This revised version (v1.1) introduces several major improvements compared to the previous release: 1. Added a physically consistent open-system model The qubit–bosonic–mode system is now described using a full Lindblad master equation, including: relaxation (T1), non-geometric dephasing, bosonic-mode damping, realistic mode–reduction from a Gaussian scalar field. This makes the model experimentally testable and physically grounded. 2. New coherence-stabilization mechanism validated in an open system We demonstrate that the proposed Energy-Balance Manifold(Δlog=0) acts as a true coherence sweet-spot,even when dissipation is present. The previous version only discussed this at a conceptual level. 3. Improved numerical simulations All figures have been recomputed using the new codebase: 2D manifold maps, analytic suppression law, 3D coherence surface, Ramsey and Spin-Echo simulations. All numerical scripts are now included in /Code and all datasets in /Data,making the results fully reproducible. 4. Added figure references, cross-citations and expanded physical explanation The manuscript now contains: figure-by-figure captions, in-text references to Figures 1–10, an expanded physical motivation for the bosonic-mode reduction, a new section 4.5 Open-System Extension and Realistic Decoherence Channels. 5. Complete package archive with checksums The ZIP now contains: report, code, figures, data, checksum file, README file. This enables independent verification of all results.
This revised version (v1.1) introduces several major improvements compared to the previous release: 1. Added a physically consistent open-system model The qubit–bosonic–mode system is now described using a full Lindblad master equation, including: relaxation (T1), non-geometric dephasing, bosonic-mode damping, realistic mode–reduction from a Gaussian scalar field. This makes the model experimentally testable and physically grounded. 2. New coherence-stabilization mechanism validated in an open system We demonstrate that the proposed Energy-Balance Manifold(Δlog=0) acts as a true coherence sweet-spot,even when dissipation is present. The previous version only discussed this at a conceptual level. 3. Improved numerical simulations All figures have been recomputed using the new codebase: 2D manifold maps, analytic suppression law, 3D coherence surface, Ramsey and Spin-Echo simulations. All numerical scripts are now included in /Code and all datasets in /Data,making the results fully reproducible. 4. Added figure references, cross-citations and expanded physical explanation The manuscript now contains: figure-by-figure captions, in-text references to Figures 1–10, an expanded physical motivation for the bosonic-mode reduction, a new section 4.5 Open-System Extension and Realistic Decoherence Channels. 5. Complete package archive with checksums The ZIP now contains: report, code, figures, data, checksum file, README file. This enables independent verification of all results.
This repository contains the numerical data and computational codes supporting the results presented in the manuscript: "Engineered non-Gaussian Coherence as a Thermodynamic Resource for Quantum Batteries". The archive (data_QB.zip) includes all datasets, Jupyter notebooks, and figure files required to reproduce the results reported in both the main text and the Supplemental Material. Each figure is organised in a separate directory containing the corresponding data (.txt), code (.ipynb), and generated plots (.png/.pdf). The provided materials are sufficient to reproduce all figures and results without restriction. Detailed instructions and directory structure are described in the accompanying README.txt file. This dataset is made openly available to ensure transparency and reproducibility of the reported results.
Silicon–germanium (Si/SiGe) quantum dots represent a preeminent architecture for scalable quantum computing; however, their performance remains fundamentally constrained by environmental decoherence. This work presents a comparative simulation study of a two-qubit system in Si/SiGe, evaluating the fidelity of various noise modeling frameworks under realistic conditions, including 1/f charge noise and phonon-mediated relaxation. We benchmark the Lindblad Master Equation against the Bloch–Redfield Master Equation, the Semiclassical Stochastic Hamiltonian method and the Monte Carlo Wavefunction (Quantum Jumps). Our analysis reveals that while semiclassical models effectively capture pure dephasing (T2*) dynamics, they fail to account for energy relaxation (T1) at cryogenic temperatures, erroneously driving the system toward a high-entropy maximally mixed state. We propose the Quantum Trajectories method to resolve this discrepancy by incorporating discrete dissipation events, providing a thermodynamically consistent semi-classical framework. To demonstrate the scalability of our approach, we extend the simulation to a 4-qubit register, showing that the Quantum Trajectories method remains numerically robust and thermodynamically consistent as the Hilbert space dimension increases. Furthermore, we perform a magnetic field optimization analysis, identifying an operational “sweet spot” within the 0.1–0.5 T range that optimally balances the trade-offs between relaxation and dephasing.
