what is difference between the following two results

Question

If this question sounds trivial please bear with me as I am beginner in QC.

Code 1

qc = QuantumCircuit(1,1)
qc.measure(0,0)
qc.draw()
job = sim.run(qc)      # run the experiment
result = job.result()  # get the results
result.get_counts()    # interpret the results as a "counts" dictionary

Output: {'0': 1024}

Code 2

from qiskit import QuantumCircuit
from qiskit.quantum_info import Statevector

qc = QuantumCircuit(1,1)
ket = Statevector(qc)
print(ket.draw())

Output:

Statevector([1.+0.j, 0.+0.j],
            dims=(2,))

Question 1

I understand that in 1st code, qubit is in zero state and in 2nd code statevector is as displayed above. As statevector tells the state of a vector so [1.+0.j, 0.+0.j] what exactly it is telling ? Is it saying that value of qubit is 1 in one basis and zero in other basis? if so, where is it defined that there are only 2 basis, why not 3 or more..

Question 2 What exactly is the difference between two results {'0': 1024} and [1.+0.j, 0.+0.j]

Question 3 If there would have been 2 qubits in the circuit, qc = QuantumCircuit(2,2) then it will be called multi-qubit state correct?

Question 4 Value of a qubit is initialized as zero by default, why so?

Answer 1

Question 1: The point here is that you are working with qubits. By definition they are objects of dimension 2.

The [1,0] is telling you that the probability amplitude for being in the first basis state is 1, and the probability amplitude for being in the second basis state is 0. These two basis states are labelled '0' and '1' respectively.

Question 2: The {'0': 1024} means "when I measure the state, if I repeat the measurement 1024 times, in this case I get the answer '0' for all 1024 of those trials. So, it's basically an experimental estimate of the probability of an outcome, which should correspond to the mod-square of the probability amplitude for that basis element.

Question 3: yes. I'm not a qiskit expert, but I think it would be sufficient to call QuantumCircuit(2) to get two qubits. The second number is the number of classical bits that you want.

Question 4: Your computation has to start from somewhere. It needs to be a fixed, known, state. By convention it's the $|0\rangle$ state. It's just a matter of labelling. Whatever state is easiest to prepare, that's the only we call '0'.