Isak Lyngfelt, Applied Quantum Physics

Abstract: 

Quantum computers are getter bigger and better every year, but the current capabilities are still below the state-of-the-art classical counterparts. How to fully utilize the current generation of noisy intermediate-scale quantum (NISQ) computers is an active field of research. One popular strategy are the hybrid variational quantum algorithms (VQAs), which performs a parameter dependent quantum circuit, and utilizes a classical computer to find optimal parameter values. While being a promising heuristic for solving optimization problem with quantum computers, 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. In our recent work, 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 [1]. 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.

[1] Lyngfelt, I., García-Álvarez, L., "Symmetry-informed transferability of optimal parameters in the quantum approximate optimization algorithm", Phys. Rev. A 111, 022418

Discussion leader: Juan José García Ripoll, Senior Researcher, Institute of Fundamental Physics

Main supervisor: Göran Johanson, Full Professor, Applied Quantum Physics Laboratory
Examiner: Mikael Fogelström, Full Professor, Applied Quantum Physics Laboratory
Assistant supervisor: Laura García-Álvarez, researcher, Applied Quantum Physics