  In these notes we show that it is impossible to obtain a quantum speedup for
a faulty Hamiltonian oracle. The effect of dephasing noise to this continuous
time oracle model has first been investigated in [1]. The authors consider a
faulty oracle described by a continuous time master equation that acts as
dephasing noise in the basis determined by the marked item. The analysis
focuses on the implementation with a particular driving Hamiltonian. A
universal lower bound for this oracle model, which rules out a better
performance with a different driving Hamiltonian has so far been lacking. In
this note, we derive an adversary type lower bound which shows that the
evolution time T has to be at least in the order of N, i.e. the size of the
search space, when the error rate of the oracle is constant. For the standard
quantum oracle model this result was first proven in [2]. This note can be seen
as an extension of their result to the continuous time setting.
