  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.
