Indirect Quantum Approximate Optimization Algorithms: application to the TSP

• URL: http://arxiv.org/abs/2311.03294v1
• Date: Mon, 6 Nov 2023 17:39:14 GMT
• Title: Indirect Quantum Approximate Optimization Algorithms: application to the TSP
• Authors: Eric Bourreau, Gerard Fleury, Philippe Lacomme
• Abstract summary: Quantum Alternating Operator Ansatz takes into consideration a general parameterized family of unitary operators to efficiently model the Hamiltonian describing the set of 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.
• Score: 1.1786249372283566
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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