Heidelberg 2022 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 5: Quantum information
MP 5.2: Talk
Wednesday, March 23, 2022, 11:30–11:50, MP-H5
Exploiting Graph Symmetries for Quantum Dynamics — Armin J. Römer1,2, Emanuel Malvetti1,2, Robert Zeier3, and •Thomas Schulte-Herbrüggen1,2 — 1Technical University of Munich (TUM) — 2Munich Centre for Quantum Science and Technology (MCQST) and Munich Quantum Valley (MQV) — 3Forschungszentrum Jülich GmbH, Peter Grünberg Institute, Quantum Control (PGI-8)
Systems of coupled spins can easily be represented by coloured graphs, where the vertices relate to the local spins while the edges stand for pairwise couplings of different type (colour). Potential graph symmetries then naturally simplify quantum dynamics in terms of generators.
We present the background for an efficient algorithmic way to exploit the graph symmetry for arriving (automatically) at a symmetry-adapted basis. It avoids explicit calculation of the entire underlying graph automorphism groups (usually taking the form of wreath products of permutation groups). It connects the well-known Weisfeiler-Leman algorithm (occurring in the context of graph isomorphism problems) with cutting-edge versions of calculating central and orthogonal idempotents.
Worked examples illustrate principles and practice as well as the advantageous connections to graph theory in a widely applicable manner.