Quantum approximate optimization using SWAP gates for mixing

Abstract

In recent years, with the emergence of more complex optimization problems scientists have begun to look at how quantum computers can be utilized to solve big problems. One algorithm that can be used is the quantum approximation algorithm(QAOA). QAOA applies two different types of operators to a qubit string representing an initial state. One regulates the problem to be optimized and the other mixes the states such that all possible solutions to the problem are being tested. My work investigates the possibility to use SWAP gates for mixing instead of the ordinary Pauli X operator for the traveling salesman problem. The advantage of the SWAP mixer is that it swaps the values of two qubits in the qubit string compared to the Pauli X operator that changes the value of a single qubit. My results show that the SWAP mixer works well for the traveling salesman problem and has the potential to be used in more complex problems.