Concatenated Code Explorer
3-qubit bit-flip repetition code · recursive concatenation · fault-tolerance threshold
[[3,1,3]] code
up to level 5
—
p (physical error rate)
0.100
p
th
= 0.500
Max level:
3
4
5
Recursive qubit structure
Logical error rate vs concatenation level
Recursion
p
L
(k+1)
= 3·(p
L
(k)
)² − 2·(p
L
(k)
)³
majority vote · bit-flip errors only
Approx. scaling
p
L
(k)
≈ p
th
· (p/p
th
)
2
k
exponential suppression below threshold
Qubit overhead
n(k) = 3
k
level 3 → 27 · level 5 → 243 qubits
p_L at max level
—
—