Week assignment 06 (Homework vault part)
Deadline: 16. 11. 2020
Upload scan, photograph, or a typesetted pdf of computation to the homework vault Assignment week 06.
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Exercise 1. [1pt] Compute A |w where A = |v w| and
|w =












3
2i
1 − i
0
4
i
2 + 2i
7












, |v =












−1
2
3i
1 − i
2
0
−3 + i
2i












.
Use the Dirac notation.
Exercise 2. [2pts] Let us have three orthonormal states
|v1 =
1
2
√
6




3
−1
−3 + i
2i



 , |v2 =
1
3
√
2




2
2i
0
−1 − 3i



 , |v3 =
1
√
3




i
1
i
0



 .
Compute Tr |u w| where
|u = |v1 + |v2 and |w = 2 |v1 + |v2 − |v3 .
Use the Dirac notation.
Exercise 3. [3pts] Consider circuit
Show that this circuit performs CCNOT, which is the controlled-controlled not operation with qubits 0
and 1 as controls, that flips the qubit 2 if and only if both control qubits are in state |1 . Here
T =
1 0
0 ei π
4
.
Use the Dirac notation.
Hint: You can show this separately for the four computational basis states of control qubits.