  We define a semantic complexity class based on the model of quantum computing
with just one pure qubit (as introduced by Knill and Laflamme) and discuss its
computational power in terms of the problem of estimating the trace of a large
unitary matrix. We show that this problem is complete for the complexity class,
and derive some further fundamental features of the class. We conclude with a
discussion of some associated open conjectures and new oracle separations
between classes.
