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NASA NTRSDate not supplied

Advancement of Extreme Environment Additively Manufactured Alloys for Next Generation Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has been involved in the development and maturation of metal additive manufacturing (AM) for space applications since the late 2000’s. Several efforts focused on the understanding of AM processes through material characterization and testing, standards development, component fabrication, and infusion into propulsion development and flight applications. NASA matured commonly used aerospace alloys from various alloy families (Nickel, Copper, Stainless and Steel, Aluminum, and Titanium-based) through detailed AM process and heat treatment characterization, in addition to mechanical and thermophysical testing. While these alloys are actively used in many propulsion applications, there is a need for ongoing AM optimized alloys using integrated computational materials engineering (ICME) and process development for high performance applications. The applications targeted are liquid rocket engines; advanced propulsion systems; and in-space propulsion with high heat fluxes, high pressure, and/or that use propellants that can degrade alloys (e.g., hydrogen). This paper highlights the characterization and physical properties of the more common AM alloys using laser powder bed fusion (L-PBF) and laser powder directed energy deposition (LP-DED) processes. Additionally, this paper discusses some of the ongoing novel alloy development and maturation using AM for use in these harsh environments, such as GRCop42, GRCop-84, NASA HR-1, GRX-810, and C-103. The results from these processes demonstrated that AM could enable rapid development and ongoing efforts for optimized alloys using ICME, yielding higher performances. These alloys have undergone modeling, fundamental metallurgical evaluations, heat treatment studies, detailed microstructure characterization, and mechanical testing campaigns. This, combined with direct application-specific component fabrication and hot-fire testing, enabled the increase of the Technology Readiness Level (TRL) through high duty-cycle testing. A background and overview of these novel AM-enabled alloys and AM processing developments including metallurgical and mechanical property studies is presented here. The latest advancement in the parallel component development and hot-fire testing and future developments for these alloys is also discussed.

Additive Manufacturing↗

NASA NTRSDate not supplied

Advancement of Extreme Environment Additively Manufactured Alloys for Next Generation Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has been involved in the development and maturation of metal additive manufacturing (AM) for space applications since the late 2000’s. Several efforts focused on the understanding of AM processes through material characterization and testing, standards development, component fabrication, and infusion into propulsion development and flight applications. NASA matured commonly used aerospace alloys from various alloy families (Nickel, Copper, Stainless and Steel, Aluminum, and Titanium-based) through detailed AM process and heat treatment characterization, in addition to mechanical and thermophysical testing. While these alloys are actively used in many propulsion applications, there is a need for ongoing AM optimized alloys using integrated computational materials engineering (ICME) and process development for high performance applications. The applications targeted are liquid rocket engines; advanced propulsion systems; and in-space propulsion with high heat fluxes, high pressure, and/or that use propellants that can degrade alloys (e.g., hydrogen). This paper highlights the characterization and physical properties of the more common AM alloys using laser powder bed fusion (L-PBF) and laser powder directed energy deposition (LP-DED) processes. Additionally, this paper discusses some of the ongoing novel alloy development and maturation using AM for use in these harsh environments, such as GRCop-42, GRCop-84, NASA HR-1, GRX-810, and C-103. The results from these processes demonstrated that AM could enable rapid development and ongoing efforts for optimized alloys using ICME, yielding higher performances. These alloys have undergone modeling, fundamental metallurgical evaluations, heat treatment studies, detailed microstructure characterization, and mechanical testing campaigns. This, combined with direct application-specific component fabrication and hot-fire testing, enabled the increase of the Technology Readiness Level (TRL) through high duty-cycle testing. A background and overview of these novel AM-enabled alloys and AM processing developments including metallurgical and mechanical property studies is presented here. The latest advancement in the parallel component development and hot-fire testing and future developments for these alloys is also discussed.

Additive Manufacturing↗

NASA NTRS1979

Computational methods for analyzing the transmission characteristics of a beta particle magnetic analysis system

Computational methods were developed to study the trajectories of beta particles (positrons) through a magnetic analysis system as a function of the spatial distribution of the radionuclides in the beta source, size and shape of the source collimator, and the strength of the analyzer magnetic field. On the basis of these methods, the particle flux, their energy spectrum, and source-to-target transit times have been calculated for Na-22 positrons as a function of the analyzer magnetic field and the size and location of the target. These data are in studies requiring parallel beams of positrons of uniform energy such as measurement of the moisture distribution in composite materials. Computer programs for obtaining various trajectories are included.

