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QI: Fachverband Quanteninformation

QI 16: Quantum Computing Theory III

QI 16.4: Vortrag

Dienstag, 11. März 2025, 14:45–15:00, HS IV

Quantum combinatorial optimization beyond the variational paradigm: simple schedules for hard problems — •Tim Bode, Krish Ramesh, and Tobias Stollenwerk — Institute for Quantum Computing Analytics, Forschungszentrum Jülich

Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large Hilbert spaces. Hence, finding annealing protocols by variation ultimately appears to be difficult. Similarly, the adiabatic theorem fails on hard problem instances with first-order quantum phase transitions. Here, we show how to use the spin coherent-state path integral to shape the geometry of quantum adiabatic evolution, leading to annealing protocols at polynomial overhead that provide orders-of-magnitude improvements in the probability to measure optimal solutions, relative to linear protocols. These improvements are not obtained on a controllable toy problem but on randomly generated hard instances (Sherrington-Kirkpatrick and Maximum 2-Satisfiability), making them generic and robust. Our method works for large systems and may thus be used to improve the performance of state-of-the-art quantum devices.

Keywords: Quantum Algorithms; Combinatorial Optimization; Spin glasses; Quantum Annealing