Adaptive Integer Linear Programming Model for Optimal Qubit Permutation

Abstract

The architecture of most current quantum computers limits the pairs of qubits that can interact. That is, not all possible CNOT gates are directly available and their implementation requires additional gates. Hence the permutation of qubits will have an effect on the circuit complexity. We formulate the permutation problem as an Integer Linear Programming (ILP) problem. The solution of the ILP guarantees the lowest cost permutation for the problem. The results are compared to the previously best-known algorithm showing an improvement of up to 57% in the number of gates.