Singh, J. J.↗

NASA NTRSDate not supplied

Maturation of Additive Manufactured Aerospace Alloys and Development of Mechanical and Thermophysical Properties for Space Applications

The National Aeronautics and Space Administration (NASA) has been involved in the development and maturation of metal additive manufacturing (AM) for space applications since the late 2000’s. Several efforts have focused on the understanding of AM processes through design optimization, component fabrication, material characterization, testing, standards development, and infusion into propulsion development for flight applications. NASA and partners have matured commonly used aerospace alloys from various alloy families (Nickel, Steel, Iron, Aluminum, and Titanium) and AM processes. An extensive effort has been ongoing between NASA, industry partners, and academia to complete detailed AM process and heat treatment characterization, in addition to generating temperature-dependent mechanical and thermophysical properties. This presentation highlights the characterization and property results using laser powder bed fusion (L-PBF) and laser powder directed energy deposition (LP-DED) processes among various alloys. In addition to commonly used alloys, there is a need for ongoing AM optimized alloys using integrated computational materials engineering (ICME) and process development for high performance applications. The applications targeted are launch vehicles, liquid rocket engines, advanced propulsion systems, advanced power systems, and in-space propulsion with high heat fluxes, high pressure, and that utilize propellants such as hydrogen, which can degrade alloys. This presentation will also discuss some of the ongoing novel alloy development and maturation using AM for use in these harsh environments, such as GRCop-42, GRCop-84, NASA HR-1, and C-103. The results from these processes have demonstrated that AM can enable rapid development and new AM optimized alloys can yield higher performance. These alloys have undergone modeling, fundamental metallurgical evaluations, heat treatment studies, and microstructure characterization and mechanical testing campaigns. This, combined with direct application-specific component fabrication and hot-fire testing, can enable the increase of the Technology Readiness Level (TRL) through high duty-cycle testing. This presentation provides a background and overview of these various common and AM-enabled alloys and processing developments including the initial effort related to metallurgical, mechanical, and thermophysical property studies. It also covers the latest advancement in the parallel component development, hot-fire testing, and future developments for these alloys.

Additive Manufacturing↗

DOE OSTI2025

Directed energy deposition of functionally graded V-4Cr-4Ti to Fe-9Cr transition for fusion power systems

This study proposes a graded structure via additive manufacturing for divertor and first wall blanket applications in fusion reactors. Materials were selected based on thermodynamic calculations to operate from 1100 °C at the plasma-facing level to 550 °C at the structural steel level. Conventional joining methods often lead to failures due to discrete reaction layers with significant mechanical property differences. Using laser beam-directed energy deposition (LB-DED), this study demonstrates the fabrication of a VCrTi-Gr91 steel functionally graded component through a novel process parameter optimization framework. A systematic approach included powder characterization, single-track depositions, and construction of printability maps. Near full-density specimens of each interlayer were additively manufactured, and a transition from V-based alloys to reduced activation ferritic martensitic steels was achieved. Computational material selection of interlayer alloys and thermodynamic/diffusion kinetics simulations prevented most interface incompatibilities. A brittle intermetallic formed at one interface, causing cracking, which was not predicted by current thermodynamic models. Transition alloy design approach was updated with a more recent database and a mitigation strategy has been proposed to eliminate the formation of deleterious intermetallic phases. Ultimately, LB-DED has proven effective for producing multi-material graded systems for fusion applications, with the demonstrated process parameter optimization framework applicable to various materials.

