Dynamic Realization of Multiple Control Toffoli Gate

Dynamic Quantum Circuits (DQC) is an inevitable solution for today's Noisy Intermediate Scale Quantum (NISQ) systems. This enables realization of an n-qubit (where,
$n > 2$
) quantum circuit using only 2-qubits with the aid of additional non-unitary operations which is evident from the recent dynamic realizations of algorithms like Quantum Phase Estimation (QPE) and Bernstein- Vazirani (BV) as well as 3-qubit Toffoli operation. In this work, we introduce two different dynamic realization schemes for Multiple Control Toffoli (MCT) gates, for the first time to the best of our knowledge. We compare the respective realizations in terms of resources (e.g., gate, depth and nearest neighbor overhead) and computational accuracy. For this purpose, we apply the proposed dynamic MCT gates in Deutsch-Jozsa (DJ) algorithm, thereby realizing the traditional DJ algorithm as DQCs. Experimental evaluations show that one dynamic scheme for MCT gates leads to DQCs with better computational accuracy, while the other one results in DQCs with better computational resources.