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

Ruslan Shaydulin; Changhao Li; Shouvanik Chakrabarti; Matthew DeCross; Dylan Herman; Niraj Kumar; Jeffrey Larson; Danylo Lykov; Pierre Minssen; Yue Sun; Yuri Alexeev; Joan M. Dreiling; John P. Gaebler; Thomas M. Gatterman; Justin A. Gerber; Kevin Gilmore; Dan Gresh; Nathan Hewitt; Chandler V. Horst; Shaohan Hu; Jacob Johansen; Mitchell Matheny; Tanner Mengle; Michael Mills; Steven A. Moses; Brian Neyenhuis; Peter Siegfried; Romina Yalovetzky; Marco Pistoia

doi:10.1126/sciadv.adm6761

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arXiv · 2308.02342

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

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Abstract

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.

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Ruslan Shaydulin, Changhao Li, Shouvanik Chakrabarti, Matthew DeCross, Dylan Herman, Niraj Kumar, Jeffrey Larson, Danylo Lykov, Pierre Minssen, Yue Sun, Yuri Alexeev, Joan M. Dreiling, John P. Gaebler, Thomas M. Gatterman, Justin A. Gerber, Kevin Gilmore, Dan Gresh, Nathan Hewitt, Chandler V. Horst, Shaohan Hu, Jacob Johansen, Mitchell Matheny, Tanner Mengle, Michael Mills, Steven A. Moses, Brian Neyenhuis, Peter Siegfried, Romina Yalovetzky, Marco Pistoia. 2024-06-02. Evidence of Scaling Advantage for the Quantum Approximate Optimization Algorithm on a Classically Intractable Problem. https://doi.org/10.1126/sciadv.adm6761

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