Additive manufacturing↗

NASA NTRSDate not supplied

Natural Fiber Simulations and Analysis for Composites

As the U.S. government and the aviation industry strive to achieve net-zero carbon emissions by 2050, the Sustainable Manufacturing of Aircraft (SUMAC) project, supported by the Convergent Aeronautics Solutions (CAS) program of the National Aeronautics and Space Administration (NASA), aims to develop sustainably derived thermoplastic composites and manufacturing technologies for future aviation. A multidisciplinary team of experts drives this initiative through a collective effort. The team’s key focus areas are sustainably derived thermoplastic resins, natural fiber reinforcement, composite manufacturing, structural health monitoring, computational materials modeling, and systems analysis. This presentation will give an overview of the SUMAC project. Fiber-scale microscopy analysis characterized fiber cross sections finding that hemp and flax fibers are very deformable and non-circular (circularities of 0.2 were observed), and diameters range from submicron to 20 μm. Fiber shapes range from flattened, with aspect ratios Rlong/Rshort up to 5, to round, Rlong/Rshort =1. And Fiber core perimeters, which likely drives deformability, were calculated Pcore=7 μm. Explicit-fiber yarn simulations, parameterized from single-fiber measurements, resolved and identified slack as a cause for yarn strain-hardening tensile behavior. The bonded network model of PLA, PHA and PA11 resins captures tensile behavior, and can model an infused weave. Computational models of the weave unit cells matched the pattern (including plain, twill and triaxial braid), yarn ply (1to 2), and yarn twist from optical microscopy.

thermoplastic↗

NASA NTRSDate not supplied

Natural Fiber Simulations and Analysis for Composites

thermoplastic↗

DOE OSTI2025

Driving rapid atomic order in MnAl via low-magnitude magnetic field annealing

Application of a mild (60 mT), uniform magnetic field during short-term thermal treatment of kinetically retained, atomically disordered (paramagnetic) ε-MnAl was found to deliver a significant ~50 % increase in the formation of L1 0 atomically ordered (ferromagnetic) τ-MnAl product phase, compared to that produced by conventional (i.e., zero-field) annealing under identical thermal conditions. The magnetic field, applied in a passive closed-circuit configuration during annealing, induced significant changes in the structural, magnetic, and phase evolution of the material. Computational results based on electronic structure calculations demonstrate that the effective magnetic susceptibility of τ-MnAl is sensitive to the orientation, rather than the magnitude, of an applied magnetic field in the vicinity of the Curie temperature. The uniaxial magnetocrystalline anisotropy of the L1 0 structure is proposed to act as a filter for selective propagation of the population of τ-MnAl variants that are favorably aligned with the applied field. In this manner, crystallographic “gridlock” is alleviated that would otherwise arise from the coexistence of multiple, energetically equivalent τ-phase variants within the parent ε-phase matrix. These results confirm that static, low-magnitude magnetic field annealing is able to accelerate L1 0 atomic ordering in the MnAl system and likely can exert similar influences in relevant magnetic systems, facilitating efficient tailoring of structure-sensitive magnetic properties for the manufacture of magnetic materials.

36 MATERIALS SCIENCE↗

NASA NTRS2004

adwTools Developed: New Bulk Alloy and Surface Analysis Software for the Alloy Design Workbench

A suite of atomistic modeling software, called the Alloy Design Workbench, has been developed by the Computational Materials Group at the NASA Glenn Research Center and the Ohio Aerospace Institute (OAI). The main goal of this software is to guide and augment experimental materials research and development efforts by creating powerful, yet intuitive, software that combines a graphical user interface with an operating code suitable for real-time atomistic simulations of multicomponent alloy systems. Targeted for experimentalists, the interface is straightforward and requires minimum knowledge of the underlying theory, allowing researchers to focus on the scientific aspects of the work. The centerpiece of the Alloy Design Workbench suite is the adwTools module, which concentrates on the atomistic analysis of surfaces and bulk alloys containing an arbitrary number of elements. An additional module, adwParams, handles ab initio input for the parameterization used in adwTools. Future modules planned for the suite include adwSeg, which will provide numerical predictions for segregation profiles to alloy surfaces and interfaces, and adwReport, which will serve as a window into the database, providing public access to the parameterization data and a repository where users can submit their own findings from the rest of the suite. The entire suite is designed to run on desktop-scale computers. The adwTools module incorporates a custom OAI/Glenn-developed Fortran code based on the BFS (Bozzolo- Ferrante-Smith) method for alloys, ref. 1). The heart of the suite, this code is used to calculate the energetics of different compositions and configurations of atoms.

