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International Conference on Graphics and Interaction (ICGI)

A Quantum Algorithm for Ray Casting using an Orthographic Camera

Carolina Alves, Luís Paulo Santos, Thomas Bashford‐Rogers

Published Nov 1, 2019• 9 citations
Publisher

Abstract

Quantum computing has the potential to provide solutions to many problems which are challenging or out of reach of classical computers. There are several problems in rendering which are amenable to being solved in quantum computers, but these have yet to be demonstrated in practice. This work takes a first step in applying quantum computing to one of the most fundamental operations in rendering: ray casting. This technique computes visibility between two points in a 3D model of the world which is described by a collection of geometric primitives. The algorithm returns, for a given ray, which primitive it intersects closest to its origin. Without a spatial acceleration structure, the classical complexity for this operation is$O(N)$. In this paper, we propose an implementation of Grover's Algorithm (a quantum search algorithm) for ray casting. This provides a quadratic speed up allowing for visibility evaluation for unstructured primitives in$O(\sqrt{N})$. However, due to technological limitations associated with current quantum computers, in this work the geometrical setup is limited to rectangles and parallel rays (orthographic projection).

DOI
10.1109/icgi47575.2019.8955061

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Quantum computing has the potential to provide solutions to many problems which are challenging or out of reach of classical computers. There are several problems in rendering which are amenable to being solved in quantum computers, but these have yet to be demonstrated in practice. This work takes a first step in applying quantum computing to one of the most fundamental operations in rendering: ray casting. This technique computes visibility between two points in a 3D model of the world which is described by a collection of geometric primitives. The algorithm returns, for a given ray, which primitive it intersects closest to its origin. Without a spatial acceleration structure, the classical complexity for this operation isO(N)O(N)O(N). In this paper, we propose an implementation of Grover's Algorithm (a quantum search algorithm) for ray casting. This provides a quadratic speed up allowing for visibility evaluation for unstructured primitives inO(N)O(\sqrt{N})O(N​). However, due to technological limitations associated with current quantum computers, in this work the geometrical setup is limited to rectangles and parallel rays (orthographic projection).
Ray tracing is a fundamental technique in computer graphics used to render realistic images by simulating light interactions with objects, known as primitives. With the rise in popularity of quantum computing, new techniques have been developed to accelerate these computationally intensive tasks, with the potential of significant speedup over classical approaches. Traditional ray tracing relies on detailed ray casting and intersection tests between rays and scene primitives, which can be extremely time-consuming for complex scenes. Grover's algorithm for unordered search has demonstrated potential quadratic speedups in unstructured search problems, creating novel approaches to accelerate intersection detection in graphics. This work aims to contribute to the practicality of quantum search techniques for hybrid ray tracing pipelines to accelerate intersection tests. We propose two hybrid approaches: a uniform spatial division method employing a 3D Digital Differential Analyzer (DDA) for rapid grid traversal and an octree traversal scheme that recursively refines the search space using hybrid leaf node detection. Our methods build upon existing quantum orthographic ray-casting algorithms to efficiently identify cells or primitives where intersections occur before applying classical refinement through detailed intersection tests using orthographic projection. Our approach extends previous quantum ray casting techniques by adapting them to complex spatial data structures and scene representations, offering theoretical runtime improvements in optimal cases. These results demonstrate how quantum computing can enhance traditional computational rendering pipelines. As quantum hardware continues to evolve, we hope these hybrid techniques will offer alternative solutions for realistic rendering, inspiring further interdisciplinary research for quantum computation in computer graphics.
