<s>
In	O
quantum	B-Architecture
computing	I-Architecture
,	O
Mølmer	B-Device
–	I-Device
Sørensen	I-Device
gate	I-Device
scheme	O
(	O
or	O
MS	O
gate	O
)	O
refers	O
to	O
an	O
implementation	O
procedure	B-Device
for	O
various	O
multi-qubit	O
quantum	B-Application
logic	I-Application
gates	I-Application
used	O
mostly	O
in	O
trapped	O
ion	O
quantum	B-Architecture
computing	I-Architecture
.	O
</s>
<s>
This	O
procedure	B-Device
is	O
based	O
on	O
the	O
original	O
proposition	O
by	O
Klaus	O
Mølmer	O
and	O
Anders	O
Sørensen	O
in	O
1999-2000	O
.	O
</s>
<s>
This	O
proposal	O
was	O
an	O
alternative	O
to	O
the	O
1995	O
Cirac	B-Device
–	I-Device
Zoller	I-Device
controlled-NOT	I-Device
gate	I-Device
implementation	O
for	O
trapped	O
ions	O
,	O
which	O
requires	O
that	O
the	O
system	O
be	O
restricted	O
to	O
the	O
joint	O
motional	O
ground	O
state	O
of	O
the	O
ions	O
.	O
</s>
<s>
Trapped	O
ions	O
were	O
identified	O
by	O
Ignacio	O
Cirac	O
and	O
Peter	O
Zoller	O
at	O
the	O
University	O
of	O
Innsbruck	O
,	O
Austria	O
in	O
1995	O
,	O
as	O
the	O
first	O
realistic	O
system	O
with	O
which	O
to	O
implement	O
a	O
quantum	B-Architecture
computer	I-Architecture
,	O
in	O
a	O
proposal	O
which	O
included	O
a	O
procedure	B-Device
for	O
implementing	O
a	O
CNOT	O
gate	O
by	O
coupling	O
ions	O
through	O
their	O
collective	O
motion	O
.	O
</s>
<s>
In	O
the	O
1999	O
papers	O
,	O
only	O
the	O
"	O
slow	O
gate	O
"	O
regime	O
is	O
considered	O
,	O
in	O
which	O
a	O
large	O
detuning	O
from	O
resonance	O
is	O
required	O
to	O
avoid	O
off-resonant	O
coupling	O
to	O
unwanted	O
phonon	B-Language
modes	O
.	O
</s>
<s>
In	O
2000	O
,	O
Mølmer	O
and	O
Sørensen	O
remove	O
this	O
restriction	O
and	O
show	O
how	O
to	O
remove	O
phonon	B-Language
number	O
dependence	O
in	O
the	O
"	O
fast	O
gate	O
"	O
regime	O
,	O
where	O
lasers	O
are	O
tuned	O
close	O
to	O
the	O
sidebands	O
.	O
</s>
<s>
MS-like	O
gates	O
have	O
also	O
been	O
developed	O
for	O
other	O
quantum	B-Architecture
computing	I-Architecture
platforms	O
.	O
</s>
<s>
The	O
Mølmer	B-Device
–	I-Device
Sørensen	I-Device
gate	I-Device
implementation	O
has	O
the	O
advantage	O
that	O
it	O
does	O
not	O
fail	O
if	O
the	O
ions	O
were	O
not	O
cooled	O
completely	O
to	O
the	O
ground	O
state	O
,	O
and	O
it	O
does	O
not	O
require	O
the	O
ions	O
to	O
be	O
individually	O
addressed	O
.	O
</s>
<s>
Lee	O
,	O
and	O
C	O
.	O
Monroe	O
where	O
this	O
gate	O
was	O
used	O
to	O
produce	O
all	O
four	O
Bell	O
states	O
and	O
to	O
implement	O
Grover	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
successfully	O
.	O
</s>
<s>
Here	O
,	O
is	O
the	O
energy	O
splitting	O
between	O
qubit	O
states	O
and	O
,	O
and	O
are	O
the	O
creation	O
and	O
annihilation	O
operators	O
of	O
phonons	B-Language
in	O
the	O
ions	O
 '	O
collective	O
motional	O
mode	O
,	O
is	O
the	O
energy	O
of	O
those	O
phonons	B-Language
,	O
and	O
is	O
the	O
Pauli	O
Z	O
matrix	O
.	O
</s>
<s>
For	O
an	O
ion	O
with	O
phonon	B-Language
occupation	O
number	O
,	O
an	O
RSB	O
-pulse	O
will	O
take	O
with	O
oscillation	O
frequency	O
.	O
</s>
<s>
For	O
an	O
ion	O
with	O
phonon	B-Language
occupation	O
number	O
,	O
a	O
BSB	O
-pulse	O
will	O
take	O
with	O
oscillation	O
frequency	O
.	O
</s>
<s>
Transition	O
paths	O
involving	O
different	O
,	O
unpopulated	O
vibrational	O
states	O
interfere	O
destructively	O
to	O
eliminate	O
the	O
dependence	O
of	O
rates	O
and	O
revolution	O
frequencies	O
on	O
phonon	B-Language
numbers	O
.	O
</s>
<s>
Summing	O
terms	O
,	O
we	O
obtain	O
the	O
effective	O
Rabi	O
frequency	O
,	O
which	O
is	O
independent	O
of	O
phonon	B-Language
number	O
due	O
to	O
destructive	O
interference	O
between	O
pathways	O
.	O
</s>
