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Computation with Unitaries and One Pure Qubit
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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.
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Simultaneous Estimation of Nonlinear Functionals of a Quantum State
Estimating k powers of a quantum state against one observable simultaneously costs Θ~(k) samples, matching the cost of the single hardest term.
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