Optimal Design of Reversible Circuits in the Strict NCT Library

The synthesis of reversible logic circuits is a fundamental step in the design of fault-tolerant quantum arithmetic. Existing literature frequently minimizes Quantum Cost (QC) by utilizing the NCV library, which permits controlled-V and Vdagger gates. However, in the context of Fault-Tolerant Quantum Computing (FTQC), the strict NCT library (NOT, CNOT, Toffoli) is often preferred due to the high cost of distilling non-Clifford states required for arbitrary V-gates. Moreover, in the classical design of reversible circuits, only the NCT library can be used as V-gates are not available. In this paper, a new design method for reversible circuits is proposed, based on Mixed-Integer Non-Linear Programming (MINLP) within the Strict NCT Library. By formulating the problem as an MINLP model in GAMS, we successfully automated the optimization of five prominent reversible primitives (TSG, MKG, MIG, SAYEM, and URG) within the strict NCT library. Comparative analysis with the NCV costs found in the literature shows that the costs within the NCT library are comparable or better.