 More precisely, the formula_20-state qubit formula_24 is an element of formula_20-dimensional complex projective space, carrying an inner product formula_26 that is the Fubini–Study metric.The state transitions, transition matrices or de Bruijn graphs are represented by a collection of formula_27 unitary matrices formula_7, with one unitary matrix for each letter formula_6.That is, given an input letter formula_30, the unitary matrix describes the transition of the automaton from its current state formula_22 to its next state formula_32