Density functional theory and quantum computation

TL;DR

This paper demonstrates that density functional theory can be adapted to analyze quantum computing systems, enabling the estimation of energy gaps in large qubit systems and potentially advancing the understanding of quantum algorithms' efficiency.

Contribution

It proves the applicability of density functional theory to quantum computing and introduces a method to evaluate properties of large quantum systems with up to 1000 qubits.

Findings

DFT applicable to quantum computing systems

Able to estimate energy gaps in large qubit systems

Potential to analyze properties of very large quantum systems

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.