This note proves the existence of a quadratic GF(2) map
$p : \{0,1\}^n \to \{0,1\}$ such that no constant-depth circuit
of size $\poly(n)$ can sample the distribution $(u,p(u))$
for uniform $u$.

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An arithmetic read-once formula (ROF) is a formula (circuit of fan-out
1) over
$+, \times$ where each variable labels at most one leaf.
Every multilinear polynomial can be expressed as the sum of ROFs.
In this work, we prove, for certain multilinear polynomials,
a tight lower bound ... more >>>

Given a problem which is intractable for both quantum and classical algorithms, can we find a sub-problem for which quantum algorithms provide an exponential advantage? We refer to this problem as the "sculpting problem." In this work, we give a full characterization of sculptable functions in the query complexity setting. ... more >>>