Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “block design”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Passive heat removal in horizontally oriented micro-HTGRs

There are novel, horizontally oriented high-temperature gas-cooled micro-reactor (HTGR) designs under consideration because of their portability, simplicity, and reliable operation. These features of the micro-HTGR design can meet the fission battery attributes, such as economic, standardize, installed, unattended and reliable. Although there have been HTGR related safety studies, micro-HTGRs when horizontally oriented are expected to exhibit significantly different thermal physics. During the unavailability of helium circulation, the internal reactor core is designed to cool by block-to-block conduction and radiation, and the reactor vessel surface is cooled by the ambient air. This scenario is anticipated during the transport of the micro-HTGR in a shipping container. The conduction and radiation between the prismatic micro-HTGR blocks in the core can be influenced by variances in the thermal contacts. This work investigated the conduction within a simulated horizontal HTGR core. An experimental setup was used to validate a numerical model. The experimental setup consisted of a hexagonal assembly with scaled prismatic blocks placed within a high-temperature vacuum environment. The gaps between the blocks were well controlled and monitored. The experimental setup was designed in such a way that the temperature variation in the axial direction was minimal, such that the experiment could be observed as a 2D (r, ) heat transfer problem. The pressurized tube was equipped with Infra-Red (IR) transparent windows, and an IR camera was used to capture the spatio-temporal temperature evolution in the hexagonal block assembly during the cooldown experiments. The experimental scenario was computationally modeled with a finite element analysis (FEA) program. Once validated, the computational model was used to investigate the impact of gap conductance on overall decay heat removal. Using a conservative estimate for gap conductance value (100 W/m 2 -K) between the prismatic blocks, there is a negligible increase in temperature observed during decay heat generation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

IEA Wind Task 49: Reference Site Conditions for Floating Wind Arrays

The commercial-scale deployment of floating offshore wind (FOW) projects is expected to take place in a diverse range of sites that may differ significantly from existing fixed-bottom projects. FOW farms are particularly sensitive to the water depth and the meteorological and oceanographic (metocean) and geotechnical conditions at the project site due to the wave-induced system motions and loads as well as the anchoring system constraints imposed by the seafloor conditions. Uncertainty around the site conditions will permeate through all aspects of project design, leading to suboptimal and overly conservative designs, increased costs, and adversely affected performance. As FOW expands into a global industry, metocean and geotechnical conditions will increasingly vary for projects located in different geographic regions or in far-from-shore, deep-water sites. This study represents the outputs of work package 1 of International Energy Agency Wind Task 49, which focuses on the integrated design of floating wind arrays. The primary goal of this study is to establish the type of parameters and constraints required to characterize FOW array reference sites; provide a realistic and publicly available set of reference site conditions to the FOW community as a baseline set of data for individual research projects; identify and categorize any critical gaps in the existing data or methodologies required to define reference site characteristics; and inform and support the design of reference FOW arrays. A building block concept was developed for synthesizing reference sites for the design of FOW arrays. The building blocks include three classes of site conditions focusing on the techno-economic design of FOW projects: metocean conditions, seabed conditions, and coastal infrastructure. All reference site data produced and collected in this study are publicly available.

17 WIND ENERGY↗
DOE OSTI2021

Processable High Electron Mobility {pi}-Copolymers via Mesoscale Backbone Conformational Ordering

The synthesis and experimental/theoretical characterization of a new series of electron-transporting copolymers based on the naphthalene bis(4,8-diamino-1,5-dicarboxyl)amide (NBA) building block are reported. Comonomers are designed to test the emergent effects of manipulating backbone torsional characteristics, and density functional theory (DFT) analysis reveals the key role of backbone conformation in optimizing electronic delocalization and transport. The NBA copolymer conformational and electronic properties are characterized using a broad array of molecular/macromolecular, thermal, optical, electrochemical, and charge transport techniques. All NBA copolymers exhibit strongly aggregated morphologies with significant nanoscale order. Copolymer charge transport properties are investigated in thin-film transistors and exhibit excellent electron mobilities ranging from 0.4 to 4.5 cm(2) V-1 s(-1). Importantly, the electron transport efficiency correlates with the film mesoscale order, which emerges from comonomer-dependent backbone planarity and extension. These results illuminate the key NBA building block structure-morphology-bulk property design relationships essential for processable, electronics-applicable high-performance polymeric semiconductors.

n‐↗
DOE OSTI2024

Self-Cleaning Highly Porous TiO 2 Coating Designed by Swelling-Assisted Sequential Infiltration Synthesis (SIS) of a Block Copolymer Template