This work presents a systematic numerical study of the dissipative Jaynes-Cummings model, consisting of a two-level system (qubit) coupled to a truncated harmonic oscillator, both subject to Markovian dissipation. The model is standard in quantum optics and open quantum systems. The master equation is solved using the Lindblad formalism with BDF integration. The study focuses on two standard observables: the qubit excited-state population P_exc(t) and the qubit Bloch vector length |r(t)|. A three-dimensional parameter scan is performed over the coupling g, the qubit dephasing rate gamma_phi, and the oscillator relaxation rate gamma_a, giving 216 cells in total. The parameters used are omega_0 = 6 Hz, omega_1 = 40 Hz, giving a detuning delta = 34 Hz, and thermal occupation n_th = 0.05. MAIN FINDINGS: The single-exponential description of the excited-state population is valid only at intermediate coupling (g approximately 4 to 8 Hz). Outside this region, the dynamics exhibits a multi-timescale structure. The decay time T is non-monotonic in g, with a minimum at g approximately 7 Hz. The location of the minimum depends only weakly on gamma_a, following a power law with exponent 0.127. At strong coupling (g greater than 15 Hz), a two-exponential model is strongly preferred by the Akaike Information Criterion in 43 out of 45 cells. The two timescales are separated by a factor of approximately 150. The fast timescale T_1 is best approximated by the Purcell formula (median ratio of numerical to theoretical value 0.68). The Fermi golden rule overestimates the decay rate by a factor of approximately 4.5. Neither the dressed-state correction nor the Bloch-Redfield calculation improves on the Purcell formula. The Bloch vector length does not follow any simple functional form (single exponential, stretched exponential, power law, or double exponential). All models have mean R-squared in the range 0.31 to 0.36. Its time derivative is, however, almost perfectly correlated with that of the population (mean correlation 0.91). The results are converged with respect to the Fock-space truncation at N_0 = 12, with identical observables for N_0 between 12 and 20. SCOPE: This is a purely numerical study of a well-defined quantum-optical model. It contains no empirical data, no claims about biological or cognitive systems, and no speculative ontology. The model, the numerical method, and the observables are standard. The results include several negative findings (the failure of perturbative formulas, the lack of a simple functional form for the Bloch vector) which are reported honestly and which identify the regime where non-perturbative methods are required. The purpose of this release is to provide reproducible numerical data and a benchmark for future analytical work on the dissipative Jaynes-Cummings model in the strong-coupling regime. CONTENTS: The LaTeX technical note (approximately 20 pages), the Python scripts for the numerical simulations, and the CSV files with the fit results, regime classification, and theoretical comparison. REFERENCES: E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).G. Lindblad, Commun. Math. Phys. 48, 119 (1976).H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press (2002).C. W. Gardiner and P. Zoller, Quantum Noise, 3rd ed., Springer (2004).E. M. Purcell, Phys. Rev. 69, 681 (1946).C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions, Wiley (1992).W. P. Schleich, Quantum Optics in Phase Space, Wiley-VCH (2001).
Abstract Elementary quantum mechanics proposes that a closed physical system consistently evolves in a reversible manner. However, control and readout necessitate the coupling of the quantum system to the external environment, subjecting it to relaxation and decoherence. Consequently, system-environment interactions are indispensable for simulating physically significant theories. A broad spectrum of physical systems in condensed-matter and high-energy physics, vibrational spectroscopy, and circuit and cavity QED necessitates the incorporation of bosonic degrees of freedom, such as phonons, photons, and gluons, into optimized fermion algorithms for near-future quantum simulations. In particular, when a quantum system is surrounded by an external environment, its basic physics can usually be simplified to a spin or fermionic system interacting with bosonic modes. Nevertheless, troublesome factors such as the magnitude of the bosonic degrees of freedom typically complicate the direct quantum simulation of these interacting models, necessitating the consideration of a comprehensive plan. This strategy should specifically include a suitable fermion/boson-to-qubit mapping scheme to encode sufficiently large yet manageable bosonic modes, and a method for truncating and/or downfolding the Hamiltonian to the defined subspace for performing an approximate but highly accurate simulation, guided by rigorous error analysis. In this pedagogical tutorial review, we aim to provide such an exhaustive strategy, focusing on encoding and simulating certain bosonic-related model Hamiltonians, inclusive of their static properties and time evolutions. Specifically, we emphasize two aspects: (1) the discussion of recently developed quantum algorithms for these interacting models and the construction of effective Hamiltonians, and (2) a detailed analysis regarding a tightened error bound for truncating the bosonic modes for a class of fermion-boson interacting Hamiltonians.
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.