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Citation: Yoganathan, Mithuna, Richard Jozsa, and Sergii Strelchuk. "Quantum advantage of unitary Clifford circuits with magic state inputs." Proceedings of the Royal Society A 475.2225 (2019): 20180427.
This paper analyzes the circuit model where all inputs are initialized to magic states, and the computer is allowed to apply Clifford gates before finally measuring in the computational basis. They show that, under a variety of standard conjectures, this model is hard to classically simulate.
The reason this paper caught my eye is because I am thinking about the realization of arbitrary Clifford gates by Pauli measurments, and in this paper the authors say this: "Thus in MBQC, Clifford gates are implemented using only Pauli measurements, and in our encoded setup we need to apply their corresponding fault tolerant encoded versions". I don't think that this paper is a good reference for the claim that all Clifford gates can be achieved by Pauli measurements, but this certainly seems to imply that for qudits this statement is classical.