# Creating Bell States with CNOT conditioned to the control qubit being set to zero

I was using qiskit to generate all of the Bell States. I created the following circuits for each state:

$$|\Phi^+\rangle :$$

$$|\Phi^-\rangle :$$

$$|\Psi^+\rangle :$$

$$|\Psi^-\rangle :$$

The $$|\Psi^\pm\rangle$$ states were creating CNOTs with X gates before, that way we have a CNOT that acts when the control qubit is set to zero.

When I execute the first 3 circuits in Qiskit, I get the expected state vectors. However, when I execute the last one, I get $$\frac{(-|01\rangle + |10\rangle)}{\sqrt{2} }$$. I can see that the state vector is $$|\Psi^-\rangle$$ up to a global phase factor. My question is: Is this a valid method to create Bell States? Or should I stick to the one that uses "normal" CNOT, X and Z?

• Hi and welcome to Quantum Computing SE. Please see this thread how to create Bell states: quantumcomputing.stackexchange.com/questions/11700/… May 1 '20 at 6:20
• Does this answer your question? How can you construct the different two-qubit Bell states? May 1 '20 at 6:21
• This is perfectly fine. A global phase is nothing to be bothered about. May 1 '20 at 7:46
• DaftWullie is right but you can prepare Bell states with one gate less than in case of circuits in the question. May 1 '20 at 8:25