Photocatalytic self-cleaning coatings with a high surface area are important for a wide range of applications, including optical coatings, solar panels, mirrors, etc. Here, we designed a highly porous TiO 2 coating with photoinduced self-cleaning characteristics and very high hydrophilicity. This was achieved using the swelling-assisted sequential infiltration synthesis (SIS) of a block copolymer (BCP) template, which was followed by polymer removal via oxidative thermal annealing. The quartz crystal microbalance (QCM) was employed to optimize the infiltration process by estimating the mass of material infiltrated into the polymer template as a function of the number of SIS cycles. This adopted swelling-assisted SIS approach resulted in a smooth uniform TiO 2 film with an interconnected network of pores. The synthesized film exhibited good crystallinity in the anatase phase. The resulting nanoporous TiO 2 coatings were tested for their functional characteristics. Exposure to UV irradiation for 1 h induced an improvement in the hydrophilicity of coatings with wetting angle reducing to unmeasurable values upon contact with water droplets. Furthermore, their self-cleaning characteristics were tested by measuring the photocatalytic degradation of methylene blue (MB). The synthesized porous TiO 2 nanostructures displayed promising photocatalytic activity, demonstrating the degradation of approximately 92% of MB after 180 min under ultraviolet (UV) light irradiation. Thus, the level of performance was comparable to the photoactivity of commercial anatase TiO 2 nanoparticles of the same quantity. Our results highlight a new robust approach for designing hydrophilic self-cleaning coatings with controlled porosity and composition.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A neural network‐enhanced reproducing kernel particle method for modeling strain localization

Abstract Modeling the localized intensive deformation in a damaged solid requires highly refined discretization for accurate prediction, which significantly increases the computational cost. Although adaptive model refinement can be employed for enhanced effectiveness, it is cumbersome for the traditional mesh‐based methods to perform while modeling the evolving localizations. In this work, neural network‐enhanced reproducing kernel particle method (NN‐RKPM) is proposed, where the location, orientation, and shape of the solution transition near a localization is automatically captured by the NN approximation via a block‐level neural network (NN) optimization. The weights and biases in the blocked parameterization network control the location and orientation of the localization. The designed basic four‐kernel NN block is capable of capturing a triple junction or a quadruple junction topological pattern, while more complicated localization topological patters are captured by the superposition of multiple four‐kernel NN blocks. The standard RK approximation is then utilized to approximate the smooth part of the solution, which permits a much coarser discretization than the high‐resolution discretization needed to capture sharp solution transitions with the conventional methods. A regularization of the NN approximation is additionally introduced for discretization‐independent material responses. The effectiveness of the proposed NN‐RKPM is verified by a series of numerical verifications.

Baek, Jonghyuk↗
DOE OSTI2021

Automating Discovery of Physics-Informed Neural State Space Models via Learning and Evolution

Recent works exploring deep learning application to dynamical systems modeling have demonstrated that embedding physical priors into neural networks can yield more effective, physically-realistic, and data-efficient models. However, in the absence of complete prior knowledge of a dynamical system's physical characteristics, determining the optimal structure and optimization strategy for these models can be difficult. In this work, we explore methods for discovering neural state space dynamics models for system identification. Starting with a design space of block-oriented state space models and structured linear maps with strong physical priors, we encode these components into a model genome alongside network structure, penalty constraints, and optimization hyperparameters. Demonstrating the overall utility of the design space, we employ an asynchronous genetic search algorithm that alternates between model selection and optimization and obtains accurate physically consistent models of three physical systems: an aerodynamics body, a continuous stirred tank reactor, and a two tank interacting system.

