Shallower CNOT circuits on realistic quantum hardware

Abstract

We focus on the depth optimization of CNOT circuits on hardwares with limited connectivity. We adapt the algorithm from Kutin et al. [17] that implements any n -qubit CNOT circuit in depth at most 5 n on a Linear Nearest Neighbour (LNN) architecture. Our proposal is a block version of Kutin et al. ’s algorithm that is scalable with the number of interactions available in the hardware: the more interactions we have the less the depth. We derive better theoretical upper bounds and we provide a simple implementation of the algorithm. Overall, we achieve better depth complexity for CNOT circuits on some realistic quantum hardware like a grid or a ladder. For instance the execution of a n -qubit CNOT circuit on a grid can be done in depth 4 n + 8.