New Structural Quantum Circuit Simulating A Toffoli Gate

Abstract

A Toffoli gate ($C^{\{}n\}$-NOT gate) is regarded as an important unitary gate in quantum computation, and is simulated by a quantum circuit composed of $C^{\{}2\}$-NOT gates. This paper presents a quantum circuit with a new configuration of $C^{\{}2\}$-NOT gates simulating a $C^{\{}2m+1\}$-NOT operation under the condition $m=2^{\{}n\}$ ($n=1,2,...$). The circuit is composed of units called multi-qubits gates (MQGs), each of which performs $m$ $C^{\{}2\}$-NOT operations simultaneously on $3m$ qubits. Simultaneous operations eliminate the need to manipulate qubits individually, as required in conventional quantum circuits. The proposed circuit thus represents a more realistic mode of operation for practical computing systems. A nuclear magnetic resonance implementation of the circuit is presented as a demonstration of the feasibility of MQG operations for practical systems.