<s>
The	O
Hidden	B-Algorithm
shift	I-Algorithm
problem	I-Algorithm
states	O
:	O
Given	O
an	O
oracle	O
that	O
encodes	O
two	O
functions	O
and	O
,	O
there	O
is	O
an	O
n-bit	O
string	O
for	O
which	O
for	O
all	O
.	O
</s>
<s>
With	O
a	O
quantum	B-Device
algorithm	I-Device
that	O
's	O
defined	O
as	O
""	O
where	O
is	O
the	O
Hadamard	O
gate	O
and	O
is	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
,	O
this	O
problem	O
can	O
be	O
solved	O
in	O
a	O
polynomial	O
number	O
of	O
queries	O
to	O
while	O
taking	O
exponential	O
queries	O
with	O
a	O
classical	O
algorithm	O
.	O
</s>
<s>
The	O
difference	O
between	O
the	O
Hidden	B-Algorithm
subgroup	I-Algorithm
problem	I-Algorithm
and	O
the	O
Hidden	B-Algorithm
shift	I-Algorithm
problem	I-Algorithm
is	O
that	O
the	O
former	O
focuses	O
on	O
the	O
underlying	O
group	O
while	O
the	O
latter	O
focuses	O
on	O
the	O
underlying	O
ring	O
or	O
field	O
.	O
</s>
