Efficient Synthesis of Linear Reversible Circuits
Abstract
In this paper we consider circuit synthesis for nwire linear reversible circuits using the CNOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LUdecomposition, yield circuits with O(n^2) gates in the worstcase. However, an information theoretic bound suggests that it may be possible to reduce this to as few as O(n^2/log n) gates. We present an algorithm that is optimal up to a multiplicative constant, as well as Theta(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.
 Publication:

arXiv eprints
 Pub Date:
 February 2003
 arXiv:
 arXiv:quantph/0302002
 Bibcode:
 2003quant.ph..2002P
 Keywords:

 Quantum Physics
 EPrint:
 12 pages, 4 figures