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QI: Fachverband Quanteninformation
QI 15: Quantum Computing Theory
QI 15.8: Vortrag
Mittwoch, 20. März 2024, 11:45–12:00, HFT-FT 101
Symmetry obstructions to the quantum approximate optimization algorithm — Sujay Kazi1,2,3, Martin Larocca2,4, Marco Farinati5, Patrick J. Coles6, Marco Cerezo7, and •Robert Zeier8 — 1Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA — 2Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA — 3Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA — 4Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA — 5Departamento de Matemática, FCEN, UBA - IMAS CONICET — 6Normal Computing Corporation, New York, New York, USA — 7Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA — 8Forschungszentrum Jülich GmbH, Peter Grünberg Institute, Quantum Control (PGI-8), 54245 Jülich, Germany
The quantum approximate optimization algorithm (QAOA) approximates ground states related to the maximum-cut graph problem. We study symmetries and algebraic properties of QAOA ansätze. For the free (or multi-angle) ansatz, the Lie algebras observed for any connected graph split into six classes corresponding to path, cycle, bipartite, and remaining graphs. We predict that polynomially and exponentially deep quantum circuits will suffer from barren plateaus when the free ansatz is applied to the remaining graphs. But shallow circuits of logarithmic depth will likely lack the resources to approximately reach the ground state. Even for the so-called standard ansatz, we indicate why the effectiveness of QAOA might be negatively affected.
Keywords: QAOA; maximum-cut problem; barren plateau