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Equation 14 · Part 3 · From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

Symbol N

Fcircuit≈(1−ε)N,F_{\text{circuit}} \approx (1-\varepsilon)^N,
NN

What this part means

N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

The reason NISQ-era hardware imposes such a hard ceiling on quantum machine learning specifically is a simple compounding effect. If a device executes a circuit of N sequential gates, each with per-gate fidelity 1-ε\varepsilon , and errors accumulate independently, the probability the whole circuit runs without error falls off as Fcircuit≈(1−ε)NF_{\text{circuit}} \approx (1-\varepsilon)^N. which decays exponentially in circuit depth for any fixed error rate ε\varepsilon > 0 . This is precisely the…

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