Synthesis of quantum arrays from Kronecker Functional Lattice Diagrams

Reversible logic is becoming more and more popular due to the fact that many novel technologies such as quantum computing, low power CMOS circuit design or quantum optical computing are becoming more and more realistic. In quantum computing, reversible computing is the main venue for the realization and design of classical functions and circuits. We present a new approach to synthesis of reversible circuits using Kronecker Functional Lattice Diagrams (KFLD). Unlike many of contemporary algorithms for synthesis of reversible functions that use n×n Toffoli gates, our method synthesizes functions using 3 × 3 Toffoli gates, Feynman gates and NOT gates. This reduces the quantum cost of the designed circuit but adds additional ancilla bits. The resulting circuits are always regular in a 4-neighbor model and all connections are predictable. Consequently resulting circuits can be directly mapped in to a quantum device such as quantum FPGA [14]. This is a significant advantage of our method, as it allows us to design optimum circuits for a given quantum technology.