Bozzolo, Guillermo↗

DOE OSTI2025

Control of solvent adsorption in porous liquids through solvent-solvent interactions

Type 3 Porous Liquids (PLs) are a new class of materials that offer transformative potential for gas capture and utilization. These PLs are comprised of a bulky solvent with a suspended empty nanoporous material that enables selective and high-capacity capture from dilute and complex gas steams. The relationship between the nanoporous material, the structure of the solvent molecules, and the time dependence of solvent adsorption into the nanoporous material governs long term adsorption properties. Herein, molecular dynamics (MD) calculations evaluated the solvent dynamics of nine neat solvents with a broad range of chemical identities and experimental density measurements probed the time-dependent adsorption of these solvents into the ZIF-8 metal-organic frameworks (MOFs) to form PL dispersions over three weeks. Two of the nine dispersion, using glyceryl triacetate and 2’-hydroxyacetopheneone as solvents, presented sufficiently low solvent infiltration—characterized by solvent adsorption less than 40% of the ZIF-8 pore volume—to be viable as PLs. The experimental solvent adsorption data for ZIF-8 dispersed in the four aromatic solvents (acetophenone, methylbenzoate, 2-isopropylphenol, and 2’-hydroxyacetophenone) was fit to a kinetic model to quantify rate of solvent adsorption into ZIF-8. The rates of adsorption of these four similar-sized solvents demonstrated that solvent adsorption is slowed and limited by solvent clustering dynamics that are, in turn, driven by intermolecular hydrogen bonding. Ultimately, experimental solvent sorption measurements indicated that glyceryl triacetate and 2’-hydroxyacetophenone with ZIF-8 formed PLs with the most stable porosity and the greatest potential for gas capture. In conclusion, the combined experimental-computational materials exploration framework used here reveals a novel relationship between molecular scale solvent dynamics and macroscale solvent adsorption kinetics critical for the discovery and rapid evaluation of Type 3 PL compositions.

Hydrogen bonding↗

DOE OSTI2026

Model-based, in-situ, non-destructive qualification and certification of parts made by autonomous additive manufacturing

To address the significant productivity challenges associated with the qualification and certification (Q&C) tasks of additively manufactured (AM) parts, which have traditionally relied on rigorous post‐build inspection and testing, we propose an integrated framework that combines model‐based qualification and certification (MBQ&C) with autonomous additive manufacturing (AAM). MBQ&C employs high‐fidelity predictive models, developed within the Integrated Computational Materials Engineering (ICME) paradigm, to simulate process–structure–property–performance relationships for assessing a part’s fitness for use. Since predictive models are commonly machine learning (ML)-based or reduced-order surrogates of validated physics models, they run efficiently, enabling timely inference. In parallel, the self-driving AAM utilises ML-based adaptive, closed‐loop control strategies to avoid, mitigate, or repair defects and anomalies during fabrication, thereby increasing the likelihood of producing acceptable parts. A key feature of the combined AAM-MBQ&C framework is that predictive models explicitly incorporate defects or anomalies that persist after the build, using instance-specific data captured via in-situ sensing. This customisation enables a build‐specific assessment of fitness for use, rather than relying on nominal or generic parameters. Such individualised evaluation provides a robust basis for Q&C-related acceptance decisions relating to each build. Additionally, the rapid solution capabilities of ML or reduced-order models enable the determination of a part’s suitability for service shortly after build completion. As the framework matures, it has the potential to substantially reduce reliance on conventional point‐design approaches—such as time‐consuming post‐build computed tomography scanning and costly destructive testing. Thus, the AAM-MBQ&C framework represents a transformative, scalable strategy for quality assurance of AM components, as parts produced within a stable, validated, and certified envelope can be certified with reduced testing. Key benefits include: (1) significant gains in Q&C productivity through efficient, model-centric assessment; (2) performance-based classification of defects into critical and non-critical categories; (3) the ability to predict potential deviations in the performance of parts affected by real-time, adaptive process control interventions relative to those produced under a certified process, and (4) the enabling of virtual Q&C for service environments that are difficult, hazardous, or impractical to access or reproduce experimentally. Collectively, these capabilities strengthen the business case for AM, particularly for high‐consequence and mission‐critical applications. Finally, although this work focuses on powder-based AM, the proposed techniques could be extended to AM processes employing alternative feedstock forms.

