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

• URL: http://arxiv.org/abs/2211.04505v2
• Date: Tue, 13 Feb 2024 17:30:41 GMT
• Title: Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry
• Authors: Kieran Dalton, Christopher K. Long, Yordan S. Yordanov, Charles G. Smith, Crispin H. W. Barnes, Normann Mertig and David R. M. Arvidsson-Shukur
• Abstract summary: Variational quantum eigensolvers (VQEs) are leading candidates to demonstrate near-term quantum advantage. We numerically quantify their level of tolerable depolarizing gate-errors.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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