  Here we investigate the role of quantum interference in the quantum
homogenizer, whose convergence properties model a thermalization process. In
the original quantum homogenizer protocol, a system qubit converges to the
state of identical reservoir qubits through partial-swap interactions, that
allow interference between reservoir qubits. We design an alternative,
incoherent quantum homogenizer, where each system-reservoir interaction is
moderated by a control qubit using a controlled-swap interaction. We show that
our incoherent homogenizer satisfies the essential conditions for
homogenization, being able to transform a qubit from any state to any other
state to arbitrary accuracy, with negligible impact on the reservoir qubits'
states. Our results show that the convergence properties of homogenization
machines that are important for modelling thermalization are not dependent on
coherence between qubits in the homogenization protocol. We then derive bounds
on the resources required to re-use the homogenizers for performing state
transformations. This demonstrates that both homogenizers are universal for any
number of homogenizations, for an increased resource cost.
