Effective Depth

Noise truncates quantum circuits to logarithmic depth — trainability is a symptom of lost advantage
32
0.30
10
Gate Influence Decay
Deeper gates lose exponential influence under noise
Circuit Cross-Section
Color = gate influence on output. Beyond the horizon: decorrelation.
32
Actual Depth
5
Effective Depth
84%
Lost to Noise
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Contraction c
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Gradient Signal
Any uncorrected noise truncates quantum circuits to effectively O(log n) depth — the last few layers dominate while deeper gates decorrelate into noise.