Christoffel-Symbol-Encoded Geodesics on Quantum Hardware: Toward an Experimental Platform for Curvature-Quantum Interplay
Hemanth Gudaparthi, Yacine Merdjemak
Overview This Zenodo repository contains the research artifacts associated with the manuscript: “Christoffel-Symbol-Encoded Geodesics on Quantum Hardware: Toward an Experimental Platform for Curvature-Quantum Interplay” The repository accompanies the APS journal submission and contains the submission manuscript, computational notebook, experimental run notes, quantum circuit files, an interactive HTML module, and handwritten theoretical and conceptual notes developed during the research. These materials are provided to support transparency, reproducibility, verification, and further exploration of the proposed framework for encoding Christoffel-symbol information into quantum circuits and studying geodesic dynamics on quantum hardware. Note: This archive contains the APS submission draft and research-development artifacts. Some files are working notes, intermediate materials, or experimental documentation and should not be interpreted as part of the final published version of the manuscript. Repository Contents 1. APS Submission Draft The Submission Draft_Final folder contains the manuscript and supporting notes associated with the APS journal submission. The primary manuscript is: ChristoffelSymbolEncoding_Final_submission_draft.pdf This PDF contains the manuscript prepared for submission to the APS journal. The folder also contains supporting documentation associated with the reported experimental results. 2. Computational Notebook The repository contains: Geodesic.ipynb This Jupyter Notebook contains computational material associated with the proposed framework and the analysis of the experimental results. The notebook includes calculations and analysis used during the development and evaluation of the Christoffel-symbol-encoded geodesic circuits. The notebook represents a research and submission working artifact and is included to document the computational workflow and analysis. The notebook can be opened using: Jupyter Notebook JupyterLab Google Colab Other compatible Jupyter environments 3. Interactive HTML Module The HTML_file folder contains an interactive HTML implementation of the setup described in the manuscript. The HTML module is designed so that users can download it and interact with or modify the setup locally without requiring an account or login. Using the HTML module Download the HTML_file folder from this repository. Open the included index.html file in a modern web browser. Explore the interactive setup. Modify the available parameters/settings directly in the interactive module. Use the modified configuration to explore how changes affect the corresponding setup. No login or external account is required to use or modify the locally downloaded HTML module. The HTML artifact is provided as an accessible, interactive research tool intended to make the experimental setup easier to inspect and explore. Note: The HTML module is a local interactive artifact. Its behavior may depend on the browser and the capabilities implemented in the provided HTML/JavaScript files. 4. QASM Quantum Circuits The repository contains the following OpenQASM circuit files: geodesic_.qasm geodesic_schwarzschild.qasm geodesic-flat.qasm These files contain the quantum circuits used to implement and investigate the proposed geodesic encoding. The QASM files can be imported into compatible IBM Quantum/Qiskit environments, including the IBM Quantum Composer where supported, for inspection and execution. Researchers can use these files to: Inspect the circuit construction. Examine the gate-level implementation. Reproduce the circuit setup. Modify the circuits for additional experiments. Execute the circuits on compatible quantum simulators. Execute the circuits on available IBM quantum hardware. Hardware execution considerations The circuits were designed for execution on real quantum hardware. Results from subsequent executions may not be numerically identical to the results reported in the manuscript. This is expected for experiments performed on noisy quantum hardware because measured results can depend on: Hardware calibration Qubit coherence and connectivity Gate and readout errors Device noise Compilation/transpilation Backend configuration Execution date and time Number of measurement shots Therefore, the QASM files are intended to provide the reproducible circuit and experimental procedure, while acknowledging the time-dependent nature of physical quantum hardware. 