Quantum Computing, Quantum Physics, Programming, Physics, Science.
Showing that this circuit is equivalent to e^[i σ_z⊗σ_z t] is not too hard. Remember that we have the Euler-like decomposition of the operator as e^[i σ_z⊗σ_z t]=cos⁡(t)I+i sin⁡(t) σ_z⊗σ_z (which works since we have that σ_z^2=I). Thus, we have to show that the circuit above simplifies to this same