Quantum Ray Marching: Reformulating Light Transport for Quantum Computers

Abstract

The use of quantum computers in computer graphics has gained some interest in recent years, especially for the application of rendering. The current state of the art in quantum rendering relies on Grover's search for finding ray intersections in O(√M) for M primitives, which 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, making it less attractive even when quantum computers become much more mature in the future. 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 to provide a complete quantum rendering pipeline capable of supporting light transport simulation and remains fundamentally faster than non-quantum counterparts. Our quantum ray marching can trace an exponential number of rays in polynomial cost and leverage quantum numerical integration to converge in O(1/N) for N estimates. These unique properties make our method asymptotically faster than Monte Carlo ray tracing on non-quantum computers for the first time. We numerically verify the proposed quantum algorithm by rendering both 2D and 3D scenes.