Variational Phase Estimation with Variational Fast Forwarding

Understand

Subspace diagonalisation methods have appeared recently as promising means to access the ground state and some excited states of molecular Hamiltonians by classically diagonalising small matrices, whose elements can be efficiently obtained by a quantum computer.

• The recently proposed Variational Quantum Phase Estimation (VQPE) algorithm uses a basis of real time-evolved states, for which the energy eigenvalues can be obtained directly from the unitary matrix U = exp(-iHt), which can be computed with cost linear in the number of states used.
• In this paper, we report a circuit-based implementation of VQPE for arbitrary molecular systems and assess its performance and costs for the H2, H3+ and H6 molecules.
• We also propose using Variational Fast Forwarding (VFF) to decrease to quantum depth of time-evolution circuits for use in VQPE.