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Recently Neil Ross and Peter Selinger analyzed the problem of approximatingz- rotations by means of single-qubit Clifford+T circuits. Their maincontribution is a deterministic-search technique which allowed them to makeapproximating circuits shallower. We adapt the deterministic-search techniqueto the case of Pauli+V circuits and prove similar results. Because of therelative simplicity of the Pauli+V framework, we use much simpler geometricmethods.

Optimal Ancilla-free Pauli+V Circuits for Axial Rotations