Computational Supremacy of Quantum Eigensolver by Extension of Optimized Binary Configurations

TL;DR

This paper introduces a quantum eigensolver that leverages quantum annealing on a D-Wave system to efficiently compute eigenstates and eigenvalues of Hamiltonians, demonstrating potential computational supremacy over classical methods.

Contribution

The paper presents a novel quantum eigensolver based on optimized binary configurations measured by quantum annealing, reducing computational costs compared to classical diagonalization methods.

Findings

Provides exact solutions within small errors for tested Hamiltonians.

Shows computational cost is not significantly affected by Hamiltonian size.

Demonstrates potential for wide application in material and drug design.

Abstract

We developed a quantum eigensolver (QE) which is based on an extension of optimized binary configurations measured by quantum annealing (QA) on a D-Wave Quantum Annealer (D-Wave QA). This approach performs iterative QA measurements to optimize the eigenstates $\vert \psi \rangle$ without the derivation of a classical computer. The computational cost is $\eta M L$ for full eigenvalues $E$ and $\vert \psi \rangle$ of the Hamiltonian $\hat{H}$ of size $L \times L$, where $M$ and $\eta$ are the number of QA measurements required to reach the converged $\vert \psi \rangle$ and the total annealing time of many QA shots, respectively. Unlike the exact diagonalized (ED) algorithm with $L^3$ iterations on a classical computer, the computation cost is not significantly affected by $L$ and $M$ because $\eta$ represents a very short time within $10^{-2}$ seconds on the D-Wave QA. We selected the tight-binding $\hat{H}$ that contains the exact $E$ values of all energy states in two systems with metallic and insulating phases. We confirmed that the proposed QE algorithm provides exact solutions within the errors of $5 \times 10^{-3}$. The QE algorithm will not only show computational supremacy over the ED approach on a classical computer but will also be widely used for various applications such as material and drug design.