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- W4381714559 abstract "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." @default.
- W4381714559 created "2023-06-24" @default.
- W4381714559 creator A5021984999 @default.
- W4381714559 date "2023-06-21" @default.
- W4381714559 modified "2023-09-30" @default.
- W4381714559 title "Critical Multi-Cubic Lattices: A Novel Implication Algebra for Infinite Systems of Qudit Gates" @default.
- W4381714559 doi "https://doi.org/10.48550/arxiv.2306.12236" @default.
- W4381714559 hasPublicationYear "2023" @default.
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