  We present an algorithm, along with its implementation that finds T-optimal
approximations of single-qubit Z-rotations using quantum circuits consisting of
Clifford and T gates. Our algorithm is capable of handling errors in
approximation down to size $10^{-15}$, resulting in optimal single-qubit
circuit designs required for implementation of scalable quantum algorithms. Our
implementation along with the experimental results are available in the public
domain.