genetic algorithms, neural architecture search, ne↗
DOE OSTI2024

IEA Wind TCP Task 49: Reference Site Conditions for Floating Wind Arrays

This report, prepared within Work package 1 of IEA Wind Task 49, presents reference site conditions for floating wind arrays to serve as a design basis for the techno-economic design of reference floating wind arrays. Data of the reference sites presented here are publicly available in an open database and thus support fast development and comparable design of floating wind arrays for various relevant conditions. The development of these reference sites drew on existing open access datasets and ongoing research projects of task participants. Six classes were identified that describe relevant key conditions for the design and development of floating wind arrays: met-ocean conditions, seabed conditions, coastal infrastructure, environmental impact, socio-economic impact, as well as regulations and permissions. The reference sites for the techno-economic design of floating wind arrays are based on a concept with building blocks to synthesize purpose-built site representations. In each of the identified classes with influencing design factors, building blocks are used to describe the characteristic properties and their spread. However, the latter three classes (i.e., environmental impact, socio-economic impact, regulations and permissions) are not included in the reference site conditions due to limited knowledge and lack of reliable criteria to quantify their impact on the techno-economic design in numeric parameters. Building blocks with key parameters for the techno-economic design of floating wind arrays are provided for met-ocean conditions, seabed conditions, and coastal infrastructure. For met-ocean conditions, multiple sites were selected for detailed analysis that represent a range of conditions across the pipeline of floating wind projects. Wind conditions and sea states are separated, and each location considers both the severity of wind and waves e.g. one site may have a moderate wave condition but severe wind condition. From this pipeline, eleven representative sites were selected where both site-specific analysis was available within the consortium, and where they represent different parts of the global pipeline. The eleven sites are: Hannibal (Italy), Humboldt (US), Ulsan (South Korea), MoneyPoint One (Ireland), Havbredey (UK), Fukushima (Japan), Utsira Nord (Norway), Gulf of Maine (US), Sud de la Bretagne II (France), Sorlige Nordsjo II (Norway). Each of these sites is summarized in the main report while more details about the studies and analyses behind the datasets are provided in the appendix. For seabed conditions, general information about the geotechnical parameters is provided and a baseline is established for the geotechnical parameters and stratigraphy that may be encountered on the sites. A set of six 'synthetic cases' is defined as building blocks providing the different parameters required for design under each case/soil condition. For the coastal infrastructure, general information about the main requirements is provided that a port should comply with to provide a satisfactory service during the construction of floating offshore wind arrays. Minimum port infrastructural requirements are provided for three types of ports.

17 WIND ENERGY↗
DOE OSTI2023

Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Hydrogen-Bonded Organic Frameworks: A Rising Class of Porous Molecular Materials

Hydrogen-bonded organic frameworks (HOFs) are a class of porous molecular materials that rely on the assembly of organic building blocks by means of hydrogen-bonding interactions to form two-dimensional (2D) and three-dimensional (3D) crystalline networks. The reversible nature of the hydrogen-bond formation endows HOFs with the attributes of solution processability and simple regeneration. High-quality single crystals of HOFs can be grown easily for unambiguous superstructure determination by single-crystal X-ray diffraction, which is crucial for the elucidation of superstructure–property relationships. During the past decade, considerable progress has been achieved in realizing stable HOFs with permanent porosities by focusing on the design of molecular building blocks in order to introduce rigidity, auxiliary [π···π] interactions, and interpenetration of their frameworks to sustain the extended networks. The applications of HOFs are far-reaching, spanning catalysis, energy, and biomedical products as well as the storage and separation of fine chemicals. In this paper, we, first of all, provide an overview of the chronological development of HOFs, starting from the seminal work by Marsh and Duchamp in 1969 on the crystal superstructure of the hydrogen-bonded networks of trimesic acid. We identify the development of novel hydrogen-bonding motifs such as diaminotriazine (DTA), the introduction of the concept of molecular tectonics, and the establishment of permanent porosity in HOFs as being some of the milestones, which incentivized the current burgeoning research endeavors on developing HOFs as multifunctional materials. This Account is focused primarily on surveying the strategies for constructing porous 3D HOFs based on organic building blocks with peripheral carboxyl groups. These strategies are presented in the following categories: (1) the polycatenation of 2D networks by trigonal building blocks to form global 3D frameworks, (2) the utilization of building blocks with 3D geometries—tetrahedral and trigonal prismatic—that are predisposed to form 3D networks, and (3) the docking by shape-fitting of geometrically labile building blocks. We emphasize how the molecular geometry of the building blocks plays an important role in modulating the superstructures of extended frameworks so as to address specific applications. Recognizing that the in silico design of HOFs is the ultimate goal of researchers in this field, we also discuss the recent advances in superstructure prediction that lead to the formation of porous supramolecular crystals and assess the complications in implementing computational methods for HOFs with complex superstructures. We hope this Account will inspire the development of new supramolecular designs and creative approaches to crystal engineering that aid and abet the assembly of multifunctional HOFs with customizable properties.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Applying Mechanistic Co-Design Towards Room-Temperature Organic, Optical, and Multiple-Center Molecular Qubits

