Abstract
The problem of finding the ground state energy of a Hamiltonian using a
quantum computer is currently solved using either the quantum phase estimation
(QPE) or variational quantum eigensolver (VQE) algorithms. For precision
$\epsilon$, QPE requires $O(1)$ repetitions of circuits with depth
$O(1/\epsilon)$, whereas each expectation estimation subroutine within VQE
requires $O(1/\epsilon^2)$ samples from circuits with depth $O(1)$. We
propose a generalised VQE algorithm that interpolates between these two regimes
via a free parameter $\alphaın0,1$ which can exploit quantum coherence over
a circuit depth of $O(1/\epsilon^\alpha)$ to reduce the number of samples to
$O(1/\epsilon^2(1-\alpha))$. Along the way, we give a new routine for
expectation estimation under limited quantum resources that is of independent
interest.
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