A Quantum Algorithm for Ray Casting using an Orthographic Camera

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).