Question

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?
Į=?
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?
Į=?
ϕ=?

Answer 1

D
Į = 2Bt
phi = pi/2

C - pi/3; 2*B*t

do you need explanation ?

Answer 2

@ David thanks but its wrong for d.

Answer 3

can you explain..please

Answer 4

try Į = 2Bt
and phi = 0

Answer 5

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

Answer 6

r u right,david abt 8d?

Answer 7

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

Answer 8

ya, this time

Answer 9

doing 8b

Answer 10

its wrong.8 d,

Answer 11

please help with 8d!!

Answer 12

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

please help with Q8D please

Answer 13

8D
θ= 2⋅B⋅t
ϕ= 3⋅π/2