Statistical Estimation in the Spiked Tensor Model via the Quantum Approximate Optimization Algorithm

Understand

The quantum approximate optimization algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization.

• In this paper, we analyze the performance of the QAOA on a statistical estimation problem, namely, the spiked tensor model, which exhibits a statistical-computational gap classically.
• We prove that the weak recovery threshold of $1$-step QAOA matches that of $1$-step tensor power iteration.
• Additional heuristic calculations suggest that the weak recovery threshold of $p$-step QAOA matches that of $p$-step tensor power iteration when $p$ is a fixed constant.