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Cartoon Computation: Quantum-like computing without quantum mechanics

Diederik Aerts, Marek Czachor

Published Nov 28, 2006• 13 citations
OpenAlex

Abstract

We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed -- they are replaced by sets of basic shapes. To test the formalism we solve in geometric terms the Deutsch-Jozsa problem, historically the first example that demonstrated the potential power of quantum computation. Each step of the algorithm has a clear geometric interpetation and allows for a cartoon representation.

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Cartoon computation: quantum-like computing without quantum mechanics

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We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed -- they are replaced by sets of basic shapes. To test the formalism we solve in geometric terms the Deutsch-Jozsa problem, historically the first example that demonstrated the potential power of quantum computation. Each step of the algorithm has a clear geometric interpetation and allows for a cartoon representation.
We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed -- they are replaced by sets of basic shapes. To test the formalism we solve in geometric terms the Deutsch-Jozsa problem, historically the first example that demonstrated the potential power of quantum computation. Each step of the algorithm has a clear geometric interpetation and allows for a cartoon representation.
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, Greenberger-Horne-Zeilinger, and Hadamard states are visualized by means of colored oriented polylines.
Quantum entanglement, a cornerstone of quantum mechanics, presents a unique challenge to conventional classical geometry. This paper explores the potential of utilizing entangled states as fundamental building blocks for computation, proposing a novel geometric paradigm based on entangled states. We introduce a non-classical geometric model that leverages the properties of entanglement to simulate complex geometric structures and topological relationships. This model emphasizes the application of geometric transformations driven by entangled states to achieve precise control over these structures. The core mechanism involves the design of an entanglement-based geometric transformation algorithm, offering a fundamentally different approach to computational geometry compared to traditional methods. We demonstrate the feasibility of this approach through illustrative examples and present a conceptual framework for future research. This work aims to push the boundaries of quantum computation by integrating the inherently non-classical nature of entanglement into the core of geometric processing.