The compact notation physicists use for quantum states: |psi> is a column vector, <psi| its conjugate transpose, and <a|b> their inner product.
Why it matters
Every paper and lecture course after the first week is written in it. Once it clicks, the notation does real work for you rather than getting in the way.
After this you will be able to
Hand-picked and ordered. If you only have time for one, take the first.
A rigorous but genuinely well-taught course by John Watrous covering single systems, multiple systems, quantum circuits and the core protocols. The cleanest bridge from intuition to real notation.
Free, self-contained and rigorous, with exercises. Widely used as the standard course text in Europe and the best single free replacement for a paid textbook.
Twenty-two short videos taking you from the basic postulates through to quantum teleportation, taught by the co-author of Nielsen & Chuang. Whiteboard-paced and easy to follow.
Topics that list Dirac (bra-ket) notation as a prerequisite.
A geometric picture where every pure single-qubit state is a point on a sphere, and every single-qubit gate is a rotation of that sphere.
IntermediateCombining qubits multiplies their state spaces via the tensor product, so n qubits live in a 2^n-dimensional space — and the states that do not factor apart are exactly the entangled ones.
Intermediate