- "> **Quantum Matrix Inversion (or Quantum Linear Solver) via QSVT** provides a framework for solving linear systems exponentially faster than known classical methods under certain conditions [\\[1\\]](#ref-grand). The algorithm employs a polynomial transformation of singular values to block-encode the inverse of a matrix, which can then be applied on a prepared quantum state to solve a linear equation. Given an efficient routine to embed the classical matrix as a quantum function (block-encoding), this algorithm gives a clean and optimal way to implement matrix inversion compared to other quantum methods. Quantum linear solvers based on block-encoding have many applications, e.g., in [Plasma Physics](https://github.com/Classiq/classiq-library/blob/main/applications/plasma/vlasov_ampere/vlasov_ampere.ipynb) and [Fluid Dynamics](https://github.com/Classiq/classiq-library/blob/main/applications/cfd/linear_qls_for_hybrid_solvers/qls_qsvt.ipynb).\n",
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