Computation with Unitaries and One Pure Qubit
arXiv:quant-ph/0608132
Abstract
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.
16 pages, no figures, submitted to QIC. This version has an improved section on oracles, adds a note on entanglement, includes minor corrections