PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · The quantum circuit model and quantum algorithms · The quantum circuit model and quantum algorithms
Quantum Information and Technology, Ch The quantum circuit model
Problem
In a quantum repeater link, qubit 1 is prepared in ∣+⟩ and qubit 2 in ∣0⟩. A CNOT gate is applied with qubit 1 as control and qubit 2 as target. In the original protocol, qubit 1 is then measured in the Z basis, and if the outcome is 1 an X gate is classically applied to qubit 2; both qubits are then measured.
((a)) Using the deferred measurement principle, replace the classically controlled correction by a quantum-controlled gate, move both measurements to the end of the circuit, and identify what the resulting all-quantum circuit does to the input ∣+⟩1∣0⟩2.
((b)) For this all-quantum version, compute the probability of each of the two possible measurement outcomes for qubit 1, and the value that qubit 2 is found to have in each case.