Journal of Theoretical & Computational Science
Open Access

Electronic Structure Computations using Quantum Machine Learning

Ioannis Martinsen^{* *}Correspondence: Ioannis Martinsen, Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway, Email:

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Description

Computational geometry is a branch of computer science that focuses on the study of algorithms that can be represented in terms of geometry. Certain purely geometrical problems might arise from the study of computational geometric methods, and these problems are also classified as a subset of computational geometry. Even while computational geometry as we know it now is a relatively recent topic, its roots in antiquity make it one of the oldest computer fields. Effective methods for addressing geometric input and output problems are devised, examined, and applied in the mathematical field of computational geometry. It can also be used to describe pattern detection as well as the solid modeling techniques used to manage surfaces and curves.

Algorithms that can be expressed using various geometries are explored in the area of computer science known as computational geometry. Despite it is a more recent invention, computational geometry is one of the earliest computing issues historically speaking. Computer graphics developments as well as improvements in computer-aided design and production are largely responsible for the evolution of computational geometry. The emergence of computational geometry as a field was primarily spurred by improvements in computer graphics and computer-aided design and manufacturing (CAD/CAM). However, many computational geometry problems are of a more traditional form and may arise from mathematical visualization. Integrated Circuit design (IC geometry design and verification), Geographic Information Systems (GIS), robotics (motion planning and visibility difficulties), Computer-Aided Engineering (CAE) (mesh generation), and computer vision are some more important uses of computational geometry (3D reconstruction). The most important tools in this case are parametric curves and surfaces, such surfaces, spline curves, and bezier curves. An important non-parametric technique is the level-set approach.

In many applications, this issue is often regarded as a single-shot issue or as belonging to the first class. For instance, a common problem in many computer graphics programs is figuring out where a pointer is clicking on the screen. The point indicates a query, although the questioned polygon is invariant in some applications. With a point representing the position of the aircraft and an input polygon representing a country's border, determine whether an aircraft crossed the line. In many query problem scenarios, it may be possible to make reasonable assumptions about the order of the queries, which can be used to either efficient data structures or more precise computation complexity estimates. Its development was also motivated by insights from computational graph theories applied in natural geometric contexts.

The initial focus of this field was mostly on two-dimensional problems, with very little attention paid to three-dimensional problems. The majority of recent research in this field has been aimed at improving the usability of theoretical discoveries for practitioners. This has been achieved by eliminating geometric degeneracies, simplifying existing methods, and constructing geometric libraries. Also, they focused on geometric problem characteristics rather than traditional continuous questions. The majority of the elements in this subject, such as lines, polygons, planes, and line segments, are flat and straight. While occasionally using curved objects like circles, it avoids the problems associated with solid modeling by using simple curves and surfaces.

For a variety of valid reasons, computational-based geometry may never completely meet the needs of practitioners and the sectors in which it is used. There are numerous natural phenomena that can be discretized into line segment collections, including road networks and geographic information systems. Because computation-based geometry typically only works with flat and straight objects, engineers and designers that work with robotics, fluid dynamics, and solid modeling struggle to achieve their goals. This inward research strategy has freed computational geometers from the discomfort of reproducing the complexity and imperfections of the physical world and coping with the limitations of practical computer technology. They may focus on the analysis of a Platonic universe consisting of simple, wellbehaved geometric objects that could be handled by fictitious computers with infinite memory and real number arithmetic.

The modern technology now allows computational geometers to model curved objects using polygons or polygonal shapes. Because of this, computation-based geometry is becoming more and more popular because it now requires more technical and computer skills than understanding of analytical and differential geometry. Due to their ease of understanding and representation, two-dimensional problems receive the majority of the field's attention; yet, this limits the field's ability to handle more complex three-dimensional application challenges and higher.

Conclusion

Computational geometry, a thriving field, is experiencing a crucial moment in the discipline's development. We have defined methodologies and computing paradigms that we think are strategically significant for the growth of the discipline and its impact on applications. The main message is that computational geometry should continue to pursue the dual goals of investigating the combinatorial structure of geometric objects and providing practical approaches and tools for the analysis and solution of fundamental geometric problems.