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Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Guido Pagano, Aniruddha Bapat, Patrick Becker, Katherine Collins, Arinjoy De, Paul Hess, Harvey Kaplan, A. Kyprianidis, Wen Lin Tan, Christopher L. Baldwin,

Proceedings of the National Academy of Sciences · 2020 · 268 citations · 42 references

DOI Full text

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TL;DR

Variational quantum algorithms combine quantum resources with classical optimization to tackle many‑body and optimization problems, but their performance scaling with qubit number remains unclear. The study applies QAOA to approximate the ground‑state energy of a long‑range Ising model and evaluates its performance on a trapped‑ion quantum simulator up to 40 qubits. QAOA is implemented on a trapped‑ion quantum simulator with up to 40 qubits to approximate the ground‑state energy of a long‑range Ising model. The algorithm shows negligible performance loss and near‑constant runtime scaling with qubit number, and error modeling explains the results, indicating progress toward general hybrid quantum‑classical algorithms.

Abstract

Significance Variational quantum algorithms combine quantum resources with classical optimization methods, providing a promising approach to solve both quantum many-body and classical optimization problems. A crucial question is how variational algorithms perform as a function of qubit number. Here, we address this question by applying a variational quantum algorithm (QAOA) to approximate the ground-state energy of a long-range Ising model, both quantum and classical, and investigating the algorithm performance on a trapped-ion quantum simulator with up to 40 qubits. A negligible performance degradation and almost constant runtime scaling is observed as a function of the number of qubits. By modeling the error sources, we explain the experimental performance, marking a stepping stone toward more general realizations of hybrid quantum–classical algorithms.