Computational Supremacy of Quantum Eigensolver by Extension of Optimized Binary Configurations

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 ψrangle without the derivation of a classical computer. The computational cost is ηM L for full eigenvalues E and vert ψrangle of the Hamiltonian hat{H} of size L times L, where M and η are the number of QA measurements required to reach the converged vert ψrangle and the total annealing time of many QA shots, respectively. Unlike the exact diagonalized (ED) algorithm with L³ iterations on a classical computer, the computation cost is not significantly affected by L and M because η 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.