Abstract
In the third lesson, we dealt with the formalism of stabilizers for the representation of quantum states. These stabilizers play a very important role in all basic quantum operations, in particular quantum error correction. These particular commutative subgroups of Pauli's register group correspond to sets of observables whose measurements are compatible with each other : the measurement of one does not modify the measurement of the others. The set of eigenstates of all these stabilizers constitutes a kind of skeleton of the Hilbert space of the system. Rather than being represented by their wave function in the calculation base, these eigenstates can be given by the list of Pauli operators making up the stabilizer. This notation becomes extremely economical when dealing with registers of more than two qubits, and brings out more clearly both the symmetries of the states, and the way in which we can pass from one to the other via primitive gates. The lesson ended with " maps " of stabilizers expressing the neighborhood relations between them. This mode of representation helps to better appreciate the conservative character of a quantum algorithm by putting all the bases on an equal footing
