<s>
quantum	B-Architecture
computing	I-Architecture
and	O
quantum	O
communication	O
devices	O
.	O
</s>
<s>
Quantum	B-Device
error-correcting	I-Device
codes	I-Device
restore	O
a	O
noisy	O
,	O
</s>
<s>
classical	O
binary	O
or	O
quaternary	O
codes	O
for	O
use	O
as	O
a	O
quantum	B-Device
code	I-Device
.	O
</s>
<s>
Nevertheless	O
,	O
it	O
is	O
still	O
useful	O
to	O
import	O
classical	O
codes	O
in	O
this	O
way	O
(	O
though	O
,	O
see	O
how	O
the	O
entanglement-assisted	O
stabilizer	B-Device
formalism	I-Device
overcomes	O
this	O
difficulty	O
)	O
.	O
</s>
<s>
the	O
Pauli	O
group	O
in	O
formulating	O
quantum	B-Device
error-correcting	I-Device
codes	I-Device
.	O
</s>
<s>
error-correction	B-Error_Name
procedure	O
of	O
a	O
quantum	B-Device
stabilizer	I-Device
code	I-Device
over	O
qubits	O
.	O
</s>
<s>
stabilizer	B-Device
code	I-Device
.	O
</s>
<s>
simplification	O
of	O
quantum	B-Device
error	I-Device
correction	I-Device
theory	O
.	O
</s>
<s>
operation	O
defined	O
as	O
binary	B-Data_Structure
vector	I-Data_Structure
addition	O
.	O
</s>
<s>
the	O
relation	O
between	O
classical	O
linear	O
error	B-Error_Name
correction	I-Error_Name
and	O
quantum	B-Device
error	I-Device
correction	I-Device
more	O
explicit	O
.	O
</s>
<s>
By	O
comparing	O
quantum	B-Device
error	I-Device
correcting	I-Device
codes	I-Device
in	O
this	O
language	O
to	O
symplectic	O
vector	O
spaces	O
,	O
we	O
can	O
see	O
the	O
following	O
.	O
</s>
