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[0]) # H
    qc3.cx(qr3[0], qr3[1]) # CNOT

    return qc3

1 Answer 1


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

enter image description here

** Note the circuit is in little endian convention (read from bottom to top).

You should be able to get the second one now.


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