  A rotation-based synthesis framework for reversible logic is proposed. We
develop a canonical representation based on binary decision diagrams and
introduce operators to manipulate the developed representation model.
Furthermore, a recursive functional bi-decomposition approach is proposed to
automatically synthesize a given function. While Boolean reversible logic is
particularly addressed, our framework constructs intermediate quantum states
that may be in superposition, hence we combine techniques from reversible
Boolean logic and quantum computation. The proposed approach results in
quadratic gate count for multiple-control Toffoli gates without ancillae,
linear depth for quantum carry-ripple adder, and quasilinear size for quantum
multiplexer.
