Why does the condition number matter in HHL?

Question: Why does the condition number κ of A matter in quantum linear-systems algorithms? A) Because κ determines the number of qubits required to store b exactly B) Because κ is identical to the sparsity parameter of A C) Because small eigenvalues require controlled inversion with large amplitudes or careful rescaling, increasing complexity and error sensitivity D) Because phase estimation cannot resolve eigenvalues unless κ=1 exactly Correct: C Explanation: Solving Ax=b involves applying something like A⁻¹ to the input state. Small eigenvalues are amplified by inversion, making the procedure sensitive to precision and increasing the dependence on κ. Topic: advanced quantum computing / HHL / condition number