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Suppression of Coherent Mode Formation in Central-Spin Systems Coupled to Spin Baths: A Quantitative Dephasing Crossover Criterion

Ali Bourizk

Published Oct 13, 2026• 0 citations
Publisher

Abstract

Changes in this version (v3.1). This version supersedes Version 3.0 deposited under DOI 10.5281/zenodo.23484399. It restores the full author metadata (Ali Bourizk) in the LaTeX/PDF files for the public Zenodo record, adds the complete numerical validation script (generate_figures.py) and the BibTeX database (references.bib) to the upload package for full reproducibility, adds a comprehensive README.md file, and includes the necessary figures. The abstract has been slightly updated to accurately reflect the use of N=2 bath spins in the exact diagonalization. The core physical derivations and analytical results remain strictly unchanged and locked from v3.0.

DOI
10.5281/zenodo.23337644

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Changes in this version (v3.1). This version supersedes Version 3.0 deposited under DOI 10.5281/zenodo.23484399. It restores the full author metadata (Ali Bourizk) in the LaTeX/PDF files for the public Zenodo record, adds the complete numerical validation script (generate_figures.py) and the BibTeX database (references.bib) to the upload package for full reproducibility, adds a comprehensive README.md file, and includes the necessary figures. The abstract has been slightly updated to accurately reflect the use of N=2 bath spins in the exact diagonalization. The core physical derivations and analytical results remain strictly unchanged and locked from v3.0.
Changes in this version (v3.1). This version supersedes Version 3.0 deposited under DOI 10.5281/zenodo.23483273. It restores the full author metadata (Ali Bourizk) in the LaTeX/PDF files for the public Zenodo record, adds the complete numerical validation script (test_pillar1.py) and the BibTeX database (references.bib) to the upload package for full reproducibility, updates the CHANGELOG.txt file, and adds a comprehensive README.md file. The mathematical results and proofs (including the exact threshold at J0 = 0.405Δ) remain strictly unchanged and locked from v3.0.
We solve the long-standing central spin problem for a general set of inhomogeneous bath couplings and a large class of initial bath states. We compute the time evolution of the coherence of a central spin coupled to a spin bath by resumming all orders of the time-convolutionless master equation, thus avoiding the need to assume weak coupling to the bath. The fully quantum, non-markovian solution is obtained in the large-bath limit and is valid up to a time scale set by the largest coupling constant. Our result captures the full decoherence of an electron spin qubit coupled to a nuclear spin bath in a GaAs quantum dot for experimentally relevant parameters. In addition, our solution is quite compact and can readily be used to make quantitative predictions for the decoherence process and to guide the design of nuclear state preparation protocols.
The study of coherence dynamics in open quantum systems, specifically addressing various physical realizations of quantum systems and environments, is a long-standing and central pillar of quantum science and technology. As such, a large body of work establishes a firm theoretical understanding of these processes. Nevertheless, a fundamental aspect of decoherence dynamics, namely the central limit theorem of qubit dephasing in the central spin model, which leads to a Gaussian approximation, lacks formal proof in realistically relevant scenarios. Here we prove this approximation for a bath depicted by an Ising spin system, in the presence of disorder and several (most relevant) functional forms of qubit-bath coupling. Importantly, we show that in certain cases, namely for short-range (exponentially decaying) coupling, this approximation breaks. These results provide a theoretical framework for studying decoherence dynamics in various systems and lead to insights into dephasing behavior with implications for applications in quantum information, quantum computing, and other quantum technologies.
This Zenodo record provides the reproducibility package for the published paper “Interference-First Reality: Multi-Observer Emergence of Objectivity and Time from Information Geometry,” published in the Journal of Applied Mathematics and Physics. The deposited material includes the scripts, data products, tables, figures, source files, and supplementary outputs required to reproduce the analyses and results reported in the article. This repository is intended to ensure methodological transparency, facilitate independent verification, and support the reuse and reproducibility of the published research. Note (2026-10). An updated version of the code supplement is available at https://doi.org/10.5281/zenodo.23269851 (record 10.5281/zenodo.17672528, updated version 2026-10). It corrects the selection of the raw GWOSC strain files, now bound to the GPS window of the requested event, and adds the HRV epoch and CMB smoothing observer constructions; all permutation null tests are generated by the released launcher with one statistic, B = 5000 and seed 12345. The observed Jensen–Shannon distances reported in the article are unchanged; the null distributions of the updated version supersede those of this supplement. See CHANGES.md in the updated package.
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