<s>
Quantum	B-Algorithm
Trajectory	I-Algorithm
Theory	I-Algorithm
(	O
QTT	O
)	O
is	O
a	O
formulation	O
of	O
quantum	O
mechanics	O
used	O
for	O
simulating	O
open	O
quantum	O
systems	O
,	O
quantum	O
dissipation	O
and	O
single	O
quantum	O
systems	O
.	O
</s>
<s>
It	O
was	O
developed	O
by	O
Howard	O
Carmichael	O
in	O
the	O
early	O
1990s	O
around	O
the	O
same	O
time	O
as	O
the	O
similar	O
formulation	O
,	O
known	O
as	O
the	O
quantum	B-Algorithm
jump	I-Algorithm
method	I-Algorithm
or	O
Monte	B-Algorithm
Carlo	I-Algorithm
wave	O
function	O
(	O
MCWF	O
)	O
method	O
,	O
developed	O
by	O
Dalibard	O
,	O
Castin	O
and	O
Mølmer	O
.	O
</s>
<s>
Other	O
contemporaneous	O
works	O
on	O
wave-function-based	O
Monte	B-Algorithm
Carlo	I-Algorithm
approaches	O
to	O
open	O
quantum	O
systems	O
include	O
those	O
of	O
Dum	O
,	O
Zoller	O
and	O
Ritsch	O
,	O
and	O
Hegerfeldt	O
and	O
Wilser	O
.	O
</s>
<s>
Like	O
the	O
quantum	B-Algorithm
jump	I-Algorithm
method	I-Algorithm
,	O
QTT	O
applies	O
to	O
open	O
quantum	O
systems	O
that	O
interact	O
with	O
their	O
environment	O
.	O
</s>
<s>
Like	O
other	O
Monte	B-Algorithm
Carlo	I-Algorithm
approaches	O
,	O
QTT	O
provides	O
an	O
advantage	O
over	O
direct	O
master-equation	O
approaches	O
by	O
reducing	O
the	O
number	O
of	O
computations	O
required	O
.	O
</s>
<s>
This	O
focus	O
on	O
measurement	O
distinguishes	O
it	O
from	O
the	O
quantum	B-Algorithm
jump	I-Algorithm
method	I-Algorithm
which	O
has	O
no	O
direct	O
connection	O
to	O
monitoring	O
output	O
fields	O
.	O
</s>
<s>
Where	O
the	O
quantum	B-Algorithm
jump	I-Algorithm
method	I-Algorithm
predicts	O
the	O
quantum	O
jumps	O
of	O
the	O
system	O
as	O
photons	O
are	O
emitted	O
,	O
QTT	O
predicts	O
the	O
"	O
clicks	O
"	O
of	O
the	O
detector	O
as	O
photons	O
are	O
measured	O
.	O
</s>
<s>
QTT	O
is	O
also	O
broader	O
in	O
its	O
application	O
than	O
the	O
quantum	B-Algorithm
jump	I-Algorithm
method	I-Algorithm
as	O
it	O
can	O
be	O
applied	O
to	O
many	O
different	O
monitoring	O
strategies	O
including	O
direct	O
photon	O
detection	O
and	O
heterodyne	B-Algorithm
detection	I-Algorithm
.	O
</s>
<s>
Like	O
the	O
quantum	B-Algorithm
jump	I-Algorithm
method	I-Algorithm
,	O
QTT	O
was	O
first	O
used	O
for	O
computer	O
simulations	O
of	O
large	O
quantum	O
systems	O
.	O
</s>