5. Handwritten Theoretical and Conceptual Notes The Handwritten Theory Notes folder contains handwritten material documenting the conceptual and theoretical development of the research. The materials include: Initial theoretical ideas Derivations and calculations Circuit-design sketches Christoffel-symbol encoding concepts Spacetime and geodesic illustrations Experimental setup notes Run-specific observations Additional conceptual development related to the curvature–quantum interplay They are included to document the development of the underlying research idea and provide additional context for the methodology presented in the manuscript. These materials should be considered research-development notes rather than polished manuscript material. Experimental Run Documentation The repository includes documentation of the experimental runs used in developing and evaluating the proposed framework. The experimental artifacts include: Quantum circuit files in QASM format Computational analysis in the Jupyter notebook Run-specific written observations Handwritten experimental notes Interactive visualization and exploration of the proposed setup The run notes are included to provide additional context concerning the observed behavior of the circuits on quantum hardware. Because the experiments involve real quantum hardware, variations between executions are expected. The purpose of providing the circuit files and associated documentation is therefore to enable researchers to reproduce the experimental setup, circuit construction, and methodology, rather than to imply that every hardware execution will produce exactly identical measurement statistics. Reproducibility The artifacts in this repository are intended to facilitate independent examination and reproduction of the work. The principal reproducibility components are: Artifact Purpose Geodesic.ipynb Computational calculations and analysis .qasm files Gate-level quantum circuit implementations index.html Interactive and locally modifiable representation of the setup Submission PDF Scientific description of the proposed methodology and experiments Results notes Documentation of experimental observations Handwritten notes Conceptual and theoretical development of the approach For quantum-hardware experiments, reproducibility should be understood in the context of noisy and time-varying physical hardware. Re-execution of the same circuit can result in different measurement statistics even when the circuit parameters and experimental protocol are unchanged. Accordingly, the repository provides the information necessary to reproduce the circuit construction and experimental methodology, while hardware-dependent numerical variations should be expected. File Organization Christoffel_Symbol_Encoding_Submission/ │ ├── Geodesic.ipynb │ ├── geodesic_.qasm ├── geodesic_schwarzschild.qasm ├── geodesic-flat.qasm │ ├── HTML_file/ │ └── index.html │ ├── Handwritten Theory Notes/ │ ├── Run1.HEIC │ ├── Run2.HEIC │ ├── Page1.HEIC │ ├── Page2.HEIC │ ├── Page3.HEIC │ ├── Fig1a) Chris_Symbol_encoding.drawio.png │ └── fig2_spacetime_geodesic.png │ └── Submission Draft_Final/ ├── ChristoffelSymbolEncoding_Final_submission_draft.pdf └── Copy of Notes-on-results.docx Authors Dr. Hemanth Gudaparthi, Dr. Yacine Merdjemak The handwritten theoretical notes, conceptual sketches, and research-development materials included in this archive were prepared by Dr. Hemanth Gudaparthi during the development of the work. He also implemented the quantum circuit, applied the error-mitigation protocol, analyzed the measurement results, and wrote the manuscript Dr. Yacine Merdjemak has provided input on the reasoning, the approach, and the quantum circuit implementation, reviewed the manuscript, and commented on the theoretical framework and result interpretation. Associated Manuscript Christoffel-Symbol-Encoded Geodesics on Quantum Hardware: Toward an Experimental Platform for Curvature-Quantum Interplay The manuscript included in this repository represents the APS journal submission draft associated with these research artifacts. Please refer to the final published version of the manuscript for the authoritative bibliographic record once publication is complete. Citation If you use the computational notebooks, QASM circuits, interactive HTML module, experimental notes, handwritten notes, or other materials from this repository, please cite the associated manuscript: Hemanth Gudaparthi, Yacine Merdjemak, Christoffel-Symbol-Encoded Geodesics on Quantum Hardware: Toward an Experimental Platform for Curvature-Quantum Interplay, 2026, https://doi.org/10.5281/zenodo.22162434 The citation should be updated to the final journal bibliographic information when the manuscript is published. Use of the Materials These materials are provided for research, educational, verification, and scholarly exploration. Users are encouraged to: Examine and modify the locally available HTML module. Inspect and modify the QASM circuits. Re-run the computational notebook. Reproduce the experimental circuit construction. Extend the framework to additional parameters, circuit depths, geometries, or quantum hardware platforms. Please cite the associated manuscript
•Aug 29, 2026•0 citations