Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm

As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of the quantum circuit output. One of these algorithms, the Qua...

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Bibliographic Details
Published in:	EPJ quantum technology 2022-12, Vol.9 (1), Article 11
Main Authors:	Moussa, Charles, Wang, Hao, Bäck, Thomas, Dunjko, Vedran
Format:	Article
Language:	eng
Subjects:	Algorithms Circuits Clustering Combinatorial analysis Cost function Iterative methods Machine learning Nanotechnology and Microengineering Optimization Optimization algorithms Parameter identification Physics Physics and Astronomy Quantum computing Quantum Information Technology Quantum Physics Spintronics
Online Access:	Get full text
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Summary:	As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of the quantum circuit output. One of these algorithms, the Quantum Approximate Optimization Algorithm stands out as a promising approach to tackling combinatorial problems. However, finding the appropriate parameters is a difficult task. Although QAOA exhibits concentration properties, they can depend on instances characteristics that may not be easy to identify, but may nonetheless offer useful information to find good parameters. In this work, we study unsupervised Machine Learning approaches for setting these parameters without optimization. We perform clustering with the angle values but also instances encodings (using instance features or the output of a variational graph autoencoder), and compare different approaches. These angle-finding strategies can be used to reduce calls to quantum circuits when leveraging QAOA as a subroutine. We showcase them within Recursive-QAOA up to depth 3 where the number of QAOA parameters used per iteration is limited to 3, achieving a median approximation ratio of 0.94 for MaxCut over 200 Erdős-Rényi graphs. We obtain similar performances to the case where we extensively optimize the angles, hence saving numerous circuit calls.
ISSN:	2662-4400 2196-0763