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I have the following initial state

$$ |\psi\rangle=\frac{1}{\sqrt{5}}(|00\rangle+\sqrt{2}|10\rangle+\sqrt{2}|11\rangle) $$

and I am trying to find the right "circuit" as combination of quantum gates (within the pool of Hadamard, CNOT, Pauli-X/Y/Z and S) to transform that state to:

$$ |\psi'\rangle=\frac{1}{\sqrt{5}}(|00\rangle+2|11\rangle) $$

As beginner I am struggling to find a "general" way to tackle a problem like this (at least for 2-qubits).

So far I tried to combine with tensor products the matrixes relative to the above gates but it is more a sort of random process from my side. Any help?

Randomize
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1 Answers1

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Note that your state can be written as $| \psi \rangle = \frac{1}{\sqrt5}(|00\rangle + 2|1+\rangle)$, so what you want is a unitary which maps $|+\rangle \to |1\rangle$ conditioned on the first qubit being in state $|1\rangle$. This is achieved by a $CH$ gate (controlled-Hadamard) followed by a $CNOT$ gate.

Sergio Escobar
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