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Towards Topological Protection of Solid-State Qubits: Three Conceptual Architectures and Their Limitations

Enrique Chacon-Pinzon

Published Mar 17, 2026• 0 citations
Publisher

Abstract

Title: Towards Topological Protection of Solid-State Qubits: Three Conceptual Architectures and Their Limitations Description: This package contains the complete reproducibility materials for a theoretical study of unconventional quantum error suppression mechanisms inspired by topological phenomena in superfluid helium-3. The work presents three conceptual architectures—fractal coupling networks, synthetic gauge fields, and non-Markovian quantum memory—with explicit analysis of their physical constraints and realistic performance bounds. Key Features: Reproducible simulations: Three Python scripts using QuTiP 5.x generate all figures and numerical data Honest assessment: Explicit limitations stated for each approach (no exponential suppression claimed for fermionic qubits) Publication-ready manuscript: LaTeX source and compiled PDF formatted for PRX Quantum or npj Quantum Information Complete bibliography: 13 peer-reviewed references Main Findings: Fractal networks: Provide 2–10× improvement through sparse connectivity, not Hausdorff dimension effects Gauge protection: Exhibits polynomial 1/√N scaling for fermions (Central Limit Theorem), not exponential Non-Markovian memory: Requires Q > 10⁹ cavities for significant improvement; current record Q~5×10⁸ Physical Constraints Acknowledged: Fermionic statistics limit collective enhancement to polynomial scaling Phase stability δφ/φ₀ < 10⁻² required for gauge protection Cavity Q-factors beyond 10⁹ remain unprecedented in integrated systems Validation Criteria: Minimal experimental demonstrations proposed: N=9 fractal with 2× improvement; N=4 gauge with 1.5× improvement; Q=10⁸ cavity with 5× improvement. Files Included: paper.tex, paper.pdf (manuscript) fractal_protect.py, gauge_protection.py, non_markovian_memory.py (simulations) requirements.txt (dependencies) README.md, README_FRACTAL.md, README_GAUGE.md, README_MEMORY.md (documentation) Generated figures and JSON data files License: MIT License Contact: rikechaconpi@gmail.com

DOI
10.5281/zenodo.19073756

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Title: Towards Topological Protection of Solid-State Qubits: Three Conceptual Architectures and Their Limitations Description: This package contains the complete reproducibility materials for a theoretical study of unconventional quantum error suppression mechanisms inspired by topological phenomena in superfluid helium-3. The work presents three conceptual architectures—fractal coupling networks, synthetic gauge fields, and non-Markovian quantum memory—with explicit analysis of their physical constraints and realistic performance bounds. Key Features: Reproducible simulations: Three Python scripts using QuTiP 5.x generate all figures and numerical data Honest assessment: Explicit limitations stated for each approach (no exponential suppression claimed for fermionic qubits) Publication-ready manuscript: LaTeX source and compiled PDF formatted for PRX Quantum or npj Quantum Information Complete bibliography: 13 peer-reviewed references Main Findings: Fractal networks: Provide 2–10× improvement through sparse connectivity, not Hausdorff dimension effects Gauge protection: Exhibits polynomial 1/√N scaling for fermions (Central Limit Theorem), not exponential Non-Markovian memory: Requires Q > 10⁹ cavities for significant improvement; current record Q~5×10⁸ Physical Constraints Acknowledged: Fermionic statistics limit collective enhancement to polynomial scaling Phase stability δφ/φ₀ < 10⁻² required for gauge protection Cavity Q-factors beyond 10⁹ remain unprecedented in integrated systems Validation Criteria: Minimal experimental demonstrations proposed: N=9 fractal with 2× improvement; N=4 gauge with 1.5× improvement; Q=10⁸ cavity with 5× improvement. Files Included: paper.tex, paper.pdf (manuscript) fractal_protect.py, gauge_protection.py, non_markovian_memory.py (simulations) requirements.txt (dependencies) README.md, README_FRACTAL.md, README_GAUGE.md, README_MEMORY.md (documentation) Generated figures and JSON data files License: MIT License Contact: rikechaconpi@gmail.com
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The construction of a large-scale fault-tolerant quantum computer is an outstanding scientific and technological goal. It holds the promise to allow us to solve a variety of complex problems such as factoring large numbers, quick database search, and the quantum simulation of many-body quantum systems in fields as diverse as condensed matter, quantum chemistry, and even high-energy physics. Sophisticated theoretical protocols for reliable quantum information processing under imperfect conditions have been de-veloped, when errors affect and corrupt the fragile quantum states during storage and computations. Arguably, the most realistic and promising ap-proach towards practical fault-tolerant quantum computation are topologi-cal quantum error-correcting codes, where quantum information is stored in interacting, topologically ordered 2D or 3D many-body quantum systems. This approach offers the highest known error thresholds, which are already today within reach of the experimental accuracy in state-of-the-art setups. A combination of theoretical and experimental research is needed to store, protect and process fragile quantum information in logical qubits effectively so that they can outperform their constituting physical qubits. Whereas small-scale quantum error correction codes have been implemented, one of the main theoretical challenges remains to develop new and improve existing efficient strategies (so-called decoders) to derive (near-)optimal error cor-rection operations in the presence of experimentally accessible measurement information and realistic noise sources. One main focus of this project is the development and numerical implementation of scalable, efficient decoders to operate topological color codes. Additionally, we study the feasibility of im-plementing quantum error-correcting codes fault-tolerantly in near-term ion traps. To this end, we use realistic modeling of the different noise sources, computer simulations, and most modern quantum information approaches to quantum circuitry and noise suppression techniques.
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Sensitivity to noise makes most of the current quantum computing schemes prone to error and nonscalable, allowing only for small proof-of-principle devices. Topologically-protected quantum computing aims at solving this problem by encoding quantum bits and gates in topological properties of the hardware medium that are immune to noise that does not impact the entire system at once. There are different approaches to achieve topological stability or active error correction, ranging from quasiparticle braidings to spin models and topological colour codes. The stability of these proposals against noise can be quantified by their error threshold. This figure of merit can be computed by mapping the problem onto complex statistical-mechanical spin-glass models with local disorder on nontrival lattices that can have many-body interactions and are sometimes described by lattice gauge theories. The error threshold for a given source of error then represents the point in the temperature-disorder phase diagram where a stable symmetry-broken phase vanishes. An overview of the techniques used to estimate the error thresholds is given, as well as a summary of recent results on the stability of different topologically-protected quantum computing schemes to different error sources. 1.