Near-optimal ground state preparation

Understand

Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks.

• However, given some additional information, these problems can be solved efficiently on a quantum computer.
• We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared, and the spectral gap between the ground energy and the first excited energy is bounded from below.
• With these assumptions we design an algorithm that prepares the ground state when an upper bound of the ground energy is known, whose runtime has a logarithmic dependence on the inverse error.