5 problems

Let $m$ be the sampling number, let $\lambda=\lVert A\rVert_2$ and $\phi=\lVert A\rVert_F$ for a symmetric matrix $A$, and let $\varepsilon_{\mathrm{abs}}$ be the threshold appeari…

Let $m$ be the sampling number, let $mu=r_{\mathrm{eff}}(A)$ for a nonzero symmetric positive semidefinite matrix $A$, and let $\varepsilon_{\mathrm{rel}}$ be the threshold appeari…

Fix $lambda>0$ and $phi>0$, and let $\hat{x}_{\mathrm{upper}}$ be the supremum of the inflection points defined in Theorem 2 for the absolute-error Gamma family. Absolute-tail boun…

Let $\bar{x}_{\mathrm{upper}}$ and $\bar{x}_{\mathrm{lower}}$ be the points defined in Theorem 1 for the relative-error Gamma family, with effective shape parameter $\mu$. Extremal…

The state preparation model accesses matrices and vectors through state preparation circuits, whereas the block encoding model accesses matrices through block encodings. State prep…