Iterative quantum-assisted eigensolver

Abstract

The task of estimating ground state and ground state energy of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. The description of the Hamiltonian is assumed to be a linear combination of unitaries. Our algorithm is iterative and systematically constructs the Ansatz using any given choice of the initial state and the unitaries describing the Hamiltonian. In a particular iteration, the task of the quantum computer remains to measure two overlap matrices. Using recent results in literature, this task can be performed efficiently on current quantum hardware without requiring any complicated measurements such as the Hadamard test. At the end of a particular iteration, the classical computer solves a quadratically constrained quadratic program. The algorithm terminates if the desired stopping criterion has been achieved, otherwise proceeds to the next iteration. Our algorithm works for almost every random choice of the initial state and provides an approach to circumvent the barren plateau problem.