A linear time complexity solver for lattice quantum field theory computations

Lattice Quantum Chromodynamics is used to investigate the behavior of quarks under the influence of the Strong Nuclear force. The computer implementation requires the solution of square sparse matrices with the number of rows up to the lOO's of millions, and this represents the major computational factor with regards to overall runtime. In this paper we present verification of an algorithm that grows only linearly with respect to matrix size in terms of the computing resources required. Once realistically sized calculations can be done on commonly available hardware, this opens the door to the investigation of quantum fields in other areas such as condensed matter physics and nanotechnology.