Phase Transitions of Logic: Bose-Einstein and String-Net Condensates as Universal Computational Substrates
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2026
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| author | Quni-Gudzinas, Rowan Brad |
| author_facet | Quni-Gudzinas, Rowan Brad |
| contents | <p>The realization of fault-tolerant universal quantum computation is currently hindered by a fundamental dichotomy between substrate controllability and intrinsic robustness. This paper introduces the "Universal Hamiltonian Computational Substrate" (UHCS) framework to quantitatively compare two distinct phases of quantum matter as computational foundations: the symmetry-breaking order of Bose-Einstein Condensates (BECs) and the topological order of String-Net Condensates. By simulating a 2D Bose-Hubbard model and a Levin-Wen String-Net model, we analyze the trade-offs between logical density and fault tolerance. Our results reveal that the transition from BEC-based to String-Net-based computation represents a "phase transition of logic," where the system shifts from high controllability with low intrinsic protection to rigid topological robustness. We find that while String-Net models exhibit constant logical density and linear scaling of fault tolerance, BECs offer a tunable universality metric that peaks near the superfluid-Mott insulator transition. These findings suggest that hybrid architectures driving substrates across this phase boundary may offer the most viable path to scalable quantum information processing.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18315328 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Phase Transitions of Logic: Bose-Einstein and String-Net Condensates as Universal Computational Substrates Quni-Gudzinas, Rowan Brad <p>The realization of fault-tolerant universal quantum computation is currently hindered by a fundamental dichotomy between substrate controllability and intrinsic robustness. This paper introduces the "Universal Hamiltonian Computational Substrate" (UHCS) framework to quantitatively compare two distinct phases of quantum matter as computational foundations: the symmetry-breaking order of Bose-Einstein Condensates (BECs) and the topological order of String-Net Condensates. By simulating a 2D Bose-Hubbard model and a Levin-Wen String-Net model, we analyze the trade-offs between logical density and fault tolerance. Our results reveal that the transition from BEC-based to String-Net-based computation represents a "phase transition of logic," where the system shifts from high controllability with low intrinsic protection to rigid topological robustness. We find that while String-Net models exhibit constant logical density and linear scaling of fault tolerance, BECs offer a tunable universality metric that peaks near the superfluid-Mott insulator transition. These findings suggest that hybrid architectures driving substrates across this phase boundary may offer the most viable path to scalable quantum information processing.</p> |
| title | Phase Transitions of Logic: Bose-Einstein and String-Net Condensates as Universal Computational Substrates |
| url | https://doi.org/10.5281/zenodo.18315328 |