Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum computational geometry

Marco O. Lanzagorta, Jeffrey K. Uhlmann

Published Aug 24, 2004• 8 citations
Publisher

Abstract

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.

DOI
10.1117/12.541624

Related papers

Quantum algorithmic methods for computational geometry

Marco O. Lanzagorta, Jeffrey K. Uhlmann

In this paper we develop novel quantum algorithms based on Quantum Multi-Object Search (QMOS) for convex hulls and general object intersection reporting, with applications to computer graphics. These algorithms are developed and described using standard concepts from computer science by encapsulating the physics of quantum computation within black-box subroutines.

Mathematical Structures in Computer Science•Nov 8, 2010•19 citations

Quantum rendering

Marco O. Lanzagorta, Richard B. Gomez, Jeffrey K. Uhlmann

In recent years, computer graphics has emerged as a critical component of the scientific and engineering process, and it is recognized as an important computer science research area. Computer graphics are extensively used for a variety of aerospace and defense training systems and by Hollywood's special effects companies. All these applications require the computer graphics systems to produce high quality renderings of extremely large data sets in short periods of time. Much research has been done in "classical computing" toward the development of efficient methods and techniques to reduce the rendering time required for large datasets. Quantum Computing's unique algorithmic features offer the possibility of speeding up some of the known rendering algorithms currently used in computer graphics. In this paper we discuss possible implementations of quantum rendering algorithms. In particular, we concentrate on the implementation of Grover's quantum search algorithm for Z-buffering, ray-tracing, radiosity, and scene management techniques. We also compare the theoretical performance between the classical and quantum versions of the algorithms.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 5, 2003•4 citations

QUANTUM COMPUTING ALGORITHMS FOR SOLVING LARGE-SCALE SCIENTIFIC PROBLEMS

Danish Rafiq, Mahira Sohail

Large-scale scientific problems in physics, chemistry, biology, and optimization often remain computationally intractable for classical computers due to exponential scaling and resource limitations. Quantum computing introduces a fundamentally new paradigm based on quantum superposition, entanglement, and interference, offering the potential to solve such problems more efficiently. This article examines major quantum computing algorithms developed for large-scale scientific applications, including quantum simulation, optimization, and linear system solvers. Emphasis is placed on algorithmic principles, performance advantages over classical methods, and real-world scientific use cases. Two graphical illustrations demonstrate quantum speedup trends and algorithm complexity comparisons. The study also highlights current limitations and future directions of quantum algorithms in scientific problem-solving.

International Research Journal of Advanced Science•Oct 20, 2025•0 citations

Quantum Computing Algorithms and Their Emerging Applications in Complex Scientific Problems

Hira Fatima, Waqar Ahmad

Quantum computing (QC) presents transformative potential for solving complex scientific problems that remain intractable for classical computers. Leveraging quantum superposition, entanglement, and interference, quantum algorithms such as Shor’s factoring algorithm, Grover’s search algorithm, variational quantum eigensolvers (VQE), and quantum approximate optimization algorithms (QAOA) enable exponential or polynomial speedups for selected problem classes. This paper explores recent advancements in quantum computing algorithms, their practical implementations, and emerging applications in fields such as molecular simulations, material science, cryptography, optimization, and machine learning. We highlight the strengths and limitations of current approaches, present performance analyses through graphical comparisons, and discuss prospective directions for integrating quantum algorithms into real-world scientific workflows. Our findings demonstrate that quantum computing is gradually transitioning from theoretical frameworks to experimental platforms capable of addressing highly complex computational challenges.

International Research Journal of Advanced Science•Jun 30, 2025•0 citations

Quantum Computing Algorithms and Their Emerging Applications in Complex Scientific Problems

Saima Parveen, Waqar Ahmad

Quantum computing (QC) presents transformative potential for solving complex scientific problems that remain intractable for classical computers. Leveraging quantum superposition, entanglement, and interference, quantum algorithms such as Shor’s factoring algorithm, Grover’s search algorithm, variational quantum eigensolvers (VQE), and quantum approximate optimization algorithms (QAOA) enable exponential or polynomial speedups for selected problem classes. This paper explores recent advancements in quantum computing algorithms, their practical implementations, and emerging applications in fields such as molecular simulations, material science, cryptography, optimization, and machine learning. We highlight the strengths and limitations of current approaches, present performance analyses through graphical comparisons, and discuss prospective directions for integrating quantum algorithms into real-world scientific workflows. Our findings demonstrate that quantum computing is gradually transitioning from theoretical frameworks to experimental platforms capable of addressing highly complex computational challenges.

International Research Journal of Advanced Science•Dec 31, 2022•0 citations

Quantum Approximate Optimization Algorithm applied to multi-objective routing for large scale 6G networks

Oumayma Bouchmal, Bruno Cimoli, Ripalta Stabile +2 more

A multi-objective optimization problem involves optimizing two or more conflicting objectives simultaneously. This type of problem arises in many scientific and industrial areas and it is classified as NP-Hard. Network routing optimization with multiple objectives falls into this category. In the context of 6G networks, solving this problem will become even more challenging due to the exponential growth of Internet of Things devices and the high quality of service requirements. Finding good quality solutions for large-scale networks will be increasingly difficult. In this paper, we introduce a quantum-inspired routing optimization scheme in which noisy-intermediate scale quantum computers (NISQ) can be used to solve the Multi-Objective Routing Problem (MORP). We evaluate the application of the proposed scheme in detail by first developing the mathematical formulas for both single-objective and multi-objective routing and mapping the problem onto gate-based models by using the quadratic unconstrained binary optimization (QUBO) approach. To validate the proposed scheme, we use the quantum approximate optimization algorithm (QAOA), the go-to approach for solving combinatorial optimization problems that are classically intractable. For the simulation, we use the IBM-Qasm simulator and Qiskit framework. Additionally, we use the Chernoff Bound as a standard technique to estimate the sample complexity of QAOA. Finally, we provide a detailed numerical and theoretical analysis of the proposed scheme, including its time complexity, resource requirements, and the challenges associated with it. Our results demonstrate that the proposed approach operates with a time complexity of O ( E 2 ) per iteration in both single and multi-objective scenarios, with an overall runtime of ( n iteration + n CB ) ⋅ O ( E 2 ) influenced by the sampling overhead, significantly outperforming Dijkstra’s algorithm in the multi-objective case, where the complexity increases to O ( 2 k ( N ( k + log N ) + 2 k E ) ) .

