  The phase resolution of interferometers is limited by the so-called
Heisenberg limit, which states that the optimum phase sensitivity is inversely
proportional to the number of interfering particles N, a 1/sqrt{N} improvement
over the standard quantum limit. We have used simulated annealing, a global
optimization strategy, to systematically search for quantum interferometer
input states that approach the Heisenberg limited uncertainty in estimates of
the interferometer phase shift. We compare the performance of these states to
that of other non-classical states already known to yield Heisenberg limited
uncertainty.
