Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry

• Published in: npj quantum information Vol. 10; no. 1; pp. 18 - 11
• Main Authors: Dalton, Kieran, Long, Christopher K., Yordanov, Yordan S., Smith, Charles G., Barnes, Crispin H. W., Mertig, Normann, Arvidsson-Shukur, David R. M.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 27.01.2024; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/483/3926; 639/766/483/481; Accuracy; Algorithms; Chemistry; Circuits; Classical and Quantum Gravitation; Codes; Depolarization; Energy; Fault tolerance; Physics; Physics and Astronomy; Probability; Quantum Computing; Quantum Field Theories; Quantum Information Technology; Quantum Physics; Relativity Theory; Simulation; Spintronics; String Theory
• ISSN: 2056-6387; 2056-6387
• DOI: 10.1038/s41534-024-00808-x

Variational quantum eigensolvers (VQEs) are leading candidates to demonstrate near-term quantum advantage. Here, we conduct density-matrix simulations of leading gate-based VQEs for a range of molecules. We numerically quantify their level of tolerable depolarizing gate-errors. We find that: (i) The best-performing VQEs require gate-error probabilities between 10 −6 and 10 −4 (10 −4 and 10 −2 with error mitigation) to predict, within chemical accuracy, ground-state energies of small molecules with 4 − 14 orbitals. (ii) ADAPT-VQEs that construct ansatz circuits iteratively outperform fixed-circuit VQEs. (iii) ADAPT-VQEs perform better with circuits constructed from gate-efficient rather than physically-motivated elements. (iv) The maximally-allowed gate-error probability, p c , for any VQE to achieve chemical accuracy decreases with the number N II of noisy two-qubit gates as p c ∝ ~ N II − 1 . Additionally, p c decreases with system size, even with error mitigation, implying that larger molecules require even lower gate-errors. Thus, quantum advantage via gate-based VQEs is unlikely unless gate-error probabilities are decreased by orders of magnitude.