IMPROVING QUANTUM STATE PREPARATION TECHNIQUES USING EIGENVECTOR CONTINUATION

Quantum state preparation is one of the key steps in many quantum algorithms, and numerous algorithms for state preparation have been proposed and studied in order to reduce the cost and improve efficiency. A number of important limitations remain, such as poor scalability, barren plateaus in parameter optimization, and difficulties with circuit implementation. Here, we consider eigenvector continuation (a quantum subspace expansion method) as a potential solution to these issues. Eigenvector continuation uses ground and/or excited states from a training set in parameter space to form a subspace in which a reduced Hamiltonian can be diagonalized.As eigenvector continuation relies on the preparation of ground states at different points in parameter space, it could be susceptible to the same issues that plague other state preparation algorithms. However, we show that eigenvector continuation is resistant to these kinds of issues, enabling the use of fewer iterations and shallower circuits. We demonstrate this within the context of several spin models namely XY model, XXZ interactive model and XXZ frustrated triangular lattice model by using eigenvector continuation based on states prepared via state of the art techniques: Quantum Imaginary Time Evolution (QITE), adiabatic time evolution, and adapt-VQE. In all cases, we find that an approximate state preparation is sufficient to span the subspace, leading to efficient implementations on NISQ hardware.