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

TL;DR

This study uses simulations to determine the tolerable gate-error rates for variational quantum eigensolvers in quantum chemistry, revealing that achieving chemical accuracy demands extremely low error probabilities, especially for larger molecules.

Contribution

It provides a quantitative analysis of gate-error thresholds for VQEs, highlighting the importance of error mitigation and circuit construction methods for quantum advantage.

Findings

Best VQEs require gate-error probabilities between 10^{-6} and 10^{-4} for small molecules.

ADAPT-VQEs outperform fixed-circuit VQEs in accuracy and efficiency.

Maximum tolerable gate-error probability decreases with the number of noisy gates and system size.

Abstract

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 $\ncx$ of noisy two-qubit gates as $p_c\approxprop\ncx^{-1}$. 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.