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Equation 7 · Part 1 · From Origins to Frontier: A History of Post-CMOS, Neuromorphic, Photonic, and Quantum AI Compute

Symbol vecx

x⃗\vec{x}
x⃗\vec{x}

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vecx 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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vecx 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

…and support vector machines all reduce, at some stage, to solving or approximating a linear system. Harrow, Hassidim, and Lloyd showed that a quantum computer could estimate certain expectation values built from x⃗\vec{x} 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…

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