Indirect Quantum Approximate Optimization Algorithms: application to the TSP

TL;DR

This paper introduces IQAOA, a quantum algorithm for solving the Traveling Salesman Problem that uses an indirect encoding to reduce circuit complexity, enabling larger problem instances to be tackled on noisy quantum hardware.

Contribution

The paper presents a novel indirect encoding approach for QAOA, reducing circuit depth and enabling larger TSP instances to be solved on current quantum simulators.

Findings

Successfully solved 8-customer TSP instances with IQAOA on IBM simulator.

IQAOA outperforms traditional QAOA in circuit complexity for TSP.

Demonstrated feasibility of solving larger TSP problems with noisy quantum devices.

Abstract

We propose an Indirect Quantum Approximate Optimization Algorithm (referred to as IQAOA) where the Quantum Alternating Operator Ansatz takes into consideration a general parameterized family of unitary operators to efficiently model the Hamiltonian describing the set of string vectors. This algorithm creates an efficient alternative to QAOA, where: 1) a Quantum parametrized circuit executed on a quantum machine models the set of string vectors; 2) a Classical meta-optimization loop executed on a classical machine; 3) an estimation of the average cost of each string vector computing, using a well know algorithm coming from the OR community that is problem dependent. The indirect encoding defined by dimensional string vector is mapped into a solution by an efficient coding/decoding mechanism. The main advantage is to obtain a quantum circuit with a strongly limited number of gates that could be executed on the noisy current quantum machines. The numerical experiments achieved with IQAOA permits to solve 8-customer instances TSP using the IBM simulator which are to the best of our knowledge the largest TSP ever solved using a QAOA based approach.