Quantum Computers, Discrete Space, and Entanglement

TL;DR

This paper explores algebraic structures of Hilbert spaces in quantum algorithms, using MMP diagrams to efficiently generate Kochen-Specker vectors, demonstrating a novel approach to quantum system simulation.

Contribution

It introduces a new algebraic and diagrammatic method using MMP diagrams for simulating quantum systems and generating Kochen-Specker vectors in higher-dimensional spaces.

Findings

Efficient generation of Kochen-Specker vectors using MMP diagrams.

Demonstration of a minimal Kochen-Specker set in higher dimensions.

A new algebraic framework for quantum system simulation.

Abstract

We consider algebras underlying Hilbert spaces used by quantum information algorithms. We show how one can arrive at equations on such algebras which define n-dimensional Hilbert space subspaces which in turn can simulate quantum systems on a quantum system. In doing so we use MMP diagrams and linear algorithms. MMP diagrams are tractable since an n-block of an MMP diagram has n elements while an n-block of a standard lattice diagram has 2^n elements. An immediate test for such an approach is a generation of minimal and arbitrary Kochen-Specker vectors and we present a minimal state-independent Kochen-Specker set of seven vectors from a Hilbert space with more than four dimensions.