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Equation 8 · Part 1 · From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

Symbol N

poly(log⁡N,κ)\text{poly}(\log N, \kappa)
NN

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N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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N is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

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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