<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
the	O
Aharonov	B-Algorithm
–	I-Algorithm
Jones	I-Algorithm
–	I-Algorithm
Landau	I-Algorithm
algorithm	I-Algorithm
is	O
an	O
efficient	O
quantum	B-Device
algorithm	I-Device
for	O
obtaining	O
an	O
additive	O
approximation	B-Algorithm
of	O
the	O
Jones	O
polynomial	O
of	O
a	O
given	O
link	O
at	O
an	O
arbitrary	O
root	O
of	O
unity	O
.	O
</s>
<s>
Finding	O
a	O
multiplicative	O
approximation	B-Algorithm
is	O
a	O
#P	O
-hard	O
problem	O
,	O
so	O
a	O
better	O
approximation	B-Algorithm
is	O
considered	O
unlikely	O
.	O
</s>
<s>
However	O
,	O
it	O
is	O
known	O
that	O
computing	O
an	O
additive	O
approximation	B-Algorithm
of	O
the	O
Jones	O
polynomial	O
is	O
a	O
BQP-complete	O
problem	O
.	O
</s>
<s>
The	O
"	O
Markov	O
trace	O
"	O
is	O
a	O
trace	O
operator	O
defined	O
on	O
the	O
Temperley	B-Application
–	I-Application
Lieb	I-Application
algebra	I-Application
as	O
follows	O
:	O
given	O
a	O
which	O
is	O
a	O
single	O
Kauffman	O
diagram	O
,	O
let	O
where	O
is	O
the	O
number	O
of	O
loops	O
attained	O
by	O
identifying	O
each	O
point	O
in	O
the	O
bottom	O
of	O
'	O
s	O
Kauffman	O
diagram	O
with	O
the	O
corresponding	O
point	O
on	O
top	O
.	O
</s>
