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Imaging a system of two qubits which at a given step of evolution is in the state

1. $|q_{1}(0)> = |0> + e^{-i\phi_{1}}|1>$,
2. $|q_{2}(0)> = |0> + e^{-i\phi_{2}}|1>$,

is there a simple two qubit quantum circuit of n gates (CNOT, Hadamard and single-qubit rotations) that produces the output

1. $|q_{1}(n)> = |0> + e^{-i\left(\phi_{1}+\phi_{2}\right)}|1>$
2. $|q_{2}(n)> = |0> + e^{-i\phi_{2}}|1>$

from the input above?

Imaging a system of two qubits which at a given step of evolution is in the state

1. $|q_{1}(0)\rangle = |0\rangle + e^{-i\phi_{1}}|1\rangle$,
2. $|q_{2}(0)\rangle = |0\rangle + e^{-i\phi_{2}}|1\rangle$,

is there a simple two qubit quantum circuit of $n$ gates (CNOT, Hadamard and single-qubit rotations) that produces the output

1. $|q_{1}(n)\rangle = |0\rangle + e^{-i\left(\phi_{1}+\phi_{2}\right)}|1\rangle$
2. $|q_{2}(n)\rangle = |0\rangle + e^{-i\phi_{2}}|1\rangle$

from the input above?

my question is the following:
Imaging a system of two qubits which at a given step of evolution is in the state

1. $|q_{1}(0)> = |0> + e^{-i\phi_{1}}|1>$,
2. $|q_{2}(0)> = |0> + e^{-i\phi_{2}}|1>$,

is there a simple two qubit quantum circuit of n gates (CNOT, Hadamard and single-qubit rotations) that produces the output

1. $|q_{1}(n)> = |0> + e^{-i\left(\phi_{1}+\phi_{2}\right)}|1>$
2. $|q_{2}(n)> = |0> + e^{-i\phi_{2}}|1>$

from the input above?

Imaging a system of two qubits which at a given step of evolution is in the state

1. $|q_{1}(0)> = |0> + e^{-i\phi_{1}}|1>$,
2. $|q_{2}(0)> = |0> + e^{-i\phi_{2}}|1>$,

is there a simple two qubit quantum circuit of n gates (CNOT, Hadamard and single-qubit rotations) that produces the output

1. $|q_{1}(n)> = |0> + e^{-i\left(\phi_{1}+\phi_{2}\right)}|1>$
2. $|q_{2}(n)> = |0> + e^{-i\phi_{2}}|1>$

from the input above?