Symmetry-informed transferability of optimal parameters in the Quantum Approximate Optimization Algorithm

Abstract

One of the main limitations of variational quantum algorithms is the classical optimization of the highly dimensional non-convex variational parameter landscape. To simplify this optimization, we can reduce the search space using problem symmetries and typical optimal parameters as initial points if they concentrate. In this article, we consider typical values of optimal parameters of the quantum approximate optimization algorithm for the MaxCut problem with d-regular tree subgraphs and reuse them in different graph instances. We prove symmetries in the optimization landscape of several kinds of weighted and unweighted graphs, which explains the existence of multiple sets of optimal parameters. However, we observe that not all optimal sets can be successfully transferred between problem instances. We find specific transferable domains in the search space and show how to translate an arbitrary set of optimal parameters into the adequate domain using the studied symmetries. Finally, we extend these results to general classical optimization problems described by Ising Hamiltonians, the Hamiltonian variational ansatz for relevant physical models, and the recursive and multi-angle quantum approximate optimization algorithms.

arXiv comment17 pages, 6 figures, v2: added results on symmetries for RQAOA, and HVA

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Cited by in corpus (6)

• Implementing transferable annealing protocols for combinatorial optimisation on neutral atom quantum processors: a case study on smart-charging of electric vehicles
• Universal Resources for QAOA and Quantum Annealing
• Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
• Generative flow-based warm start of the variational quantum eigensolver
• Optimisation-Free Recursive QAOA for the Binary Paint Shop Problem
• Investigating layer-selective transfer learning of QAOA parameters for Max-Cut problem