The Quantum Approximate Optimization Algorithm Can Require Exponential Time to Optimize Linear Functions
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| Název: | The Quantum Approximate Optimization Algorithm Can Require Exponential Time to Optimize Linear Functions |
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| Autoři: | Francisco Chicano, Zakaria Abdelmoiz Dahi, Gabriel Luque |
| Zdroj: | RIUMA. Repositorio Institucional de la Universidad de Málaga Universidad de Málaga |
| Publication Status: | Preprint |
| Informace o vydavateli: | ACM, 2025. |
| Rok vydání: | 2025 |
| Témata: | Quantum optimization, FOS: Computer and information sciences, Quantum Physics, Algoritmos computacionales, Emerging Technologies (cs.ET), Computación cuántica, gate-based quantum computers, Computer Science - Emerging Technologies, FOS: Physical sciences, linear functions, QAOA, Quantum Physics (quant-ph) |
| Popis: | 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 $p \geq n$. We conclude that we need new quantum algorithms to reach quantum supremacy in quantum optimization. This preprint has been accepted in the Quantum Optimization Workshop at the Genetic and Evolutionary Computation Conference (GECCO 2025). The accepted version can be found at https://doi.org/10.1145/3712255.3734319 |
| Druh dokumentu: | Article Conference object |
| DOI: | 10.1145/3712255.3734319 |
| DOI: | 10.48550/arxiv.2505.06404 |
| Přístupová URL adresa: | http://arxiv.org/abs/2505.06404 https://hdl.handle.net/10630/39485 |
| Rights: | CC BY |
| Přístupové číslo: | edsair.doi.dedup.....dd5b9523916124b9db3cee91c7f22ec6 |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | 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 $p \geq n$. We conclude that we need new quantum algorithms to reach quantum supremacy in quantum optimization.<br />This preprint has been accepted in the Quantum Optimization Workshop at the Genetic and Evolutionary Computation Conference (GECCO 2025). The accepted version can be found at https://doi.org/10.1145/3712255.3734319 |
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| DOI: | 10.1145/3712255.3734319 |