Trainability Barriers in Low-Depth QAOA Landscapes
CoRR(2024)
摘要
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 Ω(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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