Quantum Logic and Quantum Computation

TL;DR

This paper explores algebraic equations of Hilbert lattices to represent quantum systems, aiming to facilitate direct state input into quantum computers, and reviews recent advances in Hilbert space equations.

Contribution

It introduces a novel approach using Hilbert lattice equations for representing quantum states in quantum computing systems.

Findings

New results on states in Hilbert lattices

Review of recent Hilbert space equations research

Potential for direct state input into quantum computers

Abstract

We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers. More specifically, we look for a way to feed a quantum computer with algebraic equations of n-th order underlying an infinite dimensional Hilbert space description of quantum systems. A number of new results on states defined on Hilbert lattices are presented and discussed and a number of recently obtained results in the field of Hilbert space equations are reviewed.