Optimal Ground-State Preparation with a Guiding State
Suppose a Hamiltonian $H$ has a unique ground state $|\psi_0\rangle$ with an eigenvalue $E_0$, and we have an estimate $\tilde{E}_0$ such that $|\tilde{E}_0-E_0|\leq\delta$, and there is a gap of at least $3\delta$ between $E_0$ and all other eigenvalues. Suppose we have a unitary $A$ available that can produce a"guidi...