2026-06-03T11:43:42Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/394852026-02-03T11:49:16Zcom_10630_2254col_10630_37959

00925njm 22002777a 4500 dc Chicano-García, José-Francisco author Dahi, Zakaria Abdelmoiz author Luque-Polo, Gabriel Jesús author 2025 QAOA is a hybrid quantum-classical algorithm to solve optimization problems in gate-based quantum computers. It is based on a variational quantum circuit that can be interpreted as a discretization of the annealing process that quantum annealers follow to find a minimum energy state of a given Hamiltonian. This ensures that QAOA must find an optimal solution for any given optimization problem when the number of layers, p, used in the variational quantum circuit tends to infinity. In practice, the number of layers is usually bounded by a small number. This is a must in current quantum computers of the NISQ era, due to the depth limit of the circuits they can run to avoid problems with decoherence and noise. In this paper, we show mathematical evidence that QAOA requires exponential time to solve linear functions when the number of layers is less than the number of different coefficients of the linear function n. We conjecture that QAOA needs exponential time to find the global optimum of linear functions for any constant value of p, and that the runtime is linear only if p >= n. We conclude that we need new quantum algorithms to reach quantum supremacy in quantum optimization. https://hdl.handle.net/10630/39485 Computación cuántica Algoritmos computacionales The Quantum Approximate Optimization Algorithm Can Require Exponential Time to Optimize Linear Functions