  The ZX-calculus was introduced as a graphical language able to represent
specific quantum primitives in an intuitive way. The recent completeness
results have shown the theoretical possibility of a purely graphical
description of quantum processes. However, in practice, such approaches are
limited by the intrinsic low level nature of ZX calculus. The scalable
notations have been proposed as an attempt to recover an higher level point of
view while maintaining the topological rewriting rules of a graphical language.
We demonstrate that the scalable ZX-calculus provides a formal, intuitive, and
compact framework to describe and prove quantum algorithms. As a proof of
concept, we consider the standard oracle-based quantum algorithms:
Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Grover algorithms, and we show
they can be described and proved graphically.
