This paper proposes the Quantum Geometry® Grand Challenge, a five-year prize and benchmark program for quantum and hybrid quantum–classical methods in computational geometry, computer-aided design (CAD), geographic information science (GIS), and meshing. The central question is where, if anywhere, quantum computation improves a complete geometric workflow. Comparisons would include data preparation, encoding, execution, and output validation. The program would begin by defining benchmarks, without requiring an initial demonstration of quantum advantage. A proposed 2027 pilot would select a small number of spatial-optimization and mesh-partitioning problems and publish classical reference solvers and independent validators. Separate award categories would recognize reproducible positive and negative findings. Two illustrative problems show how the evaluation would work. The paper sets out submission requirements, comparison metrics, judging safeguards, and a staged expansion to CAD, geometric algorithms, and data representations. Quantum Geometry® LLC would initially administer the program and offer conditional founding matching support of up to $100,000 over five years. Expansion would depend on secured resources and independently reproducible pilot results. The contribution is a research-program design that can be tested and evaluation resources that others can reuse; it is not a claim of demonstrated quantum advantage.
This paper proposes the Quantum Geometry® Grand Challenge, a five-year prize and benchmark program for quantum and hybrid quantum–classical methods in computational geometry, computer-aided design (CAD), geographic information science (GIS), and meshing. The central question is where, if anywhere, quantum computation improves a complete geometric workflow. Comparisons would include data preparation, encoding, execution, and output validation. The program would begin by defining benchmarks, without requiring an initial demonstration of quantum advantage. A proposed 2027 pilot would select a small number of spatial-optimization and mesh-partitioning problems and publish classical reference solvers and independent validators. Separate award categories would recognize reproducible positive and negative findings. Two illustrative problems show how the evaluation would work. The paper sets out submission requirements, comparison metrics, judging safeguards, and a staged expansion to CAD, geometric algorithms, and data representations. Quantum Geometry® LLC would initially administer the program and offer conditional founding matching support of up to $100,000 over five years. Expansion would depend on secured resources and independently reproducible pilot results. The contribution is a research-program design that can be tested and evaluation resources that others can reuse; it is not a claim of demonstrated quantum advantage.
Quantum computing is being investigated as a computational approach for medical image analysis, but its potential role in cardiovascular imaging remains unclear. This review examines gate-based, quantum annealing, and hybrid quantum-classical techniques for cardiovascular image enhancement, image reconstruction, image segmentation, image feature extraction, and image-based disease classification, and it treats quantum-inspired classical algorithms as a separate category. The literature was identified through a structured search of four bibliographic databases and one preprint server, using stated eligibility criteria and study-level data extraction. Applications are considered in echocardiography, computed tomography, cardiac magnetic resonance imaging, nuclear imaging, and coronary angiography, and direct cardiovascular evidence is distinguished from methods developed for other medical imaging tasks. One adjacent cardiac study based on chest radiography is reported separately because it falls outside these five modalities. For each study, the imaging data, qubit count, encoding strategy, execution on a simulator or physical hardware, classical baseline, and validation design are tabulated. The review also defines the forms of quantum advantage that a study could claim, quantifies the qubit and state-preparation costs of common image encodings for realistic cardiac image sizes, and compares quantum methods with classical machine learning and deep learning in terms of computational requirements, training, interpretability, and reported performance. The existing evidence is exploratory and relies mostly on small datasets, compressed image representations, and quantum simulators. Some results are encouraging, but no consistent advantage over well-tuned classical approaches has been established. The key obstacles are image encoding, hardware noise, circuit depth, trainability, end-to-end computational cost, and the lack of external validation. Hybrid designs offer a practical setting for testing selected quantum components within current imaging pipelines. Future progress requires reproducible cardiovascular benchmarks, evaluation on physical quantum devices, and staged clinical validation. Quantum computing is therefore an emerging field of study whose role in cardiovascular imaging has to be defined through rigorous technical and clinical comparison.