Computer Networks•May 13, 2025•17 citations
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.
In recent years, computer graphics has emerged as a critical component of the scientific and engineering process, and it is recognized as an important computer science research area. Computer graphics are extensively used for a variety of aerospace and defense training systems and by Hollywood's special effects companies. All these applications require the computer graphics systems to produce high quality renderings of extremely large data sets in short periods of time. Much research has been done in "classical computing" toward the development of efficient methods and techniques to reduce the rendering time required for large datasets. Quantum Computing's unique algorithmic features offer the possibility of speeding up some of the known rendering algorithms currently used in computer graphics. In this paper we discuss possible implementations of quantum rendering algorithms. In particular, we concentrate on the implementation of Grover's quantum search algorithm for Z-buffering, ray-tracing, radiosity, and scene management techniques. We also compare the theoretical performance between the classical and quantum versions of the algorithms.
Large-scale scientific problems in physics, chemistry, biology, and optimization often remain computationally intractable for classical computers due to exponential scaling and resource limitations. Quantum computing introduces a fundamentally new paradigm based on quantum superposition, entanglement, and interference, offering the potential to solve such problems more efficiently. This article examines major quantum computing algorithms developed for large-scale scientific applications, including quantum simulation, optimization, and linear system solvers. Emphasis is placed on algorithmic principles, performance advantages over classical methods, and real-world scientific use cases. Two graphical illustrations demonstrate quantum speedup trends and algorithm complexity comparisons. The study also highlights current limitations and future directions of quantum algorithms in scientific problem-solving.
Quantum computing (QC) presents transformative potential for solving complex scientific problems that remain intractable for classical computers. Leveraging quantum superposition, entanglement, and interference, quantum algorithms such as Shor’s factoring algorithm, Grover’s search algorithm, variational quantum eigensolvers (VQE), and quantum approximate optimization algorithms (QAOA) enable exponential or polynomial speedups for selected problem classes. This paper explores recent advancements in quantum computing algorithms, their practical implementations, and emerging applications in fields such as molecular simulations, material science, cryptography, optimization, and machine learning. We highlight the strengths and limitations of current approaches, present performance analyses through graphical comparisons, and discuss prospective directions for integrating quantum algorithms into real-world scientific workflows. Our findings demonstrate that quantum computing is gradually transitioning from theoretical frameworks to experimental platforms capable of addressing highly complex computational challenges.
Quantum computing (QC) presents transformative potential for solving complex scientific problems that remain intractable for classical computers. Leveraging quantum superposition, entanglement, and interference, quantum algorithms such as Shor’s factoring algorithm, Grover’s search algorithm, variational quantum eigensolvers (VQE), and quantum approximate optimization algorithms (QAOA) enable exponential or polynomial speedups for selected problem classes. This paper explores recent advancements in quantum computing algorithms, their practical implementations, and emerging applications in fields such as molecular simulations, material science, cryptography, optimization, and machine learning. We highlight the strengths and limitations of current approaches, present performance analyses through graphical comparisons, and discuss prospective directions for integrating quantum algorithms into real-world scientific workflows. Our findings demonstrate that quantum computing is gradually transitioning from theoretical frameworks to experimental platforms capable of addressing highly complex computational challenges.
A multi-objective optimization problem involves optimizing two or more conflicting objectives simultaneously. This type of problem arises in many scientific and industrial areas and it is classified as NP-Hard. Network routing optimization with multiple objectives falls into this category. In the context of 6G networks, solving this problem will become even more challenging due to the exponential growth of Internet of Things devices and the high quality of service requirements. Finding good quality solutions for large-scale networks will be increasingly difficult. In this paper, we introduce a quantum-inspired routing optimization scheme in which noisy-intermediate scale quantum computers (NISQ) can be used to solve the Multi-Objective Routing Problem (MORP). We evaluate the application of the proposed scheme in detail by first developing the mathematical formulas for both single-objective and multi-objective routing and mapping the problem onto gate-based models by using the quadratic unconstrained binary optimization (QUBO) approach. To validate the proposed scheme, we use the quantum approximate optimization algorithm (QAOA), the go-to approach for solving combinatorial optimization problems that are classically intractable. For the simulation, we use the IBM-Qasm simulator and Qiskit framework. Additionally, we use the Chernoff Bound as a standard technique to estimate the sample complexity of QAOA. Finally, we provide a detailed numerical and theoretical analysis of the proposed scheme, including its time complexity, resource requirements, and the challenges associated with it. Our results demonstrate that the proposed approach operates with a time complexity of O ( E 2 ) per iteration in both single and multi-objective scenarios, with an overall runtime of ( n iteration + n CB ) ⋅ O ( E 2 ) influenced by the sampling overhead, significantly outperforming Dijkstra’s algorithm in the multi-objective case, where the complexity increases to O ( 2 k ( N ( k + log N ) + 2 k E ) ) .