1. A method for normalizing a representation of a quantum circuit u comprising a sequence of representations of H and T gates, the method comprising: initially transforming the quantum circuit u to an equivalent quantum circuit x comprising either a representation of a single Clifford gate or one or more representations of a single-Clifford-gate, T-gate pair followed by a representation of a single Clifford gate; transforming the quantum circuit x to an equivalent normal representation n comprising a sequence of representations of one or more gates selected from among TH, SH, and Clifford gates; and storing the normal representation n in a physical data-storage device including one of an electronic memory and a mass-storage device.