Abstract
Having discussed the basic quantum gates in detail, we were able to turn to the quantum algorithms that were the subject of the fifth lesson. We began by introducing the notion of a one-qubit operation " conditional ", i.e. one that is performed if and only if another qubit is in state one, and indicated which Hamiltonian it could be realized by. The special role of the Ising Hamiltonian was highlighted. The two classical gates C-NOT and C-PHASE were then dissected into basic primitive gates. Then we treated the example of the preparation of the Greenberger-Horne-Zeilinger (GHZ) state, which breaks down into two C-PHASE operations framed by one-qubit rotations. The mechanics of calculating using the stabilizer formalism were demonstrated, and in principle, participants in this lesson should have been convinced that it was possible to compile quantum algorithm segments using a " division " involving the start and finish stabilizers. The final part of the lecture was devoted to describing the teleportation algorithm. While remaining within the simplified framework of Clifford operations, it highlights the very special properties of quantum information, and in particular the role played by the theorem prohibiting the cloning of quantum states.