Quantum and physics-inspired solvers provide specialized sampling interfaces for Ising and quadratic unconstrained binary optimization models, but constrained optimization requires broader coordination and certification. This survey uses classical decomposition to analyze how such solvers can be integrated into hybrid quantum-classical algorithms. We distinguish formal decomposition, reformulation and reduction, and computational orchestration. For each interface, we ask what the transformation preserves, which assumptions make the outer method converge, and which certificates the implemented inner routine supplies. The central questions are whether that information meets the classical algorithm's requirements and whether hybridization improves solution quality or total cost enough to justify its coordination overhead. Benders decomposition, column generation, graph reduction, and copositive methods illustrate this distinction by separating heuristic proposals from classical certification. We also distinguish component effects within a fixed wrapper, reduction--solver interactions, and comparisons between complete quantum-enabled and classical systems. The analyzed studies provide conditional component benefits and favorable co-design evidence, but do not establish transferable end-to-end superiority over strong classical comparators. The resulting framework identifies opportunities for constraint programming and operations research in structure-preserving design, safeguarded hybrid algorithms, and controlled benchmarking.
The prospects for practical quantum computing have improved significantly over the past few years, and there is an increasing motivation for developing quantum algorithms to address problems that are presently impractical to solve using classical computing. In previous work we have indentified such problems in the areas of computer graphics applications, and we have derived quantum-based solutions. In this paper we examine quantum-based solutions to problems arising in the area of computational geometry. These types of problems are important in a variety of scientific, industrial and military applications such as large scale multi-object simulation, virtual reality systems, and multi-target tracking. In particular, we present quantum algorithms for multidimensional searches, convex hull construction, and collision detection.
This paper explores the potential of quantum computing to revolutionize geometry generation, addressing the computational challenges inherent in creating complex geometric transformations. We propose a novel paradigm leveraging quantum computation to design and optimize geometric transformations, aiming to surpass the limitations of classical methods. The core mechanism centers around quantum algorithms for generating and refining geometric primitives, offering a fundamentally different approach to complex shape creation. This research investigates the feasibility of quantum computing for handling geometric transformations with increased efficiency and precision, ultimately leading to a new generation of computational tools for geometric modeling and design. Specifically, we detail the design of a quantum algorithm for generating and manipulating geometric transformations, emphasizing its potential to overcome the computational bottlenecks encountered in traditional approaches. The paper concludes with a discussion of the challenges and future directions of this research.
Quantum-computing application studies often stop at the implementation of an isolated circuit or the solution of a small demonstration problem. Industrial adoption requires a more complete engineering process involving problem formulation, quantum encoding, algorithm selection, execution, verification, resource estimation, comparison with strong classical baselines, and assessment of operational relevance. This paper presents an application-oriented framework for QForge, extending its role as a quantum-computing design, emulation, verification, and algorithmdevelopment platform. The framework maps quantum and hybrid methods—including the Quantum Approximate Optimization Algorithm, Variational Quantum Eigensolver, Grover search, Shor period finding, quantum kernels, and amplitude-estimation extensions—to six application classes: industrial optimization, logistics and energy systems, molecular simulation, financial modelling, cybersecurity, quantum machine learning, and education. To reduce premature or misleading application claims, the paper introduces a six-stage evidence model called the QForge Application Readiness Levels (QARL), progressing from problem identification to operational validation. It also defines a reproducible application gallery, classical-baseline discipline, end-to-end time accounting, and structured evidence reports. The paper deliberately distinguishes classical emulation from physical quantum execution and does not claim quantum advantage. Instead, QForge is positioned as an engineering environment in which application hypotheses can be formulated, verified, benchmarked, and prepared for future hybrid high-performance and quantum-computing infrastructures.
Quantum Geometry Adaptive Computation is a novel approach to computation leveraging the unique properties of quantum geometry. This paper explores the potential of utilizing quantum geometric principles to develop highly efficient algorithms and computational paradigms. The core claim centers on the design of a self-adaptive computation algorithm predicated on quantum geometry, specifically aiming to enhance computational performance through the inherent advantages of this geometric framework. This work investigates the theoretical underpinnings and practical implementation of this approach, demonstrating its promise for advanced computational tasks. We present a preliminary study exploring the impact of quantum geometry on specific computational challenges, highlighting its potential to surpass conventional methods. The research will focus on outlining the core mechanism, potential applications, and preliminary results, emphasizing the advancements achieved through the application of quantum geometry.