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The Harrow-Hassidim-Lloyd (HHL) algorithm for quantum matrix inversion (linear algebra) bridges classical math to quantum math and has been adopted for quantumizing many classical applications, such as linear regression and deep neural networks.

Since solving a system of linear equations can alternatively be solved with optimization algorithms to attain an equivalent solution, how has the progress been with developing quantum versions of simple gradient-based and gradient-free algorithms used in classical optimization (e.g. gradient descent, coordinate descent, other gradient-free heuristics)? I've only come across quantum annealing so far. Some explanation of linked research articles or Python code would be nice.

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