= Solution
The <HHL algorithm> requires coherent, efficient and repeatable preparation of the normalized state $|b\rangle$, normally through a known preparation circuit and its inverse; possession of a single unknown physical specimen does not supply that access. The component of $b$ on any discarded or unresolved small-eigenvalue subspace must also be negligible. Here $U$ is a <unitary operator>, so it is invertible and all its <singular values> equal one, giving <condition number> $\kappa=1$.
Standard HHL is stated for a <Hermitian matrix> with an efficient sparse-access or <block encoding> oracle. A non-Hermitian $U$ can be embedded in the Hermitian block matrix
$$
\begin{pmatrix}0&U\\U^\dagger&0\end{pmatrix};
$$
part (a) supplies efficient access to $U^\dagger$. With inverse-polynomial target precision, $m=O(\log n)$ phase bits, and an efficient preparation oracle for $|b\rangle$, the runtime is $\operatorname{poly}(n)$. The output is the normalized <quantum state> proportional to the solution $x$, rather than a classical list of all its amplitudes.
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