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  "slug": "computational-benchmark-of-geometric-and-algebraic-models-for-multi-qubit-state-representation",
  "title": "Computational Benchmark of Geometric and Algebraic Models for Multi-Qubit State Representation",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
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  "abstract": "The Bloch sphere provides a powerful yet fundamentally limited geometric model for quantum states, excelling at single-qubit intuition but failing to represent the multi-qubit entanglement that powers quantum advantage. This work addresses the critical tension between the cognitive simplicity of geometric projections and the informational completeness required to model scalable quantum systems. The analysis herein is confined to pure quantum states, providing a foundational benchmark for future work on more complex mixed states. We introduce a unified computational framework to quantitatively benchmark quantum state representations. Three models—a baseline n-Bloch sphere, a topological model based on the Hopf fibration, and an algebraic model using Geometric Algebra—were evaluated against metrics for state fidelity and entanglement preservation using a series of numerical simulations. Our findings confirm a catastrophic failure of the n-Bloch model to represent entanglement, exhibiting 100% entanglement loss for two-qubit Bell states. [...]",
  "abstract_markdown": "The Bloch sphere provides a powerful yet fundamentally limited geometric model for quantum states, excelling at single-qubit intuition but failing to represent the multi-qubit entanglement that powers quantum advantage. This work addresses the critical tension between the cognitive simplicity of geometric projections and the informational completeness required to model scalable quantum systems. The analysis herein is confined to pure quantum states, providing a foundational benchmark for future work on more complex mixed states. We introduce a unified computational framework to quantitatively benchmark quantum state representations. Three models—a baseline n-Bloch sphere, a topological model based on the Hopf fibration, and an algebraic model using Geometric Algebra—were evaluated against metrics for state fidelity and entanglement preservation using a series of numerical simulations. Our findings confirm a catastrophic failure of the n-Bloch model to represent entanglement, exhibiting 100% entanglement loss for two-qubit Bell states. [...]",
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        "description": "The Bloch sphere provides a powerful yet fundamentally limited geometric model for quantum states, excelling at single-qubit intuition but failing to represent the multi-qubit entanglement that powers quantum advantage. This work addresses the critical tension between the cognitive simplicity of geometric projections and the informational completeness required to model scalable quantum systems. The analysis herein is confined to pure quantum states, providing a foundational benchmark for future work on more complex mixed states. We introduce a unified computational framework to quantitatively benchmark quantum state representations. Three models—a baseline n-Bloch sphere, a topological model based on the Hopf fibration, and an algebraic model using Geometric Algebra—were evaluated against metrics for state fidelity and entanglement preservation using a series of numerical simulations. Our findings confirm a catastrophic failure of the n-Bloch model to represent entanglement, exhibiting 100% entanglement loss for two-qubit Bell states. [...]",
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