# Creating a Qiskit Circuit sending $|00\rangle$ to $|1,-\rangle$ and $|11\rangle$ to $|0,-\rangle$

I am trying to create a circuit in Qiskit that performs the following transformations:

starting in state |00⟩ generates a √(2)/2 * (-|10⟩+|11⟩) state

starting in state |11⟩ generates a √(2)/2 * (|00⟩-|01⟩) state

I created a basic circuit for creating entangled states but I do not know how to infer relevant gates for such transformations.

def create_circuit():
qr3  = qiskit.QuantumRegister(2)
cr3  = qiskit.ClassicalRegister(2)
qc3  = qiskit.QuantumCircuit(qr3 ,cr3)

qc3.h(qr3) # H
qc3.cx(qr3, qr3) # CNOT

return qc3


Note that for the first state you have

$$\dfrac{|11 \rangle - |10\rangle}{\sqrt{2}} = -|1\rangle \otimes \dfrac{|0 \rangle - |1\rangle}{\sqrt{2}}$$

This is a product or separable state. Hence no entanglement and therefore you don't need a two qubit gate.

Recall the mapping $$X|0\rangle =|1\rangle$$ and and $$Z|1\rangle = -|1\rangle$$ and $$H|1\rangle = \dfrac{|0 \rangle - |1\rangle}{\sqrt{2}}$$

So you are looking for something like ** Note the circuit is in little endian convention (read from bottom to top).

You should be able to get the second one now.