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arXiv:2203.15451

A Framework for Quantum Ray Tracing

Xi Lu, Hongwei Lin

Published Mar 29, 2022• 1 citation
arXivHTMLPDF

Abstract

Ray tracing algorithm simulates the physical movements of a huge amount of rays to render a high quality image, in which the tracing procedure for each ray can be implemented in parallel. By leveraging the inherent parallelism of quantum computing, we propose a quantum ray tracing algorithm, which is proved to have a quadratic speedup over the classical path tracing.

DOI
10.48550/arxiv.2203.15451

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Ray tracing algorithm simulates the physical movements of a huge amount of rays to render a high quality image, in which the tracing procedure for each ray can be implemented in parallel. By leveraging the inherent parallelism of quantum computing, we propose a quantum ray tracing algorithm, which is proved to have a quadratic speedup over the classical path tracing.
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.
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.
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 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).
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.
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