SWAP specific phase components of two qubits

Is it possible to perform an operation on two qubits with initial states as follows:

$$q_1: 1/sqrt(2)(|0rangle + exp(0.a_1a_2a_3)|1rangle)$$
$$q_2: 1/sqrt(2)(|0rangle + |1rangle)$$

To resultant state:-

$$q_1: 1/sqrt(2)(|0rangle + exp(0.a_1a_2)|1rangle)$$
$$q_2: 1/sqrt(2)(|0rangle + exp(0.a_3)|1rangle)$$

Without knowing the value of $a_3$. Where $a_1,a_2,a_3 ∈ [0, 1].$

The idea is to shift the phase of $q_1$ by $exp(-0.00a_3)$ and $q_2$ by $exp(0.a_3)$ with the unitary operation not being aware of the value of $a_3$.