A Polynomial Size Model with Implicit SWAP Gate Counting for Exact Qubit Reordering

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