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

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Quantum Computer (opens in a new tab)Matrix (opens in a new tab)Quantum Algorithm (opens in a new tab)Local Optima (opens in a new tab)Barren Plateaus (opens in a new tab)Hamiltonian Simulation (opens in a new tab)Hadamard Test (opens in a new tab)Variational Algorithms (opens in a new tab)Speedup (opens in a new tab)Inner Product (opens in a new tab)

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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.

Identifying Bottlenecks of NISQ-friendly HHL algorithms
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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 algorithm is based on a general technique for implementing any operator with a suitable Fourier or Chebyshev series representation, and allows the quantum phase estimation algorithm, whose dependence on $\epsilon$ is prohibitive, to be bypassed.

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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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