|q⟩
Bad Qubits
Play
Quest
Questions
Learn
Playground
☕
← Question Bank
Multiple choice
When Shor's period finding for
f
(
x
)
=
a
x
m
o
d
N
f(x) = a^x \bmod N
f
(
x
)
=
a
x
mod
N
is cast as a Hidden Subgroup Problem over the group
G
=
Z
M
G = \mathbb{Z}_M
G
=
Z
M
(with
M
≥
N
2
M \geq N^2
M
≥
N
2
a power of two), what is the hidden subgroup
H
H
H
whose generator reveals the order
r
r
r
?
H
=
r
Z
M
=
{
0
,
r
,
2
r
,
…
}
H = r\mathbb{Z}_M = \{0, r, 2r, \ldots\}
H
=
r
Z
M
=
{
0
,
r
,
2
r
,
…
}
, the multiples of
r
r
r
inside
Z
M
\mathbb{Z}_M
Z
M
H
=
{
0
,
1
}
H = \{0, 1\}
H
=
{
0
,
1
}
, the two-element subgroup of smallest order
H
=
{
0
,
s
}
H = \{0, s\}
H
=
{
0
,
s
}
for a hidden bit string
s
s
s
H
=
H =
H
=
the whole group
Z
M
\mathbb{Z}_M
Z
M
Check answer