  We introduce the concept of quantum tensor product expanders. These are
expanders that act on several copies of a given system, where the Kraus
operators are tensor products of the Kraus operator on a single system. We
begin with the classical case, and show that a classical two-copy expander can
be used to produce a quantum expander. We then discuss the quantum case and
give applications to the Solovay-Kitaev problem. We give probabilistic
constructions in both classical and quantum cases, giving tight bounds on the
expectation value of the largest nontrivial eigenvalue in the quantum case.
