Print data() with statevector and qasm simulator - Qiskit

Question

I am new to Qiskit and I am trying to implement some very simple 1-qubit gates.

I want to initialize the state of the qubit (to 0 and then to 1) and then apply the gate and print the new state of the qubit.

def I(input):

  q = QuantumRegister(1) 
  c = ClassicalRegister(1)
  qc = QuantumCircuit(q, c)

  if input == '1': #if input = 1, initialize the qubit to 1
     qc.x(q[0])

  qc.iden(q[0] )

  qc.measure( q[0], c[0])


  backend = Aer.get_backend('statevector_simulator')
  result = qiskit.execute(qc, backend=backend, shots=1).result()
  output = result.data(qc)

  return output

And I call the function like this:

print('\nResults for the Iden gate')
for input in ['0','1']:
print('    Input',input,'gives output',I(input))

Now the output of all this is:

Results for the Iden gate
Input 0 gives output {'statevector': [[1.0, 0.0], [0.0, 0.0]], 'counts': {'0x0': 1}}
Input 1 gives output {'statevector': [[0.0, 0.0], [1.0, 0.0]], 'counts': {'0x1': 1}}

I know that the data() function returns the Instruction object, a list of Qubits objects and a list of classical bits with the order they added. So here the second list is the list with the qubits.

But when the qubit is '0', shouldn't it return a list with all 0? I am not sure about the meaning of the output.

Answer 1

The return from result.data(qc) is information about the result of running the circuit qc. In your example, there are 2 pieces of information returned - the statevector and the counts.

The statevector is a way of describing the state of the qubit, and the result contains the statevector from the end of the circuit. Each of the arrays in the overall array corresponds to a coefficient in front of one of the basis states, the first element is the real part and the second is the imaginary. So, for your Input 0 this statevector is saying at the end of the circuit the qubit was in the state
$(1+0i)\vert 0 \rangle + (0+0i)\vert 1 \rangle$, which is the same as saying the qubit is in the $\vert 0 \rangle$ state.

The counts is saying how many times each output occurred in the results, so for Input 0 0x0 (aka 0) was the result once, which can be seen from the 1. This field is mainly used with the qasm_simulator.