Simulating fermions on a quantum computer

Abstract

The real-time probabilistic simulation of quantum systems in classical computers is known to be limited by the so-called dynamical sign problem, a problem leading to exponential complexity. In 1981 Richard Feynman raised some provocative questions in connection to the “exact imitation” of such systems using a special device named a “quantum computer”. Feynman hesitated about the possibility of imitating fermion systems using such a device. Here we address some of his concerns and, in particular, investigate the simulation of fermionic systems. We show how quantum computers avoid the sign problem in some cases by reducing the complexity from exponential to polynomial. Our demonstration is based upon the use of isomorphisms of algebras. We present specific quantum algorithms that illustrate the main points of our algebraic approach.