D5.6 Diagrammatical languages to represent Hamiltonians and how to compute the exponential of Hamiltonians
Creators: name: Jeandel, Emmanuel
Publisher: name: Zenodo
Year: 2023
Subjects: QAOA
Hamiltonians
ZX-Calculus

description: This deliverable provides a graphical representation of Ising Hamiltonians, with the explicit goal of using this repre-sentation to analyse later the QAOA algorithm. This analysis entails computations with both the Hamiltonian and its exponential.<br> To reach this goal, a language should be provided where both a matrix and its exponential can be described using the same diagrammatic formalism. This deliverable achieves this goal by first building a specific graphical language, called UHD, to represent Hermitian matrices, then provide an algorithm to compute from this representation a representation in the ZX-calculus of both this matrix and its exponential.<br> Translations from the Hamiltonian to its exponential are streamlined as much as possible by use of monoidal func-tors. This implies the exponential is constructed brick by brick by putting together representation of each part of the Hamiltonian. An example of such a translation is provided.
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