Synthesis of Semi-Classical Quantum Circuits

This paper proposes an efficient synthesis method for semi-classical quantum circuits (SCQCs) based on decision diagrams for a matrix function (DDMFs). The underlying technique is similar to the one used in previous work on reversible circuit synthesis methods based on binary decision diagrams (BDDs). Our method can be considered to be a generalization of the previous work in the sense that we can synthesis SCQCs which include reversible circuits as a special case. Moreover, we introduce some new ideas concerning how to consider the trade-off between the numbers of gates and qubits, and how to optimize the designed circuit by changing the variable order of the given DDMF.