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[Quantum] Machine Learning Is A Solved Problem

Quantum Machine Learning offers certain advantages over classical machine learning e.g. speedup, feature space and parallelism.

The world is pegging its hopes on the HHL Algorithm to deliver Quantum Machine Learning.

But it has serious drawbacks that renders it useless for any practical purpose.

Automatski has made a breakthrough that Solves Machine Learning completely and absolutely.

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The HHL Algorithm

The HHL (Harrow-Hassidim-Lloyd) algorithm is a quantum algorithm that was developed to solve linear systems of equations efficiently on a quantum computer. It was introduced by Aram Harrow, Avinatan Hassidim, and Seth Lloyd in 2009. Solving linear systems of equations is a fundamental problem in mathematics and has many practical applications in various fields, including physics, engineering, computer science, and machine learning.

The standard classical approach to solving a linear system of equations of the form Ax = b, where A is a known matrix and b is a known vector, involves methods like Gaussian elimination or matrix factorization. These classical methods have a computational complexity that can be polynomial or worse, making them inefficient for large-scale problems.

The HHL algorithm, on the other hand, is designed to solve linear systems of equations exponentially faster than the best-known classical algorithms. It leverages the unique properties of quantum computing to achieve this speedup.

But there are many disadvantages and limitations of the HHL Algorithm.
- The Solution of Ax=b is obtained only as a Quantum State. So it can only be used as a subroutine in another Quantum Algorithm. And if we try to extract the explicit solution from the Quantum State it takes an Exponential Number of Steps.
- The matrix has to be Hermitian and s-sparse
- State Preparation requires Exponential Effort
- The Matrix A needs to be well conditioned. The condition number 𝜅 of a Hermitian matrix is the ratio of the largest to smallest eigenvalue magnitude.

Machine Learning Is Now A Solved Problem

"We can now solve Billion Sized Matrix Algebra in near linear time"

So what can we do now?

Given an s-sparse matrix we can get the explicit solution in near linear time. Without any effort of state preparation, limitations of condition number etc.

Do Production Grade Quantum Machine Learning Applications "Today"

This has led to major breakthroughs in...

- Geometry
- Networks/Circuits
- Heat Transfer
- Static/Dynamics
- Chemistry
- Economics
- Linear Programming
- Games

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HHL & Quantum Machine Learning

1+ Billion Qubit/Parameters

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