<s>
The	O
Deutsch	B-Algorithm
–	I-Algorithm
Jozsa	I-Algorithm
algorithm	I-Algorithm
is	O
a	O
deterministic	B-General_Concept
quantum	B-Device
algorithm	I-Device
proposed	O
by	O
David	O
Deutsch	O
and	O
Richard	O
Jozsa	O
in	O
1992	O
with	O
improvements	O
by	O
Richard	O
Cleve	O
,	O
Artur	O
Ekert	O
,	O
Chiara	O
Macchiavello	O
,	O
and	O
Michele	O
Mosca	O
in	O
1998	O
.	O
</s>
<s>
Although	O
of	O
little	O
current	O
practical	O
use	O
,	O
it	O
is	O
one	O
of	O
the	O
first	O
examples	O
of	O
a	O
quantum	B-Device
algorithm	I-Device
that	O
is	O
exponentially	O
faster	O
than	O
any	O
possible	O
deterministic	B-General_Concept
classical	O
algorithm	O
.	O
</s>
<s>
The	O
Deutsch	O
–	O
Jozsa	O
problem	O
is	O
specifically	O
designed	O
to	O
be	O
easy	O
for	O
a	O
quantum	B-Device
algorithm	I-Device
and	O
hard	O
for	O
any	O
deterministic	B-General_Concept
classical	O
algorithm	O
.	O
</s>
<s>
It	O
is	O
a	O
black	B-Device
box	I-Device
problem	O
that	O
can	O
be	O
solved	O
efficiently	O
by	O
a	O
quantum	O
computer	O
with	O
no	O
error	O
,	O
whereas	O
a	O
deterministic	B-General_Concept
classical	O
computer	O
would	O
need	O
a	O
exponential	O
number	O
of	O
queries	O
to	O
the	O
black	B-Device
box	I-Device
to	O
solve	O
the	O
problem	O
.	O
</s>
<s>
Simon	B-Algorithm
's	I-Algorithm
problem	I-Algorithm
is	O
an	O
example	O
of	O
a	O
problem	O
that	O
yields	O
an	O
oracle	O
separation	O
between	O
BQP	O
and	O
BPP	O
.	O
</s>
<s>
In	O
the	O
Deutsch	O
–	O
Jozsa	O
problem	O
,	O
we	O
are	O
given	O
a	O
black	B-Device
box	I-Device
quantum	O
computer	O
known	O
as	O
an	O
oracle	O
that	O
implements	O
some	O
function	O
:	O
</s>
<s>
We	O
are	O
promised	O
that	O
the	O
function	O
is	O
either	O
constant	O
(	O
0	O
on	O
all	O
inputs	O
or	O
1	O
on	O
all	O
inputs	O
)	O
or	O
balanced	O
(	O
1	O
for	O
exactly	O
half	O
of	O
the	O
input	O
domain	B-Algorithm
and	O
0	O
for	O
the	O
other	O
half	O
)	O
.	O
</s>
<s>
For	O
a	O
conventional	O
deterministic	B-General_Concept
algorithm	I-General_Concept
where	O
is	O
the	O
number	O
of	O
bits	O
,	O
evaluations	O
of	O
will	O
be	O
required	O
in	O
the	O
worst	O
case	O
.	O
</s>
<s>
For	O
a	O
conventional	O
randomized	B-General_Concept
algorithm	I-General_Concept
,	O
a	O
constant	O
evaluations	O
of	O
the	O
function	O
suffices	O
to	O
produce	O
the	O
correct	O
answer	O
with	O
a	O
high	O
probability	O
(	O
failing	O
with	O
probability	O
with	O
)	O
.	O
</s>
<s>
The	O
Deutsch-Jozsa	O
quantum	B-Device
algorithm	I-Device
produces	O
an	O
answer	O
that	O
is	O
always	O
correct	O
with	O
a	O
single	O
evaluation	O
of	O
.	O
</s>
<s>
The	O
Deutsch	B-Algorithm
–	I-Algorithm
Jozsa	I-Algorithm
algorithm	I-Algorithm
generalizes	O
earlier	O
(	O
1985	O
)	O
work	O
by	O
David	O
Deutsch	O
,	O
which	O
provided	O
a	O
solution	O
for	O
the	O
simple	O
case	O
where	O
.	O
</s>
<s>
The	O
algorithm	O
as	O
Deutsch	O
had	O
originally	O
proposed	O
it	O
was	O
not	O
,	O
in	O
fact	O
,	O
deterministic	B-General_Concept
.	O
</s>
<s>
In	O
1992	O
,	O
Deutsch	O
and	O
Jozsa	O
produced	O
a	O
deterministic	B-General_Concept
algorithm	I-General_Concept
which	O
was	O
generalized	O
to	O
a	O
function	O
which	O
takes	O
bits	O
for	O
its	O
input	O
.	O
</s>
<s>
Unlike	O
Deutsch	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
this	O
algorithm	O
required	O
two	O
function	O
evaluations	O
instead	O
of	O
only	O
one	O
.	O
</s>
<s>
Further	O
improvements	O
to	O
the	O
Deutsch	B-Algorithm
–	I-Algorithm
Jozsa	I-Algorithm
algorithm	I-Algorithm
were	O
made	O
by	O
Cleve	O
et	O
al.	O
,	O
resulting	O
in	O
an	O
algorithm	O
that	O
is	O
both	O
deterministic	B-General_Concept
and	O
requires	O
only	O
a	O
single	O
query	O
of	O
.	O
</s>
<s>
This	O
algorithm	O
is	O
still	O
referred	O
to	O
as	O
Deutsch	B-Algorithm
–	I-Algorithm
Jozsa	I-Algorithm
algorithm	I-Algorithm
in	O
honour	O
of	O
the	O
groundbreaking	O
techniques	O
they	O
employed	O
.	O
</s>
<s>
For	O
the	O
Deutsch	B-Algorithm
–	I-Algorithm
Jozsa	I-Algorithm
algorithm	I-Algorithm
to	O
work	O
,	O
the	O
oracle	O
computing	O
from	O
must	O
be	O
a	O
quantum	O
oracle	O
which	O
does	O
not	O
decohere	O
.	O
</s>
<s>
Deutsch	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
is	O
a	O
special	O
case	O
of	O
the	O
general	O
Deutsch	B-Algorithm
–	I-Algorithm
Jozsa	I-Algorithm
algorithm	I-Algorithm
where	O
n	O
=	O
1	O
in	O
.	O
</s>
<s>
We	O
begin	O
with	O
the	O
two-qubit	O
state	O
and	O
apply	O
a	O
Hadamard	B-Algorithm
transform	I-Algorithm
to	O
each	O
qubit	O
.	O
</s>
