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

Variational quantum eigen solvers (VQEs) are leading candidates to demonstrate near-term quantum advantage. Here, we conductdensity-matrix simulations of leading gate-based VQEs for a range of molecules. We numerically quantify their level of tolerable depolarizing gate-errors. Wefind 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 out perform 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)alpha N-II(-1). 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.