Classics gone quantum: The Fly

Challenge: Teleport the fly from one teleportation capsule to the other 

The quantum teleportation algorithm makes it possible to teleport the unknown state of a qubit to another—here represented by… a fly. At the beginning of the algorithm, the qubit on the second line is entangled (H gate + CNOT gate) with the qubit on the third line. A Bell measurement (CNOT gate, H gate, and measurements) is then performed between the qubit containing the fly’s state and the second qubit. When the first two qubits are measured, the system collapses while keeping the third qubit in one of four possible states. The third qubit must then be corrected to the fly’s original state. 

We know how to correct the qubit depending on the measurement results of the first two qubits: 00, 01, 10, or 11. The correction is done by applying conditional X and Z transformations (these transformations are only applied to the target qubit if the control qubit is in the 1 state). Finally, the fly’s state is perfectly teleported from the first qubit to the third.