I will discuss our ongoing efforts aimed at constraining the systematic errors in long-baseline neutrino experiments through ab initio computations of neutrino-nucleus quasielastic scattering cross sections using a powerful quantum many-body method---the coupled-cluster theory---with nuclear forces and electroweak currents derived in chiral effective field theory ($\chi$EFT). After showing  precision results for the electroweak properties of the deuteron, which we use to benchmark our harmonic oscillator-basis representation of the $\chi$EFT electroweak currents, I will present recent results for some electron-scattering observables of $^4$He and $^{40}$Ca.