The statevector of three-qubit bit-flip encoding circuit for entangled state

Question

I was trying to implement a three-qubit bit-flip code for shared entangled state. I was curious to analyze this mathematically, but the problem is I can't calculate the statevector after encoding. Here is the circuit:

I used Qiskit to calculate the statevector, but it turns out to be 0's for every qubit. I am very confused because I don't know if this is valid or not!

Could you please guide me a bit? Also, should this circuit have higher fidelity? Please comment on this as well.

Answer 1

The method Statevector.evolve()^[1] returns the evolution result. It does not change the instance it called in. So all what you need is to change your code to become:

av = Statevector.from_label('000000')
result = av.evolve(bit_flip_qc)
result.data

Answer 2

I suggest you make 2 repetition logical qubits first and entangle them with logical CNOT operator. you can check every single steps separately.

1. Make $|+_L\rangle_{Alice} = {1\over\sqrt{2}} (|000 \rangle + |111 \rangle )$ and $|0_L\rangle_{bob} = |000 \rangle$

2. Apply three CNOT operators transversally

3. Final state will be ${1\over\sqrt{2}} (|000_{Alice}000_{bob} \rangle + |111_{Alice}111_{bob} \rangle )$