Efficient Synthesis of Linear Reversible Circuits

gates. We present an algorithm that is optimal up to a multiplicative constant, as well as Θ(log n) times faster than previous methods. While our results are primarily asymptotic, simulation results show that even for relatively small n our algorithm is faster and yields more efficient circuits than the standard method. Generically our algorithm can be interpreted as a matrix decomposition algorithm, yielding an asymptotically efficient decomposition of a binary matrix into a product of elementary matrices.