We develop the first constructive algorithms for compiling single-qubit unitary gates into circuits over the universal V basis. The V basis is an alternative universal basis to the more commonly studied {H,T} basis. We propose two classical algorithms for quantum circuit compilation: the first algorithm has expected polynomial time (in precision log(1/epsilon)) and offers a depth/precision guarantee that improves upon state-of-the-art methods for compiling into the {H,T} basis by factors ranging from 1.86 to log_2(5). The second algorithm is analogous to direct search and yields circuits a factor of 3 to 4 times shorter than our first algorithm, and requires time exponential in log(1/\epsilon); however, we show that in practice the runtime is reasonable for an important range of target precisions.

PDF file

Details