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Published equation contexts

Ax⃗=b⃗A\vec{x} = \vec{b}

Why this formula appears here

In 2009, Aram Harrow, Avinatan Hassidim, and Seth Lloyd published “Quantum Algorithm for Linear Systems of Equations” in Physical Review Letters . The problem they addressed — given a system Ax⃗\vec{x} = b⃗\vec{b} , estimate some property of the solution x⃗\vec{x} rather than compute x⃗\vec{x} itself in full — is not framed as a machine-learning problem in the paper. But it is one of the most common subroutines inside machine-learning problems: linear regression, principal component analysis, 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…

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Ax⃗=b⃗A\vec{x} = \vec{b}

Equation 4 · Future Hardware

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

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

In 2009, Aram Harrow, Avinatan Hassidim, and Seth Lloyd published “Quantum Algorithm for Linear Systems of Equations” in Physical Review Letters . The problem they addressed — given a system Ax⃗\vec{x} = b⃗\vec{b} , estimate some property of the solution x⃗\vec{x} rather than compute x⃗\vec{x} itself in full — is not framed as a machine-learning problem in the paper. But it is one of the most common subroutines inside machine-learning problems: linear regression, principal component analysis, 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…

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