Iterative quantum-assisted eigensolver

The task of estimating the ground state Hamiltonians is an important problem in physics with numerous applications ranging from solid-state to combinatorial optimization. We provide a hybrid quantum-classical algorithm for approximating Hamiltonian that builds on powerful Krylov subspace method way suitable current quantum computers. Our systematically constructs ansatz by using any given choice initial and unitaries describing Hamiltonian. only computer measure overlaps no feedback loops are required. measurements can be performed efficiently hardware without requiring complicated such as Hadamard test. Finally, classical solves well-characterized quadratically constrained optimization program. reuse previous calculate wide range additional resources. Further, we demonstrate our solving class problems thousands qubits. works almost every random circumvents barren plateau problem.