Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers

• Published in: npj quantum information 2023-06, Vol.9 (1), p.60-9, Article 60
• Main Authors: Zhao, Luning, Goings, Joshua, Shin, Kyujin, Kyoung, Woomin, Fuks, Johanna I., Kevin Rhee, June-Koo, Rhee, Young Min, Wright, Kenneth, Nguyen, Jason, Kim, Jungsang, Johri, Sonika
• Format: Article
• Language: English
• Subjects: 639/638/563/758; 639/766/483/3926; Classical and Quantum Gravitation; Computers; Physics; Physics and Astronomy; Quantum Computing; Quantum Field Theories; Quantum Information Technology; Quantum Physics; Relativity Theory; Spintronics; String Theory
• ISSN: 2056-6387; 2056-6387
• DOI: 10.1038/s41534-023-00730-8

Variational quantum eigensolvers (VQE) are among the most promising approaches for solving electronic structure problems on near-term quantum computers. A critical challenge for VQE in practice is that one needs to strike a balance between the expressivity of the VQE ansatz versus the number of quantum gates required to implement the ansatz, given the reality of noisy quantum operations on near-term quantum computers. In this work, we consider an orbital-optimized pair-correlated approximation to the unitary coupled cluster with singles and doubles (uCCSD) ansatz and report a highly efficient quantum circuit implementation for trapped-ion architectures. We show that orbital optimization can recover significant additional electron correlation energy without sacrificing efficiency through measurements of low-order reduced density matrices (RDMs). In the dissociation of small molecules, the method gives qualitatively accurate predictions in the strongly-correlated regime when running on noise-free quantum simulators. On IonQ’s Harmony and Aria trapped-ion quantum computers, we run end-to-end VQE algorithms with up to 12 qubits and 72 variational parameters—the largest full VQE simulation with a correlated wave function on quantum hardware. We find that even without error mitigation techniques, the predicted relative energies across different molecular geometries are in excellent agreement with noise-free simulators.