Week assignment 10 (Homework vault part)
Deadline: 18. 12. 2020
Upload scan, photograph, or a typesetted pdf of computation to the corresponding homework vault. Do
not forget to include your name and personal ID number (uˇco) on the page(s).
Exercise 1. [2pts] Compute the state on the outcome of the following circuit
|0 H X X H
|0 H H
|0 X H H X
Exercise 2. [2pts] Compute the average value N |ψ of observable
N =


3 i 1
−i 5 −i
1 i 3


when measured in state
|ψ =
1
√
5
(2 |0 + i |1 ).
Exercise 3. [3pts] Consider again observable N and state |ψ from the previous exercise. Find eigenvalues
λj and corresponding eigenvectors µj of N and cosider measurement of the state |ψ in the basis { µj }.
Compute probabilities pj for particular measurement outcomes µj and compute
[N]|ψ = ∑
j
λj pj.