Optimal ancilla-free Clifford+T approximation of z-rotations

@article{Ross2014OptimalAC,
  title={Optimal ancilla-free Clifford+T approximation of z-rotations},
  author={Neil J. Ross and Peter Selinger},
  journal={Quantum Inf. Comput.},
  year={2014},
  volume={16},
  pages={901-953}
}
We consider the problem of approximating arbitrary single-qubit z-rotations by ancilla-free Clifford+T circuits, up to given epsilon. We present a fast new probabilistic algorithm for solving this problem optimally, i.e., for finding the shortest possible circuit whatsoever for the given problem instance. The algorithm requires a factoring oracle (such as a quantum computer). Even in the absence of a factoring oracle, the algorithm is still near-optimal under a mild number-theoretic hypothesis… 
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