  The thermodynamic cost of resetting an arbitrary initial state to a
particular desired state is lower bounded by Landauer's bound. However, here we
demonstrate that this lower bound is necessarily unachievable for nearly every
initial state, for any reliable reset mechanism. Since local heating threatens
rapid decoherence, this issue is of substantial importance beyond mere energy
efficiency. For the case of qubit reset, we find the minimally dissipative
state analytically for any reliable reset protocol, in terms of the
entropy-flow vector introduced here. This allows us to verify a recent theorem
about initial-state dependence of entropy production for any finite-time
transformation, as it pertains to quantum state preparation.
