Quantum eigensolver on 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 $|\ensuremath{\psi}\ensuremath{\rangle}$ without the derivation of a classical computer. The computational cost is $\ensuremath{\eta}ML$ for full eigenvalues $E$ and $|\ensuremath{\psi}\ensuremath{\rangle}$ of the Hamiltonian $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}$ of size $L\ifmmode\times\else\texttimes\fi{}L$, where $M$ and $\ensuremath{\eta}$ are the number of QA measurements required to reach the converged $|\ensuremath{\psi}\ensuremath{\rangle}$ and the total annealing time of many QA shots, respectively. Unlike the exact diagonalization algorithm with ${L}^{3}$ iterations on a classical computer, the computation cost is not significantly affected by $L$ and $M$ because $\ensuremath{\eta}$ represents a very short time within ${10}^{\ensuremath{-}2}$ seconds on the D-Wave QA. We selected the tight-binding $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}$ 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 $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. Finally, we believe that the newly developed QE algorithm will be widely used for various applications such as material and drug design.