A multiobjective approach to linear nearest neighbor optimization for 2D quantum circuits

The linear nearest neighbor (LNN) restriction, present in several current implementations of 1D and 2D quantum circuits, limits the interaction of qubits to those which are adjacent to each other. While there have been several proposals to optimize the process of achieving LNN compliance in 1D circuits, there are few proposals for 2D circuits. Here, we present a new perspective on this problem for 2D quantum circuits. We propose to see this as a multiobjective optimization problem with two objectives: minimizing the size of the 2D grid in the circuit, and minimizing the number of SWAP gates required to achieve LNN compliance. We present some preliminary results which show that these are two contradictory objectives. Since this is common in multiobjective problems, these results indicate that a multiobjective algorithm might be a suitable way to address this problem, since it would make considerations which currently available methods do not make.