Efficient decomposition of single-qubit gates intoVbasis circuits

Alex Bocharov, Yuri Gurevich, Krysta M. Svore
2013 Physical Review A. Atomic, Molecular, and Optical Physics  
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 (1/ϵ)) 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
more » ... 6 to _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 (1/ϵ); however, we show that in practice the runtime is reasonable for an important range of target precisions.
doi:10.1103/physreva.88.012313 fatcat:26na6doulbbjrci2nsfji2qxvu