Tensor-product vs. geometric-product coding

TL;DR

This paper explores an alternative to quantum computation using geometric products and multivectors instead of tensor products and entangled states, providing a classical geometric framework with similar computational features.

Contribution

It introduces a geometric algebra-based model that mimics quantum computation without relying on quantum mechanics, offering new visualization tools for quantum states.

Findings

Geometric algebra can replicate quantum state structures.

Multivectors visualize Bell, GHZ, and Hadamard states.

The approach offers a classical alternative to quantum computation.

Abstract

Quantum computation is based on tensor products and entangled states. We discuss an alternative to the quantum framework where tensor products are replaced by geometric products and entangled states by multivectors. The resulting theory is analogous to quantum computation but does not involve quantum mechanics. We discuss in detail similarities and differences between the two approaches and illustrate the formulas by explicit geometric objects where multivector versions of the Bell-basis, GHZ, and Hadamard states are visualized by means of colored oriented polylines.