Trainability Barriers in Low-Depth QAOA Landscapes
<|reference_start|>Trainability Barriers in Low-Depth QAOA Landscapes: The Quantum Alternating Operator Ansatz (QAOA) is a prominent variational quantum algorithm for solving combinatorial optimization problems. Its effectiveness depends on identifying input parameters that yield high-quality solutions. However, understanding the complexity of training QAOA remains an under-explored area. Previous results have given analytical performance guarantees for a small, fixed number of parameters. At the opposite end of the spectrum, barren plateaus are likely to emerge at $\Omega(n)$ parameters for $n$ qubits. In this work, we study the difficulty of training in the intermediate regime, which is the focus of most current numerical studies and near-term hardware implementations. Through extensive numerical analysis of the quality and quantity of local minima, we argue that QAOA landscapes can exhibit a superpolynomial growth in the number of low-quality local minima even when the number of parameters scales logarithmically with $n$. This means that the common technique of gradient descent from randomly initialized parameters is doomed to fail beyond small $n$, and emphasizes the need for good initial guesses of the optimal parameters.<|reference_end|>
@article{rajakumar2024trainability,
    title={Trainability Barriers in Low-Depth QAOA Landscapes},
    author={Joel Rajakumar, John Golden, Andreas B"artschi, Stephan Eidenbenz},
    journal={21st ACM International Conference on Computing Frontiers CF'24,
  pages 199-206, May 2024},
    year={2024},
    doi={10.1145/3649153.3649204},
    number={LA-UR-24-20039},
    archivePrefix={arXiv},
    eprint={2402.10188},
    primaryClass={quant-ph cs.DS}
}