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Tclassical=O ⁣(poly(k)log⁡(mn))≈TquantumT_{\text{classical}} = O\!\left(\mathrm{poly}(k)\log(mn)\right) \approx T_{\text{quantum}}

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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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TclassicalT_{\text{classical}}

Symbol T_classical

TcT_classical is part of the quantity the equation computes from the expression on the right.

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TquantumT_{\text{quantum}}

Symbol T_quantum

TqT_quantum is an input to the expression that computes the quantity on the left.

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Published contexts (1)

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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}},

Equation 1 · Future Hardware

Comparing the Main Approaches to Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

This equation gives an approximation: it relates the quantities while allowing an approximation.

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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