Reducing T-count When Decomposing Many MPMCT Gates Simultaneously

Abstract

To realize fault-tolerant quantum circuits, one of the important task is to reduce the number of T gates (T-count) when we decompose MPMCT (Mixed Polarity Multiple-Control Toffoli) gates into elementary gates. When we have enough auxiliary qubits, we have an efficient decomposition of a single MPMCT gate. However, it has not been studied intensively how to decompose many MPMCT gates efficiently at the same time. Thus, this paper studies what is an efficient decomposition method when we have many MPMCT gates. We consider two situations to reduce T-count when we need to decompose many MPMCT gates. Then, we propose a heuristic method to reorder MPMCT gates if possible so that we can find the two situations as much as possible. Our preliminary experiments show that our heuristic can reduce T-count drastically.