# 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…

## 172 Citations

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