# quantum physics

posted by Anonymous

8(a) Consider a spin qubit in the state 3ã2|0⟩+12|1⟩. What are the coordinates (ƒÆ,ϕ) of this qubit on the Bloch sphere?
ƒÆ=?
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 (ƒÆ,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 |ƒÕ(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 (ƒÆ,ϕ) of this qubit on the Bloch sphere at time t, as a function of B and t?
ƒÆ=?
ϕ=?

1. Anonymous

2. david

D
ƒÆ = 2Bt
phi = pi/2

C - pi/3; 2*B*t

do you need explanation ?

3. Anonymous

@ David thanks but its wrong for d.

4. Anonymous

5. ss01

try ƒÆ = 2Bt
and phi = 0

6. david

sorry for that
@ss01 your phi is wrong that i am for sure it cannot be 0

7. david

got my error
8d ƒÆ= 0 and ϕ = 2bt
check and tell me if i am right?
8a ƒÆ = pi/3 and ϕ = 0

8. stuart

r u right,david abt 8d?

9. stuart

r u right,david abt 8d?and wat abt 8 b?

10. david

ya, this time

11. david

doing 8b

12. stuart

its wrong.8 d,

13. Anonymous

14. Anonymous

8b:
e^(-i*B*t)*sqrt(3)/2
e^(i*B*t)/2

15. Tu papi

8D
θ= 2⋅B⋅t
ϕ= 3⋅π/2

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