The next generation of qubits, the building blocks of quantum technologies, are designed using molecules. Molecular qubits have natural advantages over solid-state equivalents in biological and chemical sensing. Chemistry allows the properties of molecular qubits to be fine-tuned, such as the ability of multiple qubits to work together using qubit-qubit coupling. Molecules and structures containing multiple qubits, made from both inorganic and organic elements, are developed in this work to bring quantum technologies closer to room-temperature operation. The goal is achieved by understanding how the core of the qubit, known as spin, interacts with the vibrating parts of the molecule, other spins, and the surrounding environment. A combined approach involving theory, spectroscopy, and synthesis is used to achieve the design goal.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Structural Diversity in Dimension-Controlled Assemblies of Tetrahedral Gold Nanocrystals

Polyhedron packings have fascinated humans for centuries and continue to inspire scientists of modern disciplines. Despite extensive computer simulations and a handful of experimental investigations, understanding of the phase behaviors of synthetic tetrahedra has remained fragmentary largely due to the lack of tetrahedral building blocks with tunable size and versatile surface chemistry. Here, in this study, we report the remarkable richness of and complexity in dimension-controlled assemblies of gold nanotetrahedra. By tailoring nanocrystal interactions from long-range repulsive to hard-particle-like or to systems with short-ranged directional attractions through control of surface ligands and assembly conditions, nearly a dozen of two-dimensional and three-dimensional superstructures including the cubic diamond and hexagonal diamond polymorphs are selectively assembled. We further demonstrate multiply twinned icosahedral supracrystals by drying aqueous gold nanotetrahedra on a hydrophobic substrate. This study expands the toolbox of the superstructure by design using tetrahedral building blocks and could spur future computational and experimental work on self-assembly and phase behavior of anisotropic colloidal particles with tunable interactions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The Analog Front-end for the LGAD Based Precision Timing Application in CMS ETL

The analog front-end for the Low Gain Avalanche Detector (LGAD) based precision timing application in the CMS Endcap Timing Layer (ETL) has been prototyped in a 65 nm CMOS mini-ASIC named ETROC0. Serving as the very first prototype of ETL readout chip (ETROC), ETROC0 aims to study and demonstrate the performance of the analog frontend, with the goal to achieve 40 to 50 ps time resolution per hit with LGAD (therefore reach about 30ps per track with two detector-layer hits per track). ETROC0 consists of preamplifier and discriminator stages, which amplifies the LGAD signal and generates digital pulses containing time of arrival and time over threshold information. This paper will focus on the design considerations that lead to the ETROC front-end architecture choice, the key design features of the building blocks, the methodology of using the LGAD simulation data to evaluate and optimize the front-end design. The ETROC0 prototype chips have been extensively tested using charge injection and the measured performance agrees well with simulation. The initial beam test results are also presented, with time resolution of around 33 ps observed from the preamplifier waveform analysis and around 41 ps from the discriminator pulses analysis. A subset of ETROC0 chips have also been tested to a total ionizing dose of 100 MRad with X-ray and no performance degradation been observed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Modular Wide-bandgap String Inverters for Low-cost Medium-voltage Transformerless PV Systems

The proposed technology combines advances in wide-bandgap power electronics with breakthroughs in distributed and decentralized control to produce ultra-low-cost medium-voltage transformerless PV inverters that are composed of stackable lightweight blocks. Taken together, the proposed circuit designs and accompanying control strategies will yield integrated control+circuit (C2) blocks, each comprising a converter and local controller, that can be assembled in a modular fashion to obtain distributed conversion interfaces for next-generation commercial and utility-scale PV systems. We will utilize SiC devices to obtain C2 blocks that can individually operate at a voltage and power in excess of 1 kV and 100 kW, respectively, such that ensembles of series-connected blocks perform direct dc to three-phase ac conversion at medium voltages (e.g., 12 kV–35 kV) and at multi-MW power levels.

42 ENGINEERING↗
DOE OSTI2022

Porous but Mechanically Robust All-Inorganic Antireflective Coatings Synthesized using Polymers of Intrinsic Microporosity

