QE doesn't require low rates. The causality works in the other direction. QE suppresses rates. QE could be done at any level of rates, with the exception of if

QE doesn't require low rates. The causality works in the other direction. QE suppresses rates. QE could be done at any level of rates, with the exception of if long duration was too low or even negative I which case it may become politically or practically infeasible