Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry
Kieran Dalton, Christopher K. Long, Yordan S. Yordanov, Charles G. Smith, C. H. W. Barnes, Normann Mertig, David R. M. Arvidsson-Shukur
Abstract
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 II of noisy two-qubit gates as $${p}_{c}\mathop{\propto }\limits_{\displaystyle{ \sim }}{N}_{{{{\rm{II}}}}}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</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:mi>N</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>II</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> . 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.