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Equation 1 · Part 7 · Comparing the Main Approaches to Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

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Tclassical=O ⁣(poly(k)log⁡(mn))≈Tquantum,T_{\text{classical}} = O\!\left(\mathrm{poly}(k)\log(mn)\right) \approx T_{\text{quantum}},
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

For quantum algorithms proposed to accelerate machine learning on ordinary classical data — the sense in which “quantum AI” is usually marketed — the evidence points the other way on two grounds. The first is trainability: McClean and colleagues showed in 2018 that for a wide class of the parameterized quantum circuits used in most proposed quantum machine learning models, the probability that a gradient in any direction is non-negligible shrinks exponentially with qubit count — a “barren plateau” that makes gradient-based training intractable at exactly the scale where an advantage would need to appear [ 12 ] . The second is the comparison baseline itself. In 2018, Ewin Tang showed that a…

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An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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