Synthesis of quantum arrays with low quantum costs from Kronecker Functional Lattice Diagrams

Reversible logic has many applications such as Quantum computing, low power CMOS circuit design, Optical computing. Hence reversible logic synthesis has attracted attention especially in quantum computing community. A logic function is reversible if it is a one-to-one mapping between input and output vectors. In this paper we present a new approach to synthesis of reversible circuits using Kronecker Functional Lattice Diagrams. Unlike other contemporary algorithms for synthesis of reversible function that use n × n Toffoli gates, our method invariably synthesizes functions using only 3×3 Toffoli gates, Feynman gates and NOT gates. This reduces the quantum cost. Our method adds small cost by adding extra ancilla bits. Moreover, our circuits are always (4-neighbors) regular, which is an asset when they are mapped to 2-Dimensional arrays in Ion Trap (quantum) technology.