Symmetry-informed transferability of optimal parameters in the quantum approximate optimization algorithm
Journal article, 2025

One of the main limitations of variational quantum algorithms is the classical optimization of the highly dimensional nonconvex 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 multiangle quantum approximate optimization algorithms.

Optimization problems

Quantum algorithms

Adiabatic quantum optimization

Author

Isak Lyngfelt

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Laura Garcia Alvarez

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Physical Review A

24699926 (ISSN) 24699934 (eISSN)

Vol. 111 2 022418

Subject Categories (SSIF 2025)

Nano-technology

DOI

10.1103/PhysRevA.111.022418

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Latest update

2/28/2025