Entangling gates in even Euclidean lattices such as Leech lattice

Michel Planat (1)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

We point out a organic relationship between real entangling n-qubit gates of quantum computation and the group of automorphisms of even Euclidean lattices of the corresponding dimension 2^n. The type of entanglement that is found in the gates/generators of Aut() depends on the lattice. In particular, we investigate Zn lattices, Barnes-Wall lattices D4, E8, 16 (associated to n = 2, 3 and 4 qubits), and the Leech lattices h24 and 24 (associated to a 3-qubit/qutrit system). Balanced tripartite entanglement is found to be a basic feature of Aut(), a nding that bears out our recent work related to the Weyl group of E8 [1, 2].

Mots clés: Three-partite entanglement; Euclidean lattices; quantum error correction

Domaines: Physique Quantique [quant-ph]; Théorie des groupes [math.GR]

Michel Planat. Entangling gates in even Euclidean lattices such as Leech lattice. 2010. ⟨hal-00459045v2⟩