Partial trace - experimental implementation and calculation

How does one actually take the partial trace on a quantum computer/real experiment? Wikipedia says that this is a valid quantum operation but I can't see how to implement it. Given an entangled pure state $$\psi_{AB} \in H_{A}\otimes H_{B}$$, I wish to do some operations and measurements to obtain $$\rho_A = \sum_{i\in H_B} \langle i\vert \rho_{AB} \vert i\rangle$$.

Since $$\rho_A$$ has many possible purifications, this computation is not unitary but $$\rho_A$$ is unique. Applying a projective measurement $$\sum_i \vert i\rangle\langle i\vert$$ on $$B$$, doesn't work. I somehow need to "forget" that the state is actually entangled and "lose" the $$H_{B}$$ part of the state but this is (correct me if I'm wrong) not allowed in quantum information.

So if I have a single copy of a quantum bipartite state, what quantum circuit should I use that spits out the partial trace? Also, I'd love to know if such a circuit exists, what the computational complexity of it would be.