OE-4.3 Quantum Logic Gates & Circuits
You can apply Pauli, Hadamard, phase-shift, C-NOT and CCNOT gates, construct entangled Bell states, and describe quantum teleportation.
Every quantum gate is a unitary matrix, so 'applying a gate' is matrix multiplication and nothing more mysterious. The Hadamard gate is the workhorse because it manufactures superposition from a basis state, and almost every algorithm opens with it. Teleportation is the unit's famous result and also its most misread one - no matter and no information travels faster than light; a classical message is still required, and saying so correctly is how you show you understood it.
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Single-qubit gates: Pauli, Hadamard and phase shift
The operations on one unit at a time, and their effect on the sphere from the previous topic. Learn what each does geometrically and the algebra follows.
Controlled gates: C-NOT and CCNOT (Toffoli)
Operations where one unit decides whether another is acted on. These are what make computation possible rather than merely rotation.
Quantum entanglement
The property with no classical equivalent: two units whose states cannot be described separately. Everything surprising in the rest of the course rests on it.
Quantum teleportation and the EPR model
Moving a state without moving a particle, and the thought experiment that showed the theory was strange. Note that nothing travels faster than light, which is the usual misreading.
Bell states
Four specific entangled states that come up everywhere. They are worth memorising because so many protocols are written in terms of them.
Introduction to the discrete Fourier transform
The classical transform, introduced here because the quantum version in the next topic is where the speedup comes from. Comparing the two is the point of putting it here.
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