RT Conference Proceedings
T1 The Quantum Approximate Optimization Algorithm Can Require Exponential Time to Optimize Linear Functions
A1 Chicano-García, José-Francisco
A1 Dahi, Zakaria Abdelmoiz
A1 Luque-Polo, Gabriel Jesús
K1 Computación cuántica
K1 Algoritmos computacionales
AB 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.
YR 2025
FD 2025
LK https://hdl.handle.net/10630/39485
UL https://hdl.handle.net/10630/39485
LA eng
NO Universidad de Málaga
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026