Herein, we introduce polymer of intrinsic microporosity 1 (PIM-1) to design single-layer and multilayered all-inorganic antireflective coatings (ARCs) with excellent mechanical properties. Using PIM-1 as a template in sequential infiltration synthesis (SIS), we can fabricate highly uniform, mechanically stable conformal coatings of AlO x with porosities of ~50% and a refractive index of 1.41 compared to 1.76 for nonporous AlO x that is perfectly suited for substrates commonly used in high-end optical systems or touch screens (e.g., sapphire, conductive glass, bendable glass, etc.). We show that such films can be used as a single-layer ARC capable of reduction of the Fresnel reflections of sapphire to as low as 0.1% at 500 nm being deposited only on one side of the substrate. We also demonstrate that deposition of the second layer with higher porosity using block copolymers enables the design of graded-index double-layered coatings. AlO x structures with just two layers and a total thickness of less than 200 nm are capable of reduction of Fresnel reflections under normal illumination to below 0.5% in a broad spectral range with 0.1% reflection at 700 nm. Additionally, and most importantly, we show that highly porous single-layer and graded-index double-layered ARCs are characterized by high hardness and scratch resistivity. The hardness and the maximum reached load were 7.5 GPa and 13 mN with a scratch depth of about 130 nm, respectively, that is very promising for the structures consisting of two porous AlO x layers with 50% and 85% porosities, correspondingly. Such mechanical properties of coatings can also allow their application as protective layers for other optical coatings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Example Evaluation of a Representative Heat Pipe Test Article Design for Structural Acceptability using ASME Design Rules

This report describes a design analysis of a test article mimicking a core block of a heat-pipe mi-croreactor using the ASME Boiler & Pressure Vessel Code Section III, Division 5, Subsection HB, Subpart B rules. These rules cover the design and construction of elevated temperature nu-clear reactor structural components, like the core block of a heat-pipe microreactor emulated by the test article. The purposes of the report are to: (1) provide a step-by-step example of applying the ASME rules to a reasonable core block geometry and corresponding loading conditions, (2) to provide design feedback on the test article, and (3) to evaluate the ASME rules for use in the design of complex heat-pipe microreactor components. The test article design has a relatively short ASME design life, limited by high thermal stresses. The current ASME rules are adequate for evaluating the core block component designs, though they could be optimized to increase the design efficiency and reduce the amount of designer/analyst time required to execute the design process. The report covers both the current, 2019 edition ASME rules and modified, currently unapproved, rules designed to improve the design process for components with complex geometries and high secondary stresses, like the core block test article.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm

Directed self-assembly (DSA) of block copolymers (BCPs) is one of the most promising developments in the cost-effective production of nanoscale devices. The process makes use of the natural tendency for BCP melts to form nanoscale structures upon phase separation. The phase separation can be directed through the use of chemically patterned substrates to promote the formation of morphologies that are essential to the production of semiconductor devices. Moreover, the design of substrate pattern can be formulated as an optimization problem for which we seek optimal substrate designs that effectively produce given target morphologies. In this paper, we adopt a phase field model given by a nonlocal Cahn–Hilliard partial differential equation (PDE) based on the minimization of the Ohta–Kawasaki free energy, and present an efficient PDE-constrained optimization framework for the optimal design problem. The design variables are the locations of circular- or strip-shaped guiding posts that are used to model the substrate chemical pattern. To solve the ensuing optimization problem, we propose a variant of an inexact Newton conjugate gradient algorithm tailored to this problem. Additionally, we demonstrate the effectiveness of our computational strategy on numerical examples that span a range of target morphologies. Owing to our second-order optimizer and fast state solver, the numerical results demonstrate five orders of magnitude reduction in computational cost over previous work. The efficiency of our framework and the fast convergence of our optimization algorithm enable us to rapidly solve the optimal design problem in not only two, but also three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Augmented DNA Nanoarchitectures: A Structural Library of 3D Self-Assembling Tensegrity Triangle Variants

The DNA tensegrity triangle is known to reliably self-assemble into a 3D rhombohedral crystalline lattice via sticky-end cohesion. Here, in this study, the library of accessible motifs is expanded through covalent extensions of intertriangle regions and sticky-end-coordinated linkages of adjacent triangles with double helical segments using both geometrically symmetric and asymmetric configurations. The molecular structures of 18 self-assembled architectures at resolutions of 3.32–9.32 Å are reported; the observed cell dimensions, cavity sizes, and cross-sectional areas agree with theoretical expectations. These data demonstrate that fine control over triclinic and rhombohedral crystal parameters and the customizability of more complex 3D DNA lattices are attainable via rational design. It is anticipated that augmented DNA architectures may be fine-tuned for the self-assembly of designer nanocages, guest–host complexes, and proscriptive 3D nanomaterials, as originally envisioned. Finally, designer asymmetric crystalline building blocks can be seen as a first step toward controlling and encoding information in three dimensions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Cost function dependent barren plateaus in shallow parametrized quantum circuits

Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is Ο(logn). Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

97 MATHEMATICS AND COMPUTING↗