[PDF] A near-term quantum algorithm for solving linear systems of equations based on the Woodbury identity | Semantic Scholar (2024)

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Near term algorithms for linear systems of equations
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This paper focuses on the Variational Quantum Linear Solvers (VQLS), and other closely related methods and adaptions, and implements and contrasts the first application of the Evolutionary Ansatz to the VQLS, the first implementation of the Logical Ansatz VZLS, based on the Classical Combination of Quantum States (CQS) method.

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This work performs an empirical study to test scaling properties and directly related noise resilience of the the most resources-intense component of the HHL algorithm, namely QPE and its NISQ-adaptation Iterative QPE and deduces an approximate bottleneck for algorithms that consider a similar time evolution as QPE.

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This work addresses two further requirements for solving geologic fracture flow systems with quantum algorithms: efficient system state preparation and efficient information extraction that are consistent with an overall exponential speed-up.

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The complexity of quantum state verification in the context of solving systems of linear equations of the form $A \vec x = \vec b$ is analyzed, where state preparation, gate, and measurement errors will need to decrease rapidly with $\kappa$ for worst-case and typical instances if error correction is not used, and present some open problems.



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