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+---
+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)
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