Symbol varepsilon
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which decays exponentially in circuit depth for any fixed error rate > 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 quantum computing borrowed, whether its practitioners framed it this way or not, from the same lesson optical computing learned two decades earlier: work within what the noisy substrate actually does well, rather than against it.
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Equation 15 · Future Hardware
From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute
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which decays exponentially in circuit depth for any fixed error rate > 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 quantum computing borrowed, whether its practitioners framed it this way or not, from the same lesson optical computing learned two decades earlier: work within what the noisy substrate actually does well, rather than against it.
Equation guide → · Article →Equation 7 · AI Agents & Systems
Embeddings and the Geometry of Similarity
This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.
for every > 0 [ 11 ] . The condition is on the relative variance of the distance distribution: when distances stop varying much relative to their own mean, the nearest neighbour stops being distinguishable from everything else. The authors call such a query unstable , and their empirical work shows the effect appearing with as few as 10 to 15 dimensions on both synthetic and real data — while explicitly warning that the result does not mean high-dimensional indexing is never meaningful, since particular workloads escape the conditions [ 11 ] .
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