<s>
The	O
five-qubit	B-Device
error	I-Device
correcting	I-Device
code	I-Device
is	O
the	O
smallest	O
quantum	B-Device
error	I-Device
correcting	I-Device
code	I-Device
that	O
can	O
protect	O
a	O
logical	B-Device
qubit	I-Device
from	O
any	O
arbitrary	O
single	O
qubit	O
error	O
.	O
</s>
<s>
In	O
this	O
code	O
,	O
5	O
physical	B-Device
qubits	I-Device
are	O
used	O
to	O
encode	O
the	O
logical	B-Device
qubit	I-Device
.	O
</s>
<s>
With	O
and	O
being	O
Pauli	O
matrices	O
and	O
the	O
Identity	B-Algorithm
matrix	I-Algorithm
,	O
this	O
code	O
's	O
generators	O
are	O
.	O
</s>
<s>
Once	O
the	O
logical	B-Device
qubit	I-Device
is	O
encoded	O
,	O
errors	O
on	O
the	O
physical	B-Device
qubits	I-Device
can	O
be	O
detected	O
via	O
stabilizer	O
measurements	O
.	O
</s>
<s>
A	O
lookup	B-Data_Structure
table	I-Data_Structure
that	O
maps	O
the	O
results	O
of	O
the	O
stabilizer	O
measurements	O
to	O
the	O
types	O
and	O
locations	O
of	O
the	O
errors	O
gives	O
the	O
control	O
system	O
of	O
the	O
quantum	O
computer	O
enough	O
information	O
to	O
correct	O
errors	O
.	O
</s>
<s>
Stabilizer	O
measurements	O
are	O
parity	O
measurements	O
that	O
measure	O
the	O
stabilizers	O
of	O
physical	B-Device
qubits	I-Device
.	O
</s>
<s>
A	O
logical	B-Device
qubit	I-Device
can	O
be	O
measured	O
in	O
the	O
computational	O
basis	O
by	O
performing	O
a	O
parity	O
measurement	O
on	O
.	O
</s>
<s>
If	O
the	O
measured	O
ancilla	O
is	O
,	O
the	O
logical	B-Device
qubit	I-Device
is	O
.	O
</s>
<s>
If	O
the	O
measured	O
ancilla	O
is	O
,	O
the	O
logical	B-Device
qubit	I-Device
is	O
.	O
</s>
<s>
To	O
correct	O
an	O
error	O
,	O
the	O
same	O
operation	O
is	O
performed	O
on	O
the	O
physical	B-Device
qubit	I-Device
based	O
on	O
its	O
syndrome	O
.	O
</s>
<s>
The	O
first	O
step	O
in	O
executing	O
error	O
corrected	O
quantum	O
computation	O
is	O
to	O
encode	O
the	O
computer	O
's	O
initial	O
state	O
by	O
transforming	O
the	O
physical	B-Device
qubits	I-Device
into	O
logical	O
codewords	O
.	O
</s>
<s>
Stabilizer	O
measurements	O
followed	O
by	O
a	O
measurement	O
can	O
be	O
used	O
to	O
encode	O
5	O
physical	B-Device
qubits	I-Device
into	O
a	O
logical	B-Device
qubit	I-Device
.	O
</s>
