Juq470

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• Utilises a Quantum Subspace Projector (QSP) to construct a low‑dimensional effective basis for (\mathbfA) that captures dominant spectral components.
• Embeds this subspace into a Classical Preconditioned Krylov Solver (e.g., preconditioned CG), wherein matrix‑vector products are performed on the quantum processor, thereby exploiting quantum parallelism.
• Incorporates an Adaptive Error‑Mitigation Loop that monitors the residual norm and dynamically refines the quantum subspace, ensuring convergence within a prescribed tolerance.

With more details, I can give you a targeted and useful answer. Utilises a Quantum Subspace Projector (QSP) to construct

Identification:

2.3 Quantum Subspace Projection

The concept of projecting a large Hilbert space onto a low‑dimensional subspace spanned by quantum‑generated basis vectors has been employed in quantum chemistry (e.g., QSE [6]) and in quantum singular‑value transformation (QSVT) [7]. By selecting a set of K orthonormal quantum states (\phi_k\rangle_k=1^K), one can construct the effective matrix