  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.
