I am a quantum computing enthusiast, and recently I stumbled upon this the following two propositions:
$$ \alpha|1\rangle + \beta|0\rangle$$
What does this mean?
My understanding of this is that: the two bits, 1 and 0 are represented in a state of superposition, hence the bra-ket notation (which is commonly used for quantum mechanics), i.e., this is a qubit.
Or is there a more concise explanation of this?
$$(\alpha|1\rangle + \beta|0\rangle)^N$$
What does it mean to raise this quantity (of superimposed bits, i.e., qubit) to the $N$th degree? If we take $2^N$ where $N$ is the number of qubits then this tells us the number of bits in the desired number of qubits.
Is what I have stated in this post, generally correct?