Quantum 2025 – scientific programme
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THU: Thursday Contributed Sessions
THU 6: Quantum Computing and Communication: Contributed Session II (Concepts)
THU 6.2: Talk
Thursday, September 11, 2025, 14:30–14:45, ZHG007
Regular parameterizations of the special unitary group and convergence of variational algorithms — •Marco Wiedmann1, Daniel Burgarth1, and Christian Arenz2 — 1Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstraße 7 91058 Erlangen, Germany — 2Arizona State University, 650 E Tyler Mall, Tempe, AZ 85281, USA
Variational algorithms have gained a lot of attention in the recent years as a potential application of quantum computers. In broad terms, a parameterized unitary is implemented on a quantum computer, which is then used to measure some objective function that should be minimized by a classical optimization routine.
Gradient based optimizers can however get stuck at singular points of the parameterization, which resembles a gimbal lock like effect. We show that some popular parameterizations do indeed admit these singular points and propose alternatives which are globally regular. Finally, we use these parameterizations to prove that if the Variational Quantum Eigensolver does not run off to infinity, it almost always converges to a true ground state of the problem Hamiltonian.
Keywords: Variational Quantum Algorithms; Differential Geometry; Convergence of gradient algorithms; Optimization; Singular points