Gunasegaram, Dayalan↗

NASA NTRSDate not supplied

Ab initio ground states of strongly-correlated materials on quantum computers

The accurate first-principles description of strongly-correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving accurate many-body Hamiltonians including strong correlations, representing a subspace of interest of a material, using density functional theory calculations as a starting point. However, the solution of these material-specific models can scale exponentially on classical computers, constituting a challenge. Here we propose that utilizing quantum computers for obtaining the properties of downfolded Hamiltonians yields an accurate description of the ground state properties of strongly-correlated systems, while circumventing the exponential scaling problem. We benchmark the solution of Hubbard-like models obtained through downfolding by utilizing a classical tensor network implementation of variational quantum eigensolvers (VQE), and we reveal a strategy for driving the optimization through a hybrid minimization of the energy and maximization of the overlap with an approximate solution obtained through low-cost computational methods. This results in a reduction of the energy error by orders of magnitude compared to conventional VQE approaches, and allows us to reproduce long-range correlations for the first time. We demonstrate our first-principles approach for diverse strongly-correlated materials, correctly predicting the antiferromagnetic state of one-dimensional cuprate Ca 2 CuO 3 , the excitonic ground state of monolayer WTe2, and the charge-ordered state of correlated metal SrVO 3 . Our efficient computational implementation allows us to simulate large systems with up to 54 qubits and encompassing up to four correlated bands, which is indicative of the complexity that our framework can address.

Antonios M Alvertis↗

DOE OSTI2025

The design space of E(3)-equivariant atom-centred interatomic potentials

Abstract Molecular dynamics simulation is an important tool in computational materials science and chemistry, and in the past decade it has been revolutionized by machine learning. This rapid progress in machine learning interatomic potentials has produced a number of new architectures in just the past few years. Particularly notable among these are the atomic cluster expansion, which unified many of the earlier ideas around atom-density-based descriptors, and Neural Equivariant Interatomic Potentials (NequIP), a message-passing neural network with equivariant features that exhibited state-of-the-art accuracy at the time. Here we construct a mathematical framework that unifies these models: atomic cluster expansion is extended and recast as one layer of a multi-layer architecture, while the linearized version of NequIP is understood as a particular sparsification of a much larger polynomial model. Our framework also provides a practical tool for systematically probing different choices in this unified design space. An ablation study of NequIP, via a set of experiments looking at in- and out-of-domain accuracy and smooth extrapolation very far from the training data, sheds some light on which design choices are critical to achieving high accuracy. A much-simplified version of NequIP, which we call BOTnet (for body-ordered tensor network), has an interpretable architecture and maintains its accuracy on benchmark datasets.

Computer Science↗

DOE OSTI2025

Compressing Hamiltonians with ab initio downfolding for simulating strongly-correlated materials on quantum computers

The accurate first-principles description of strongly correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving compressed many-body Hamiltonians that maintain the essential physics of strongly correlated materials. The solution of these material-specific models is still exponentially difficult to generate on classical computers, but quantum algorithms allow for a significant speed-up in obtaining the ground states of these compressed Hamiltonians. Here, we demonstrate that using quantum algorithms to obtain the properties of downfolded Hamiltonians can indeed yield high-fidelity solutions. By combining ab initio downfolding and variational quantum eigensolvers, we correctly predict the antiferromagnetic state of one-dimensional cuprate Ca 2 Cu O 3 , the excitonic ground state of monolayer W Te 2 , and the charge-ordered state of correlated metal Sr VO 3 . Numerical simulations using a classical tensor network implementation of variational quantum eigensolvers allow us to simulate large models with up to 54 qubits and encompassing up to four bands in the correlated subspace, which is indicative of the complexity that our framework can address. Through these methods we demonstrate the potential of classical preoptimization and downfolding techniques for enabling efficient materials simulation using quantum algorithms.

Alvertis, Antonios M. [NASA, Ames; LBNL, Berkeley]↗

DOE OSTI2026

Benchmarking of massively parallel phase-field codes for directional solidification

We present a detailed benchmark comparing two state-of-the-art phase-field implementations for simulating alloy solidification under experimentally relevant conditions. The study investigates the directional solidification of Al-3wt%Cu under high-velocity solidification conditions and SCN-0.46wt% camphor under microgravity conditions from National Aeronautics and Space Administration (NASA) DECLIC-DSI-R experiments. Both codes, one employing finite-difference discretization with uniform mesh and GPU-acceleration (GPU-PF) and the other one employing finite-element discretization with adaptive-mesh and CPU-parallelization (PRISMS-PF), solve the same quantitative phase-field formulation that incorporates an anti-trapping current for the solidification of dilute alloys. We evaluate the predictions of each code for dendritic morphology, primary spacing, and tip dynamics in both 2D and 3D, as well as their numerical convergence and computational performance. While existing benchmark problems have primarily focused on simplified or small-scale simulations, they do not reflect the computational and modeling challenges posed by employing experimentally relevant time and length scales. Our results provide a practical framework for assessing phase-field code performance as well as validating and facilitating their application in integrated computational materials engineering (ICME) workflows that require integration with realistic experimental data.

