Nearest Neighbor Mapping of Quantum Circuits to Two-Dimensional Hexagonal Qubit Architecture

Motivated by physical realization of hexagonal architectures, in this paper we have introduced the hexagonal neighborhood structure for a set of qubits in a two-dimensional (2-D) plane along with a simple measure for estimating neighborhood distance. As compared to the traditional layout of qubits on a 2-D Cartesian plane, the hexagonal arrangement offers greater flexibility in mapping the logical qubits from a quantum circuit into an array of physical qubits. In most of the prior works, the neighborhood cost is estimated as number of Swap operations required to ensure that all 2-qubit quantum gates operate on physically adjacent qubits. However, in recent times, CNOT Templates have been used to execute 2-qubit gates where the interacting qubits are not adjacent to each other. In this paper we exploit the benefits of CNOT Templates in mapping quantum circuits to hexagonal 2-D arrays. We propose an evolutionary algorithm to obtain a good placement of qubits in the hexagonal structure. We also show the benefits of this approach over a simple greedy qubit placement method. We have carried out experiments on a set of benchmark suites to evaluate the efficiency of the proposed approach. The results show an average improvement of 42.9% over a very recent state-of-the-art method.