Evidence of Scaling Advantage for the Quantum Approximate Optimization Algorithm on a Classically Intractable Problem

• Published in: arXiv.org
• Main Authors: Shaydulin, Ruslan, Li, Changhao, Chakrabarti, Shouvanik, DeCross, Matthew, Herman, Dylan, Kumar, Niraj, Larson, Jeffrey, Danylo Lykov, Minssen, Pierre, Sun, Yue, Alexeev, Yuri, Dreiling, Joan M, Gaebler, John P, Gatterman, Thomas M, Gerber, Justin A, Gilmore, Kevin, Gresh, Dan, Hewitt, Nathan, Horst, Chandler V, Hu, Shaohan, Johansen, Jacob, Matheny, Mitchell, Tanner Mengle, Mills, Michael, Moses, Steven A, Neyenhuis, Brian, Siegfried, Peter, Yalovetzky, Romina, Pistoia, Marco
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 02.06.2024
• Subjects: Algorithms; Computer Science - Emerging Technologies; Error detection; Optimization; Optimization algorithms; Physics - Quantum Physics; Physics - Statistical Mechanics; Quantum computers; Quantum computing; Qubits (quantum computing); Solvers
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2308.02342

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.