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September 1, 2015

Homework Help: quantum physics

Posted by Anonymous on Friday, October 18, 2013 at 2:06am.

8(a) Consider a spin qubit in the state 32|0⟩+12|1⟩. What are the coordinates (,ϕ) of this qubit on the Bloch sphere?
=?
ϕ=?

8b. We turn on a magnetic field in the z^ direction at time t=0. This corresponds to the Hamiltonian H=BZ, where B is a constant and Z is the usual phase flip. What is the state of our qubit at time t as a function of B and t?

8c. What are the coordinates (,ϕ) of this qubit on the Bloch sphere at time t, as a function of B and t?

8d. Now suppose we start with the qubit |(0)⟩=|0⟩ and we apply a magnetic field 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 (,ϕ) of this qubit on the Bloch sphere at time t, as a function of B and t?
=?
ϕ=?

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