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

Ruslan Shaydulin,Changhao Li，Romina Yalovetzky,Marco Pistoia

Science Advances（2024）SCI 1区

JPMorgan Chase

Cited 23|Views46

Abstract

The quantum approximate optimization algorithm (QAOA) is a leading candidatealgorithm for solving optimization problems on quantum computers. However, thepotential of QAOA to tackle classically intractable problems remains unclear.Here, we perform an extensive numerical investigation of QAOA on the lowautocorrelation binary sequences (LABS) problem, which is classicallyintractable even for moderately sized instances. We perform noiselesssimulations with up to 40 qubits and observe that the runtime of QAOA withfixed parameters scales better than branch-and-bound solvers, which are thestate-of-the-art exact solvers for LABS. The combination of QAOA with quantumminimum finding gives the best empirical scaling of any algorithm for the LABSproblem. We demonstrate experimental progress in executing QAOA for the LABSproblem using an algorithm-specific error detection scheme on Quantinuumtrapped-ion processors. Our results provide evidence for the utility of QAOA asan algorithmic component that enables quantum speedups.

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Key words

Quantum Machine Learning,Variational Quantum Algorithms,Quantum Computation,Fault-tolerant Quantum Computation,Quantum Algorithms

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