36 MATERIALS SCIENCE↗

DOE OSTI2025

CALPHAD-based ICME design of single-step aging to enhance mechanical strength of WAAM Haynes 282

To match the strength of wire-arc additive manufactured Haynes 282 to its wrought counterpart via a single-step aging heat treatment, the CALPHAD (Calculation of Phase Diagrams) method is integrated with physics-based process-structure-property models and experimental validation. The integrated computational materials engineering (ICME) framework simulates the effects of aging on γ′ and M 23 C 6 precipitation and the resulting yield strength. To improve simulation reliability, the interfacial energies between γ/γ′ and γ/M 23 C 6 carbides were estimated by comparison with precipitation kinetic modeling and measured precipitate sizes. γ′ and M23C6 were found to precipitate simultaneously between 640 and 860 °C, producing microstructures similar to those produced by two-step aging. The optimal γ′ size for peak yield stress was calculated to be 20–23 nm. WAAM Haynes 282 aged at 780 °C for 50 h exceeded the mechanical performance of its wrought counterpart subjected to two-step aging, though desired properties can also be achieved at 800 °C for 16 h or less. The error in yield strength is less than 20 MPa, demonstrating good agreement between the modeling framework and experiments. Creep studies showed that WAAM Haynes 282 exceeded the calculated rupture time, reaching 481 h. This proposed methodology can accelerate the design of aging heat treatments for any γ′-strengthened nickel-base alloy, minimizing the resources required for trial-and-error experiments.

CALPHAD↗

DOE OSTI2025

Come for predictions, stay for complexity: synthesis and experimental probing of ionic conductivity in Li 9 B 19 S 33

Lithium thioborates, despite their potential cost-effectiveness and low density, have received considerably less attention as solid electrolytes compared to their thiophosphate counterparts. A primary obstacle to their widespread investigation has been the inherent challenge in synthesizing single-phase materials. Computational studies have predicted several lithium thioborate phases exhibiting high ionic conductivity, with Li 9 B 19 S 33 notably predicted to reach 80 mS cm −1 . However, experimental validation of these theoretical predictions remains absent. This work addresses this gap by detailing a successful synthesis of the previously elusive Li 9 B 19 S 33 phase, facilitated by in situ temperature dependent powder X-ray diffraction. Our findings reveal the peritectic nature of phase formation, necessitating an excess of boron sulfide in the reaction mixture. We further present a comprehensive structural characterization of Li 9 B 19 S 33 utilizing spectroscopic techniques like NMR, FT-IR, and diffuse reflectance and report on its ionic conductivity. Solid-state 6 Li NMR line narrowing experiments revealed an ion mobility activation energy of 0.26 eV whereas activation energies derived from impedance spectroscopy measurements were significantly higher, resulting in lower than theoretically predicted ionic conductivity.

Oppong, Richeal A. [Iowa State Univ., Ames, IA (Un↗

DOE OSTI2025

Quantum graph learning and algorithms applied in quantum computer sciences and image classification

Graph and network theory play a fundamental role in quantum computer sciences, including quantum information and computation. Random graphs and complex network theory are pivotal in predicting novel quantum phenomena, where entangled links are represented by edges. Quantum algorithms have been developed to enhance solutions for various network problems, giving rise to quantum graph computing and quantum graph learning (QGL). Here, in this review, we explore graph theory and graph learning methods as powerful tools for quantum computers to generate efficient solutions to problems beyond the reach of classical systems. We delve into the development of quantum complex network theory and its applications in quantum computation, materials discovery, and research. We also discuss quantum machine learning (QML) methodologies for effective image classification using qubits, quantum gates, and quantum circuits. Additionally, the paper addresses the challenges of QGL and algorithms, emphasizing the steps needed to develop flexible QGL solvers. This review presents a comprehensive overview of the fields of QGL and QML, highlights recent advancements, and identifies opportunities for future research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