Quantum advantage and noise reduction in distributed quantum computing

Distributed quantum computing can provide substantial noise reduction due to shallower circuits. An experiment illustrates the advantages in case of a Grover search. This motivates study advantage distributed version Simon and Deutsch-Jozsa algorithms. We show that algorithm retains exponential advantage, but complexity deteriorates from $O(n)$ $O({n}^{2})$, where $n={log}_{2}(N)$. The being probabilistic over classical random sampling.