Quantum Circuit Design of a T-count Optimized Integer Multiplier

Abstract

Quantum circuits of many qubits are extremely difficult to realize; thus, the number of qubits is an important metric in a quantum circuit design. Further, scalable and reliable quantum circuits are based on fault tolerant implementations of quantum gates such as Clifford+T gates. An efficient quantum circuit saves quantum hardware resources by reducing the number of T gates without substantially increasing the number of qubits. This work presents a T-count optimized quantum circuit for integer multiplication with only $4 \cdot n + 1$4·n+1 qubits and no garbage outputs. The proposed quantum multiplier design reduces the T-count by using a novel quantum conditional adder circuit. Also, where one operand to the conditional adder is zero, the conditional adder is replaced with a Toffoli gate array to further save T gates. Average T-count savings of $46.12$46.12, $47.55$47.55, $62.71$62.71 and 26.30 percent are achieved compared to the recent works by Kotiyal et al., Babu, Lin et al., and Jayashree et al., respectively.