--- tags: VQE, NISQ, Noise, Numerical sort-date: 2024-01-27 description: We benchmark the response to noise of a range of VQE algorithms. --- Kieran Dalton, [[/index|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](https://doi.org/10.1038/s41534-024-00808-x) [[PDFs/Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry.pdf|PDF Download]] [[PDFs/Supplementary Information for: Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry.pdf|Supplementary Information PDF Download]] # 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](https://doi.org/10.1038/s41534-024-00808-x). ## BibTeX ```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*](https://arxiv.org/abs/2211.04505v2). Downloads: [[PDFs/2211.04505v2.pdf|PDF]], [[TeX_Source/2211.04505v2.tar.gz|TeX Source]] - Tue, 8 Nov 2022 19:05:38 UTC: [*https://arxiv.org/abs/2211.04505v1*](https://arxiv.org/abs/2211.04505v1). Downloads: [[PDFs/2211.04505v1.pdf|PDF]], [[TeX_Source/2211.04505v1.tar.gz|TeX Source]] # Analytics - [Google Scholar](https://scholar.google.com/citations?view_op=view_citation&citation_for_view=GRSIcsEAAAAJ:9yKSN-GCB0IC) - [SciRate](https://scirate.com/arxiv/2211.04505) - [INSPIRE-HEP](https://inspirehep.net/literature/2752844) - [Semantic Scholar](https://www.semanticscholar.org/paper/Quantifying-the-effect-of-gate-errors-on-quantum-Dalton-Long/d52cf32c9a989ffe0646bad0018d9a7324f702ba)