Quantum Computation Magnetic Spin

  • #1

Homework Statement


A qubit is in the state |ψ(0)>=|0> . A magnetic field is applied in the x^ direction at t=0. This corresponds to the Hamiltonian H=BX, where B is a constant and X is the usual bit flip gate. What are the coordinates (θ,ϕ) of this qubit on the Bloch sphere at time t, as a function of B and t?


Homework Equations



I think i have to introduce e^(-i*H*t) into the qubit state.
The generic form of |ψ (t)> = cos(θ/2)|0> + (e^(iϕ))*sin(θ/2)|1>

The Attempt at a Solution


I have followed this through and have got θ = ∏ and ϕ = B*t
However looking at the Bloch sphere it would seem that theta is ∏/2. Also from the diagram i would think that ϕ would be 0 or 2BT but i am not sure.
 

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