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Equation 14 · Part 6 · From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

superscript

Fcircuit≈(1−ε)N,F_{\text{circuit}} \approx (1-\varepsilon)^N,
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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 noise floor Preskill’s paper is about, and it is why serious NISQ-era quantum machine learning proposals are built around short, shallow circuits matched to a specific problem rather than long, general-purpose programs — the strategy…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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