Fully graphical treatment of the quantum algorithm for the Hidden Subgroup Problem

Understand

The abelian Hidden Subgroup Problem (HSP) is extremely general, and many problems with known quantum exponential speed-up (such as integers factorisation, the discrete logarithm and Simon's problem) can be seen as specific instances of it.

• The traditional presentation of the quantum protocol for the abelian HSP is low-level, and relies heavily on the the interplay between classical group theory and complex vector spaces.
• Instead, we give a high-level diagrammatic presentation which showcases the quantum structures truly at play.
• Specifically, we provide the first fully diagrammatic proof of correctness for the abelian HSP protocol, showing that strongly complementary observables are the key ingredient to its success.