Let \(f: \mathbb {F}_2^n \rightarrow {F}_2^n\) be a Boolean function with period \(\mathbf {s}\). It is well-known that Simon’s algorithm finds {s}\) in time polynomial n on quantum devices are capable of performing error-correction. However, today’s inherently noisy, too limited for error correction, and not error-tolerant.

Inferring probabilistic networks from data is a notoriously difficult task. Under various goodness-of-fit measures, finding an optimal network NP-hard, even if restricted to polytrees of bounded in-degree. Polynomial-time algorithms are known only for rare special cases, perhaps most notably branchings, that is, in which the in-degree every node at one. Here, we study complexity polytree can be...