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NκN\sqrt{\kappa}

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in time that scales as poly(log⁡N,κ)\text{poly}(\log N, \kappa) , an exponential improvement in the matrix dimension N over the best classical algorithms available at the time, which scale roughly as Nκ\sqrt{\kappa} for a matrix with condition number κ\kappa [ 6 ] . What became known as the HHL algorithm is now routinely cited as the theoretical seed that later, explicitly labeled “quantum machine learning” proposals built their linear-algebra subroutines on top of.

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NN

Symbol N

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κ\kappa

Symbol kappa

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NκN\sqrt{\kappa}

Equation 10 · Future Hardware

From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

in time that scales as poly(log⁡N,κ)\text{poly}(\log N, \kappa) , an exponential improvement in the matrix dimension N over the best classical algorithms available at the time, which scale roughly as Nκ\sqrt{\kappa} for a matrix with condition number κ\kappa [ 6 ] . What became known as the HHL algorithm is now routinely cited as the theoretical seed that later, explicitly labeled “quantum machine learning” proposals built their linear-algebra subroutines on top of.

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