Exploiting the Extended Neighborhood of Hexagonal Qubit Architecture for Mapping Quantum Circuits

In this work mapping of quantum circuits to regular hexagonal grid with coupling degree of six has been investigated. Architectures involving superconducting qubits impose restrictions on 2-qubit gate operations to be carried out only between physically coupled qubits, also referred to as Nearest Neighbour (NN) Constraint. The noise introduced by the 2-qubit gates and the execution time greatly affect the computational reliability. Existing mapping techniques suffer either from the adopted approach to reduce gate overhead or from their inability to take advantage of such architectural regularity. We outlined three different qubit mapping approaches using Remote-CNOT templates, Swap gates and combination of both. We show the benefits of assigning the Cartesian coordinate system in hexagonal grid for runtime elevation and devised approaches for reduction in gate overheads. While the template-based approach gives a strict upper bound of additional gate overheads for a particular qubit mapping, the combined approach provides better result employing a larger lookahead window. Experiments on benchmark quantum circuits confirm that the proposed Swap-based method provides an average \(25\%\) improvement in gate overheads over a recent work and the combined approach contributes further \(15\%\) average improvement on the result at the expense of a little higher runtime.