Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems

Journal Article · Fri Apr 03 00:00:00 EDT 2020 · Proceedings of the AAAI Conference on Artificial Intelligence

DOI:https://doi.org/10.1609/aaai.v34i03.5616· OSTI ID:1726173

Khairy, Sami ^[1]; Shaydulin, Ruslan ^[2]; Cincio, Lukasz ^[3]; Alexeev, Yuri ^[4]; Balaprakash, Prasanna ^[4]

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1. Illinois Institute of Technology, Chicago, IL (United States)
2. Clemson Univ., SC (United States)
3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
4. Argonne National Lab. (ANL), Argonne, IL (United States)

Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading candidates for demonstrating quantum advantage in the near term. QAOA is a variational hybrid quantum-classical algorithm for approximately solving combinatorial optimization problems. The quality of the solution obtained by QAOA for a given problem instance depends on the performance of the classical optimizer used to optimize the variational parameters. In this paper, we formulate the problem of finding optimal QAOA parameters as a learning task in which the knowledge gained from solving training instances can be leveraged to find high-quality solutions for unseen test instances. To this end, we develop two machine-learning-based approaches. Our first approach adopts a reinforcement learning (RL) framework to learn a policy network to optimize QAOA circuits. Our second approach adopts a kernel density estimation (KDE) technique to learn a generative model of optimal QAOA parameters. In both approaches, the training procedure is performed on small-sized problem instances that can be simulated on a classical computer; yet the learned RL policy and the generative model can be used to efficiently solve larger problems. Furthermore, extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our proposed RL- and KDE-based approaches reduce the optimality gap by factors up to 30.15 when compared with other commonly used off-the-shelf optimizers.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: 89233218CNA000001; AC02-06CH11357
• OSTI ID: 1726173
• Report Number(s): LA-UR--19-28945
• Journal Information: Proceedings of the AAAI Conference on Artificial Intelligence, Journal Name: Proceedings of the AAAI Conference on Artificial Intelligence Journal Issue: 03 Vol. 34; ISSN 2159-5399
• Publisher: Association for the Advancement of Artificial Intelligence
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING