  We propose a method to achieve quantum supremacy using ensembles of qubits,
using only spin squeezing, basis rotations, and Fock state measurements. Each
ensemble is assumed to be controllable only with its total spin. Using a
repeated sequence of random basis rotations followed by squeezing, we show that
the probability distribution of the final measurements quickly approaches a
Porter-Thomas distribution. We show that the sampling probability can be
related to a #P-hard problem with a complexity scaling as $(N+1)^M$, where $N$
is the number of qubits in an ensemble and $ M $ is the number of ensembles.
The scheme can be implemented with hot or cold atomic ensembles. Due to the
large number of atoms in typical atomic ensembles, this allows access to the
quantum supremacy regime with a modest number of ensembles or gate depth.
