  Due to the physics behind quantum computing, quantum circuit designers must
adhere to the constraints posed by the limited interaction distance of qubits.
Existing circuits need therefore to be modified via the insertion of SWAP
gates, which alter the qubit order by interchanging the location of two qubits'
quantum states. We consider the Nearest Neighbor Compliance problem on a linear
array, where the number of required SWAP gates is to be minimized. We introduce
an Integer Linear Programming model of the problem of which the size scales
polynomially in the number of qubits and gates. Furthermore, we solve $131$
benchmark instances to optimality using the commercial solver CPLEX. The
benchmark instances are substantially larger in comparison to those evaluated
with exact methods before. The largest circuits contain up to $18$ qubits or
over $100$ quantum gates. This formulation also seems to be suitable for
developing heuristic methods since (near) optimal solutions are discovered
quickly in the search process.
