Critical Multi-Cubic Lattices: A Novel Implication Algebra for Infinite Systems of Qudit Gates

Autor:	Turnansky, Morrison
Rok vydání:	2023
Předmět:	Quantum Physics Mathematics - Functional Analysis Mathematics - Operator Algebras 06B15 47A80 46L40 46L60 03G12
Druh dokumentu:	Working Paper
Popis:	We introduce a new structure, the critical multi-cubic lattice. Notably the critical multi-cubic lattice is the first true generalization of the cubic lattice to higher dimensional spaces. We then introduce the notion of a homomorphism in the category of critical multi-cubic lattices, compute its automorphism group, and construct a Hilbert space over which we represent the group. With this unitary representation, we re-derive the generalized Pauli matrices common in quantum computation while also defining an algebraic framework for an infinite system of qudits. We also briefly explore the critical multi-cubic lattice as a novel implication algebra serving as a logical framework for qudit gates. Comment: 16 pages, 0 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.12236 Zobrazit plný text záznamu View this record from Arxiv