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

Kieran Dalton, Christopher K. Long, Yordan S. Yordanov, Charles G. Smith, Crispin H. W. Barnes, Normann Mertig, and David R. M. Arvidsson-Shukur

Published: 27 January 2024

DOI: 10.1038/s41534-024-00808-x

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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 $N_{\text{II}}$ of noisy two-qubit gates as $p_c\underset{\sim }{\propto }{N}_{\text{II}}$. 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.

Citation

Kieran Dalton, Christopher K. Long, Yordan S. Yordanov, Charles G. Smith, Crispin H. W. Barnes, Normann Mertig, and David R. M. Arvidsson-Shukur. Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry, npj Quantum Inf 10, 18 (2024), DOI: 10.1038/s41534-024-00808-x.

BibTeX

@article{Dalton2024,
    author={Dalton, Kieran
    and Long, Christopher K.
    and Yordanov, Yordan S.
    and Smith, Charles G.
    and Barnes, Crispin H. W.
    and Mertig, Normann
    and Arvidsson-Shukur, David R. M.},
    title={Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry},
    journal={npj Quantum Information},
    year={2024},
    month={Jan},
    day={27},
    volume={10},
    pages={18},
    issn={2056-6387},
    doi={10.1038/s41534-024-00808-x},
    url={https://doi.org/10.1038/s41534-024-00808-x}
}

Other versions

• Tue, 13 Feb 2024 17:30:41 UTC: https://arxiv.org/abs/2211.04505v2. Downloads: PDF, TeX Source
• Tue, 8 Nov 2022 19:05:38 UTC: https://arxiv.org/abs/2211.04505v1. Downloads: PDF, TeX Source

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