2025/05/12 by Boulebnane, Sami, Khan, Abid, Liu, Minzhao +4 · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2505.07929
The Sherrington-Kirkpatrick (SK) model serves as a foundational framework for understanding disordered systems. The Quantum Approximate Optimization Algorithm (QAOA) is a quantum optimization algorithm whose performance monotonically improves with its depth p. We analyze QAOA applied to the SK model in the infinite-size limit and provide numerical evidence that it obtains a (1-ε) approximation to the optimal energy with circuit depth O(n/ε1.13) in the average case. Our results are enabled by mapping the task of evaluating QAOA energy onto the task of simulating a spin-boson system, which we perform with modest cost using matrix product states. We optimize QAOA parameters and observe that QAOA achieves ε\lesssim2.2% at p=160 in the infinite-size limit. We then use these optimized QAOA parameters to evaluate the QAOA energy for finite-sized instances with up to 30 qubits and find convergence to the ground state consistent with the infinite-size limit prediction. Our results provide strong numerical evidence that QAOA can efficiently approximate the ground state of the SK model in the average case.