Trainability Barriers in Low-Depth QAOA Landscapes

• URL: http://arxiv.org/abs/2402.10188v2
• Date: Wed, 09 Oct 2024 14:51:54 GMT
• Title: Trainability Barriers in Low-Depth QAOA Landscapes
• Authors: Joel Rajakumar, John Golden, Andreas Bärtschi, Stephan Eidenbenz,
• Abstract summary: Quantum Alternating Operator Ansatz (QAOA) is a prominent variational quantum algorithm for solving optimization problems. Previous results have given analytical performance guarantees for a small, fixed number of parameters. We study the difficulty of training in the intermediate regime, which is the focus of most current numerical studies.
• Score: 0.0
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• Abstract: 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.

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