4 problems

Let $n$ denote the number of modes and let $d$ denote the depth of a random brickwall linear optical network, with the input and sampling setting as considered in the paper. Classi…

Let $F({\bm z})=\frac{1}{m}\sum_{j=1}^m \left(\lvert\langle {{\bm a}_j,{\bm z}} \rangle\rvert^2-y_j^2\right)^2$ be the phase-retrieval loss function, where $y_j$ are measurements a…

A sampling task is one in which a computer produces samples from a target probability distribution $\pi$. A noisy intermediate-scale quantum (NISQ) computer is a quantum computer w…

Uniform-sampling sample-complexity conjecture. The same sample complexity as for $\mathcal{TAM}$ under the paper's regular-graph sampling, namely $O(n\log^2(1/\epsilon))$ samples,…