Berlin 2024 – scientific programme

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QI: Fachverband Quanteninformation

QI 15: Quantum Computing Theory

QI 15.9: Talk

Wednesday, March 20, 2024, 12:00–12:15, HFT-FT 101

Discrete adiabatic quantum optimization — •Vanessa Dehn and Thomas Wellens — Fraunhofer Institut für Angewandte Festkörperphysik IAF, Freiburg, Deutschland

The Quantum Approximate Optimization Algorithm (QAOA) is a well-known candidate for solving combinatorial optimization problems more efficiently than classical computers in the current noisy intermediate-scale quantum (NISQ) era. The form of the QAOA circuit is inspired by adiabatic quantum computing (AQC) in terms of starting in the ground state of the mixing Hamiltonian, which is then gradually transferred to the ground state of the cost Hamiltonian by approximating the adiabatic annealing path via Trotterization for an increasing and very large iteration depth p. Therefore, the performance of QAOA is expected to improve with increasing p. However, recent studies [1] showed, that QAOA can exhibit a poor performance for large circuit parameters, even in the adiabatic limit.

To explain this behavior, a modification of the continous adiabatic theorem, namely the discrete adiabatic theorem, is applied, where the state evolves by applying a product of gradually varying unitaries. To understand the decrease of the ground state population, we track the population and population changes of each state throughout the whole protocol for different sets of parameters. Furthermore, we explore how these insights may be used in order to find optimized schedules for the QAOA angles.

[1] V. Kremenetski et al., arXiv:2305.04455 (2023).

Keywords: Quantum optimization; Quantum approximate optimization algorithm; adiabatic theorem