Abstract

We present here a quantum circuit implementation of the variational quantum phase estimation (VQPE) algorithm, which uses a series of time-evolved states as a basis for non-orthogonal configuration interaction. On an equally spaced time grid, the diagonalisation of the Hamiltonian can be replaced with a diagonalisation of a time-evolution matrix, the computation of which scales linearly with the number of basis states. We combine the VQPE approach with variational fast-forwarding (VFF), which provides a constant-depth approximation to time-evolution. This approximation provides a good basis for Hamiltonian diagonalisation even when fidelity is low and, in the case of high-fidelity, allows us to preserve the linear scaling of the VQPE algorithm. This is based on this paper : https://quantum-journal.org/papers/q-2024-03-13-1278/