The use of quantum computers in computer graphics has gained interest in recent years, especially for the application to rendering. The current state of the art in quantum rendering relies on Grover’s search for finding ray intersections in for M primitives. This quantum approach is faster than the naive approach of O(M) but slower than O(log M) of modern ray tracing with an acceleration data structure. Furthermore, this quantum ray tracing method is fundamentally limited to casting one ray at a time, leaving quantum rendering scales for the number of rays the same as non-quantum algorithms. We present a new quantum rendering method, quantum ray marching, based on the reformulation of ray marching as a quantum random walk. Our work is the first complete quantum rendering pipeline capable of light transport simulation and remains asymptotically faster than non-quantum counterparts. Our quantum ray marching can trace an exponential number of paths with polynomial cost, and it leverages quantum numerical integration to converge in O(1/N) for N estimates as opposed to non-quantum . These properties led to first quantum rendering that is asymptotically faster than non-quantum Monte Carlo rendering. We numerically tested our algorithm by rendering 2D and 3D scenes.
Quantum computing holds the potential to solve problems that are practically unsolvable by classical computers due to its ability to significantly reduce time complexity. We aim to harness this potential to enhance ray casting, a pivotal technique in computer graphics for simplifying the rendering of 3D objects. To perform ray casting in a quantum computer, we need to encode the defining parameters of primitives into qubits. However, during the current noisy intermediate-scale quantum (NISQ) era, challenges arise from the limited number of qubits and the impact of noise when executing multiple gates. Through logic optimization, we reduced the depth of quantum circuits as well as the number of gates and qubits. As a result, the event count of correct measurements from an IBM quantum computer significantly exceeded that of incorrect measurements.
Rendering on conventional computers is capable of generating realistic imagery, but the computational complexity of these light transport algorithms is a limiting factor of image synthesis. Quantum computers have the potential to significantly improve rendering performance through reducing the underlying complexity of the algorithms behind light transport. This article investigates hybrid quantum-classical algorithms for ray tracing, a core component of most rendering techniques. Through a practical implementation of quantum ray tracing in a 3D environment, we show quantum approaches provide a quadratic improvement in query complexity compared to the equivalent classical approach. Based on domain specific knowledge, we then propose algorithms to significantly reduce the computation required for quantum ray tracing through exploiting image space coherence and a principled termination criteria for quantum searching. We show results obtained using a simulator for both Whitted style ray tracing, and for accelerating ray tracing operations when performing classical Monte Carlo integration for area lights and indirect illumination.
Quantum search is one of the most important algorithmic developments in quantum computing because it demonstrates how quantum principles can improve the efficiency of solving unstructured search problems. Grover’s algorithm provides a quadratic speed-up over classical linear search by reducing query complexity from O(N) to O(√N), where N represents the size of the search space. This review examines the principles, performance, and applications of Grover’s algorithm, with emphasis on its theoretical foundation and practical relevance. The discussion covers the roles of superposition, quantum interference, oracle operations, diffusion operators, and amplitude amplification in increasing the probability of measuring a desired solution. The manuscript also reviews the computational performance of quantum search in comparison with classical search methods and considers its relevance to database searching, combinatorial optimisation, cryptography, machine learning, bioinformatics, quantum chemistry, and materials science. The review highlights that Grover’s algorithm is not limited to database retrieval, as many computationally intensive problems can be reformulated as search or optimisation tasks. However, practical implementation remains constrained by current quantum hardware limitations, including decoherence, quantum noise, limited qubit availability, circuit depth, and the difficulty of designing efficient oracles. Despite these challenges, continuing progress in quantum hardware, error correction, cloud-based quantum platforms, and hybrid quantum-classical architectures suggests that quantum search will remain an important area of research. Overall, Grover’s algorithm represents a foundational quantum algorithm with significant theoretical value and potential long-term application in computational domains involving large and unstructured search spaces.
Rendering is a computer graphics process that generates images from a three-dimensional scene including models, lights and cameras. Ray tracing is a category of rendering algorithms that calculates pixel colors by simulating the physical movements of light rays such as reflections, refractions and scatterings. The core problem of ray tracing is a high-dimensional numerical integration, and the classical Monte Carlo ray tracing requires a big number of rays to reduce error. By leveraging the inherent parallelism of quantum computing, we propose a framework of quantum ray tracing algorithm, and do simulation experiments to prove that it has a quadratically faster error convergence than classical Monte Carlo ray tracing.