Quantum States
How should we describe quantum states mathematically?
Classical vs. Quantum States
To express the complex-value amplitudes of the state a quantum system, we use an N-dimensional complex unit vector. In quantum mechanics, quantum states are often infinite dimensional. For the purposes of quantum computing finite dimensions are sufficient.
The simplest quantum system is the qubit.
In short, quantum states are superpositions of basis/classical states.
We can perform transformations on multiple qubits in parallel and in series. Below is a representation of a quantum circuit that enables the phenomena of quantum teleportation.
Quantum Teleportation Circuit
From Quantum Computation and Quantum Information written by Michael A. Nielsen, Isaac L. Chuang