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
Chapter 1 gives Rz(θ)=diag(e−iθ/2,eiθ/2) for a single qubit. Consider the four-gate circuit on two qubits, in time order: CNOT (control qubit 1, target qubit 2), then Rz(−ϕ/2) on qubit 2 alone, then CNOT again (same control and target), then Rz(ϕ/2) on qubit 2 alone.
((a)) Show that this circuit realises C(Rz(ϕ)) exactly, control qubit 1, target qubit 2: it acts as the identity on qubit 2 when qubit 1 reads 0, and as Rz(ϕ) on qubit 2 when qubit 1 reads 1.
((b)) State the circuit's total gate count and its depth (the number of time steps it needs, given that no two of its gates act on disjoint wires here).