PHYSICS · Multi-part · Fermi University Physics · Quantum Information & Technology · Quantum states, measurement and entanglement · Quantum states, measurement and entanglement
Quantum Information and Technology, Ch Qubits, registers and the Bloch sphere
Problem
The gate SH (apply H first, then S) acts on one qubit, where S=diag(1,i) and H=21(111−1).
((a)) Find where SH sends the Bloch vectors +x^, +y^ and +z^, i.e. the states ∣+⟩, ∣+i⟩ and ∣0⟩.
((b)) Hence give the axis n^ and angle θ of the rotation SH performs, up to a global phase.
((c)) Find α,β,γ,δ with SH=eiαRz(β)Ry(γ)Rz(δ), and check the decomposition by multiplying the three factors out.