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

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Long, CK 
Yordanov, YS 
Smith, CG 
Barnes, CHW 


jats:titleAbstract</jats:title>jats:pVariational 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 10jats:sup−6</jats:sup> and 10jats:sup−4</jats:sup> (10jats:sup−4</jats:sup> and 10jats:sup−2</jats:sup> 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, jats:italicp</jats:italic>jats:subjats:italicc</jats:italic></jats:sub>, for any VQE to achieve chemical accuracy decreases with the number jats:italicN</jats:italic>jats:subII</jats:sub> of noisy two-qubit gates as jats:inline-formulajats:alternativesjats:tex-math$${p}{c}\mathop{\propto }\limits{\displaystyle{ \sim }}{N}_{{{{\rm{II}}}}}^{-1}$$</jats:tex-math><mml:math xmlns:mml=""> mml:mrow mml:msub mml:mrow mml:mip</mml:mi> </mml:mrow> mml:mrow mml:mic</mml:mi> </mml:mrow> </mml:msub> mml:munder mml:mrow mml:mo∝</mml:mo> </mml:mrow> mml:mrow mml:mo~</mml:mo> </mml:mrow> </mml:munder> mml:msubsup mml:mrow mml:miN</mml:mi> </mml:mrow> mml:mrow mml:miII</mml:mi> </mml:mrow> mml:mrow mml:mo−</mml:mo> mml:mn1</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. Additionally, jats:italicp</jats:italic>jats:subjats:italicc</jats:italic></jats:sub> 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.</jats:p>


Acknowledgements: We thank Hugo V. Lepage, Flavio Salvati, Frederico Martins, Joseph G. Smith, Wilfred Salmon, and the Hitachi QI team for useful discussions. NM and DRMAS acknowledge useful discussions with Tatsuya Tomaru, Saki Tanaka and Ryo Nagai.


5108 Quantum Physics, 5102 Atomic, Molecular and Optical Physics, 51 Physical Sciences

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npj Quantum Information

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Springer Science and Business Media LLC