Density functional theory and quantum computation

Abstract

This paper establishes the applicability of density functional theory methods to quantum computing systems. We show that ground-state and time-dependent density functional theory can be applied to quantum computing systems by proving the Hohenberg-Kohn and Runge-Gross theorems for a fermionic representation of an N qubit system. As a first demonstration of this approach, time-dependent density functional theory is used to determine the minimum energy gap Delta(N) arising when the quantum adiabatic evolution algorithm is used to solve instances of the NP-Complete problem MAXCUT. It is known that the computational efficiency of this algorithm is largely determined by the large-N scaling behavior of Delta(N), and so determining this behavior is of fundamental significance. As density functional theory has been used to study quantum systems with N ~ 1000 interacting degrees of freedom, the approach introduced in this paper raises the realistic prospect of evaluating the gap Delta(N) for systems with N ~ 1000 qubits. Although the calculation of Delta(N) serves to illustrate how density functional theory methods can be applied to problems in quantum computing, the approach has a much broader range and shows promise as a means for determining the properties of very large quantum computing systems.