Quantum Computing quiz 1

Quiz – PH534 Spring 2022-2023
Date: 28 March 2023


Name: ____________________ LDAP: _____________________ Dept: _______________

Question 1: Consider the circuit and the oracle below:


Since (f(n)) 10) 10),


3
=




the original state (2) must
be the pre-image of f(x)

:(4) (f-(00))
=




3 After measurement you
10) 10)
are left with




What is |"⟩? (2 Marks)

!
i. {|0000⟩ + |0110⟩}
√#
!
ii. {|0000⟩ + |0010⟩ + |0100⟩ + |0110⟩}
#
!
iii. {|0000⟩ + |1111⟩}
√#
!
iv.
~ {|0000⟩ + |1001⟩ + |0110⟩ + |1111⟩}
#

v. |0000⟩
vi. None of the options.

This space is for justification and carries 50% of the marks allotted for the question. Do not use this for rough work.
Use extra page if necessary.

The circuit simply implements the oracle Op (n) x(y)] (x) x 1yt f(n))
=




(x) 0
=




me
If (n)>
u
as
ly) =
1007
x=30,134 f(x) = 30,132
the state IP) is nothing
Since f(x) 00,
=
as the
shown in post meas mementstate,
If -001), which the superposition of
all (as that
but the pre-image state is




produces the output100).



outpost
I
INPUT

So, the states 10000), 10110), 11001) and 11111) will generate
18
000 O 00

from 1001 to
01 the output1007
0010


11001)+111117}
11
I(10000)
00111011
...(t) = + 10110) +




·
0100 1100 01
01011101
01 101110
!8
-
-




01111111 10
-