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The Bravyi-Kitaev 15-to-1 magic-state distillation protocol (built from the
[
[
15
,
1
,
3
]
]
[[15,1,3]]
[[
15
,
1
,
3
]]
Reed-Muller code) takes 15 input copies of error rate
p
p
p
and outputs one cleaner copy. Approximately what is the output error rate
p
o
u
t
p_{out}
p
o
u
t
?
p
o
u
t
p_{out}
p
o
u
t
is approximately
35
p
3
35 p^3
35
p
3
p
o
u
t
p_{out}
p
o
u
t
is approximately
35
p
35 p
35
p
(linear in
p
p
p
)
p
o
u
t
p_{out}
p
o
u
t
is approximately
15
p
15 p
15
p
p
o
u
t
p_{out}
p
o
u
t
is approximately
p
15
p^{15}
p
15
Check answer