<s>
In	O
quantum	B-Architecture
computing	I-Architecture
,	O
the	O
Brassard-Høyer-Tapp	B-Algorithm
algorithm	I-Algorithm
or	O
BHT	B-Algorithm
algorithm	I-Algorithm
is	O
a	O
quantum	B-Device
algorithm	I-Device
that	O
solves	O
the	O
collision	B-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
The	O
BHT	B-Algorithm
algorithm	I-Algorithm
only	O
makes	O
queries	O
to	O
f	O
,	O
which	O
matches	O
the	O
lower	O
bound	O
of	O
in	O
the	O
black	B-Device
box	I-Device
model	O
.	O
</s>
<s>
It	O
uses	O
Grover	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
which	O
was	O
discovered	O
the	O
year	O
before	O
.	O
</s>
<s>
Otherwise	O
,	O
all	O
these	O
inputs	O
map	O
to	O
distinct	O
values	O
by	O
f	O
.	O
Then	O
Grover	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
is	O
used	O
to	O
find	O
a	O
new	O
input	O
to	O
f	O
that	O
collides	O
.	O
</s>
<s>
Since	O
there	O
are	O
n	O
inputs	O
to	O
f	O
and	O
n1/3	O
of	O
these	O
could	O
form	O
a	O
collision	O
with	O
the	O
already	O
queried	O
values	O
,	O
Grover	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
can	O
find	O
a	O
collision	O
with	O
extra	O
queries	O
to	O
f	O
.	O
</s>
