<s>
Randomized	B-Device
benchmarking	I-Device
is	O
an	O
experimental	O
method	O
for	O
measuring	O
the	O
average	O
error	O
rates	O
of	O
quantum	B-Architecture
computing	I-Architecture
hardware	O
platforms	O
.	O
</s>
<s>
Randomized	B-Device
benchmarking	I-Device
is	O
the	O
industry-standard	O
protocol	O
used	O
by	O
quantum	O
hardware	O
developers	O
such	O
as	O
IBM	O
and	O
Google	O
to	O
test	O
the	O
performance	O
of	O
the	O
quantum	O
operations	O
.	O
</s>
<s>
The	O
original	O
theory	O
of	O
randomized	B-Device
benchmarking	I-Device
,	O
proposed	O
by	O
Joseph	O
Emerson	O
and	O
collaborators	O
,	O
considered	O
the	O
implementation	O
of	O
sequences	O
of	O
Haar-random	O
operations	O
,	O
but	O
this	O
had	O
several	O
practical	O
limitations	O
.	O
</s>
<s>
The	O
now-standard	O
protocol	O
for	O
randomized	B-Device
benchmarking	I-Device
(	O
RB	O
)	O
relies	O
on	O
uniformly	O
random	O
Clifford	O
operations	O
,	O
as	O
proposed	O
in	O
2006	O
by	O
Dankert	O
et	O
al	O
.	O
</s>
<s>
In	O
current	O
usage	O
randomized	B-Device
benchmarking	I-Device
sometimes	O
refers	O
to	O
the	O
broader	O
family	O
of	O
generalizations	O
of	O
the	O
2005	O
protocol	O
involving	O
different	O
random	O
gate	O
sets	O
that	O
can	O
identify	O
various	O
features	O
of	O
the	O
strength	O
and	O
type	O
of	O
errors	O
affecting	O
the	O
elementary	O
quantum	O
gate	O
operations	O
.	O
</s>
<s>
Randomized	B-Device
benchmarking	I-Device
protocols	O
are	O
an	O
important	O
means	O
of	O
verifying	O
and	O
validating	O
quantum	O
operations	O
and	O
are	O
also	O
routinely	O
used	O
for	O
the	O
optimization	O
of	O
quantum	O
control	O
procedures	O
.	O
</s>
<s>
Randomized	B-Device
benchmarking	I-Device
offers	O
several	O
key	O
advantages	O
over	O
alternative	O
approaches	O
to	O
error	O
characterization	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
number	O
of	O
experimental	O
procedures	O
required	O
for	O
full	O
characterization	O
of	O
errors	O
(	O
called	O
tomography	B-Algorithm
)	O
grows	O
exponentially	O
with	O
the	O
number	O
of	O
quantum	O
bits	O
(	O
called	O
qubits	O
)	O
.	O
</s>
<s>
In	O
contrast	O
,	O
randomized	B-Device
benchmarking	I-Device
protocols	O
are	O
the	O
only	O
known	O
approaches	O
to	O
error	O
characterization	O
that	O
scale	O
efficiently	O
as	O
number	O
of	O
qubits	O
in	O
the	O
system	O
increases	O
.	O
</s>
<s>
Thus	O
RB	O
can	O
be	O
applied	O
in	O
practice	O
to	O
characterize	O
errors	O
in	O
arbitrarily	O
large	O
quantum	B-Architecture
processors	I-Architecture
.	O
</s>
<s>
Additionally	O
,	O
in	O
experimental	O
quantum	B-Architecture
computing	I-Architecture
,	O
procedures	O
for	O
state	O
preparation	O
and	O
measurement	O
(	O
SPAM	O
)	O
are	O
also	O
error-prone	O
,	O
and	O
thus	O
quantum	B-Algorithm
process	I-Algorithm
tomography	I-Algorithm
is	O
unable	O
to	O
distinguish	O
errors	O
associated	O
with	O
gate	O
operations	O
from	O
errors	O
associated	O
with	O
SPAM	O
.	O
</s>
<s>
Randomized	B-Device
benchmarking	I-Device
protocols	O
estimate	O
key	O
features	O
of	O
the	O
errors	O
that	O
affect	O
a	O
set	O
of	O
quantum	O
operations	O
by	O
examining	O
how	O
the	O
observed	O
fidelity	O
of	O
the	O
final	O
quantum	O
state	O
decreases	O
as	O
the	O
length	O
of	O
the	O
random	O
sequence	O
increases	O
.	O
</s>
<s>
Randomized	B-Device
benchmarking	I-Device
was	O
proposed	O
in	O
Scalable	O
noise	O
estimation	O
with	O
random	O
unitary	O
operators	O
,	O
where	O
it	O
was	O
shown	O
that	O
long	O
sequences	O
of	O
quantum	O
gates	O
sampled	O
uniformly	O
at	O
random	O
from	O
the	O
Haar	O
measure	O
on	O
the	O
group	O
SU(d )	O
would	O
lead	O
to	O
an	O
exponential	O
decay	O
at	O
a	O
rate	O
that	O
was	O
uniquely	O
fixed	O
by	O
the	O
error	O
model	O
.	O
</s>
<s>
This	O
Clifford-group	O
approach	O
to	O
Randomized	B-Device
Benchmarking	I-Device
is	O
the	O
now	O
standard	O
method	O
for	O
assessing	O
error	O
rates	O
in	O
quantum	B-Architecture
computers	I-Architecture
.	O
</s>
