made possible Beam's Eye View (BEV) displays, making conformal beam shaping and much more sophisticated beam arrangements possible. These conformal plans significantly improved target dose coverage as well as normal tissue sparing. The use of dose volume histograms, gross/clinical/planning target volumes, MRI and PET imaging, multileaf collimators, and computer-controlled treatment delivery made sophisticated planning approaches practical. The significant improvements in dose distributions and analysis achievable with 3D conformal therapy made possible formal dose escalation and normal tissue tolerance clinical studies that set new and improved expectations for improved local control and decreasing complications in many clinical sites. From the Art to the State of the Art: Inverse Planning and IMRT - Thomas R. Bortfeld While the potential of intensity modulation was recognized in the mid- 1980's, intensity-modulated radiotherapy (IMRT) did not become a reality until the mid-1990's. Broad beams of photons could be sub-divided into narrow beamlets whose intensities could be determined using sophisticated optimization algorithms to appropriately balance tumor dose with normal tissue sparing. The development of dynamic multi-leaf collimators (on conventional linear accelerators as well as in helical delivery devices) enabled the efficient delivery of IMRT. The evolution of IMRT planning is continuing in the form of Volumetric Modulated Arc Therapy (VMAT) and through advanced optimization tools, such as multi-criteria optimization, automated IMRT planning, and robust optimization to protect dose distributions against uncertainties. IMRT also facilitates “dose painting” in which different sub-volumes of the target are prescribed different doses. Clearly, these advancements are being made possible by the increasing power and lower cost of computers and developments in other fields such as imaging and operations research. Summary - Radhe Mohan The history does not end here. The advancement of treatment planning is expected to continue, leading to further automation and improvements in conformality and robustness of dose distributions, particularly in the area of particle therapy. Radiobiological modeling will gain emphasis as part of the planning process. Learning Objectives: The scope of changes in technology and the capabilities of radiation treatment planning The impact of these changes in the quality of treatment plans and optimality of dose distributions The impact of development in other fields (imaging, computers, operations research, etc.) on the evolution of radiation treatment planning.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the “optimize-then-discretize” approach. This challenge motivates us to propose an adjoint DSMC method following the “discretize-then-optimize” approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Here, several numerical examples are presented to demonstrate their accuracy and efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Model-Based Iterative Reconstruction of Magnetization Using Vector Field Electron Tomography

Vector field electron tomography (VFET) is extensively used for three-dimensional (3-D) imaging of magnetic materials at nanometer resolutions. The conventional approach is to reconstruct and visualize the magnetic vector potential or the magnetic field associated with the sample. There is a lack of algorithms capable of reconstructing the 3-D distribution of magnetization from VFET data. Unlike magnetic vector potential and magnetic field, magnetization is a fundamental physical property of the sample that does not extend beyond the dimensions of the sample. We present a model-based iterative reconstruction algorithm (MBIR) that reconstructs the magnetization by minimizing a cost function consisting of a forward model term and a prior model term. The forward model uses the physics of imaging to model the VFET data as a function of the magnetization, and the prior model enforces sparsity in the magnetization reconstruction. We then formulate an optimization algorithm based on the theory of alternate direction method of multipliers to minimize the resulting MBIR cost function. In conclusion, using simulated and real data, we show that our algorithm accurately reconstructs both the magnetization and the magnetic vector potential.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Generalized Quantum Signal Processing

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that | P | ≤ 1 , a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where P and Q are known. In cases where only P is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding Q for polynomials of degree on the order of 10 7 . We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the ϵ -approximate fractional query problem that requires O ( ( 1 / δ ) + log ( 1 / ϵ ) ) queries to perform where O ( 1 / δ ) is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only O ( d log N + log 2 N ) 1 and 2-qubit gates for a filter of lengths d . Published by the American Physical Society 2024

Motlagh, Danial↗