We defined ρ s 0 as a diagonal N × N matrix containing the classical Maximum Likelihood probability Estimation to have a specific symbol at the first sequence position: where S is again the set of all sequences in the training set and w 1 is the first word in each sequence w. With regard to the ancilla system we do not know anything about it and thus we have to define ρ a 0 as the D × D diagonal matrix .
we can define ρ 0 as Putting all the ingredients together, we can finally write down the formula for the probability P (w|ρ 0 , U) for a sequence w in the QLM specified by ρ 0 and U.