<s>
The	O
Eastin	B-Device
–	I-Device
Knill	I-Device
theorem	I-Device
is	O
a	O
no-go	O
theorem	O
that	O
states	O
:	O
"	O
No	O
quantum	B-Device
error	I-Device
correcting	I-Device
code	I-Device
can	O
have	O
a	O
continuous	O
symmetry	O
which	O
acts	O
transversely	O
on	O
physical	O
qubits	O
"	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
no	O
quantum	B-Device
error	I-Device
correcting	I-Device
code	I-Device
can	O
transversely	O
implement	O
a	O
universal	O
gate	O
set	O
.	O
</s>
<s>
Since	O
quantum	O
computers	O
are	O
inherently	O
noisy	O
,	O
quantum	B-Device
error	I-Device
correcting	I-Device
codes	I-Device
are	O
used	O
to	O
correct	O
errors	O
that	O
affect	O
information	O
due	O
to	O
decoherence	O
.	O
</s>
<s>
Due	O
to	O
the	O
Eastin	B-Device
–	I-Device
Knill	I-Device
theorem	I-Device
,	O
a	O
universal	O
set	O
like	O
}	O
gates	O
ca	O
n't	O
be	O
implemented	O
transversally	O
.	O
</s>
<s>
In	O
addition	O
to	O
investigating	O
fault	O
tolerant	O
quantum	O
computation	O
,	O
the	O
Eastin	B-Device
–	I-Device
Knill	I-Device
theorem	I-Device
is	O
also	O
useful	O
for	O
studying	O
quantum	O
gravity	O
via	O
the	O
AdS/CFT	O
correspondence	O
and	O
in	O
condensed	O
matter	O
physics	O
via	O
quantum	O
reference	O
frame	O
or	O
many-body	B-Algorithm
theory	I-Algorithm
.	O
</s>
<s>
The	O
approximate	O
version	O
of	O
the	O
Eastin	B-Device
–	I-Device
Knill	I-Device
theorem	I-Device
states	O
:	O
"	O
If	O
a	O
code	O
admits	O
a	O
continuous	O
symmetry	O
pertaining	O
to	O
a	O
Lie	O
group	O
and	O
corrects	O
erasure	O
with	O
fixed	O
accuracy	O
,	O
then	O
for	O
each	O
logical	O
qubit	O
,	O
a	O
number	O
of	O
physical	O
qubits	O
per	O
subsystem	O
that	O
is	O
inversely	O
proportional	O
to	O
the	O
error	O
parameter	O
is	O
needed	O
"	O
.	O
</s>
<s>
The	O
approximate	O
version	O
of	O
the	O
Eastin	B-Device
–	I-Device
Knill	I-Device
theorem	I-Device
is	O
more	O
robust	O
than	O
the	O
original	O
because	O
it	O
explains	O
why	O
it	O
's	O
impossible	O
to	O
have	O
continuous	O
symmetries	O
for	O
transversal	O
gates	O
on	O
the	O
microscopic	O
scale	O
while	O
also	O
explaining	O
how	O
it	O
's	O
possible	O
to	O
have	O
continuous	O
symmetries	O
for	O
transversal	O
gates	O
on	O
the	O
macroscopic	O
scale	O
.	O
</s>
<s>
The	O
Eastin	B-Device
–	I-Device
Knill	I-Device
theorem	I-Device
does	O
not	O
prohibit	O
protocols	O
that	O
provide	O
fault	O
tolerant	O
quantum	O
computation	O
.	O
</s>
