Juq470

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The solution of large, sparse linear systems is a cornerstone of scientific computing, underpinning applications from climate modelling to quantum chemistry. Classical iterative solvers (e.g., CG, GMRES) scale poorly when faced with ill‑conditioned matrices of dimension >10⁶, while current quantum algorithms such as HHL are limited by qubit counts, circuit depth, and stringent data‑loading requirements. Here we introduce , a Hybrid Quantum‑Classical (HQC) algorithm that synergistically combines a variational quantum subspace method with a classical preconditioned Krylov‑subspace routine. JUQ‑470 achieves a quadratic reduction in effective condition number and exponential speed‑up in the matrix‑vector multiplication kernel on near‑term quantum hardware (≤150 noisy qubits). Numerical experiments on benchmark problems (2‑D Poisson, Maxwell’s equations, and graph Laplacians) demonstrate up to 5.3× wall‑time improvement over state‑of‑the‑art classical solvers on a high‑performance cluster, while maintaining solution fidelity (relative error <10⁻⁴). We also provide a detailed error‑analysis, resource estimation, and a roadmap for scaling JUQ‑470 to fault‑tolerant quantum processors. , the view shifts to the rolling hills

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