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Equation 14 · Part 5 · From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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