OE-4.2 Qubits & Quantum States
You can write single and multi-qubit states in bra-ket notation, place a state on the Bloch sphere, and use tensor products to build composite systems.
The qubit is not a bit that is secretly both values - it is a unit vector in a two-dimensional complex space, and superposition is just that vector not lying on an axis. Bra-ket notation is compact once you accept it is only column and row vectors in disguise. Tensor products are the step where the state space grows exponentially with qubit count, which is the whole source of quantum computing's promise and of the difficulty of simulating it classically.
Work through these
Quantum mechanics background: Huygens' wave theory, the photoelectric effect
Where the physics came from, at the level of the experiments that forced it. Read for the shape of the argument rather than the detail.
De Broglie hypothesis and Heisenberg's uncertainty principle
Two more results that fix the strangeness in place: matter behaves like waves, and some pairs of quantities cannot both be sharp. The second is the one that constrains computation.
Origin of quantum computing and motivation for studying it
Why anyone wants to build these machines, and what problem they are for. Worth reading carefully, because the honest answer is narrower than the popular one.
NPTEL: Introduction to Quantum Computing - Quantum Algorithms and Qiskit · CourseQubits and multi-qubit states; bra-ket notation
The unit of information here, and the notation everything below is written in. Get comfortable writing states in this notation before the gates arrive.
Quantum superposition
The property that makes the whole field possible: a state can be a combination of others until it is measured. It is also the property most often described badly in popular accounts.
Major players in the industry: IBM, Microsoft, Rigetti, D-Wave
Who is actually building this hardware and along which competing approaches. Useful for orientation and likely to date faster than anything else in the course.
NPTEL: Introduction to Quantum Computing - Quantum Algorithms and Qiskit · CourseBloch sphere representation
A picture of a single unit of information as a point on a sphere. It makes the single-qubit gates in the next topic visual instead of algebraic.
Inner and outer products of multiple qubits; tensor product
How states of several units combine, which is where the size of the problem explodes. The tensor product is why simulating these machines is hard.
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