Title: Spectral Diagnostics of Superconducting Quantum Circuits via the Witten Laplacian on Configuration Space Authors: Frédéric David Blum (Catalyst AI); Claude (Anthropic) continue work : https://zenodo.org/records/18776120 email : dvid75113@gmail.com We construct the Witten Laplacian on the configuration torus T² of coupled transmon qubits and compute it for 772 qubit pairs across six IBM Quantum processors (Sherbrooke, Brisbane, Osaka, Kawasaki, Kyiv, Quebec — real calibration snapshots via Qiskit FakeProvider). Three principal findings: 1. Spectral Universality (CV = 1.4%) — Rescaled eigenvalue ratios collapse across all processors with sub-percent coefficient of variation. The Witten spectrum possesses a universal structure independent of fabrication and noise environment. 2. Orthogonal Information Content (r = 0.205, p < 10⁻³) — After removing all variance explained by 10 raw calibration parameters, Witten spectral features still predict gate-length residuals with r = 0.205. The spectral transform extracts information invisible to standard characterization. In a rigorous 5-fold cross-validated benchmark, Witten features (R² = 0.134) outperform raw features (R² = 0.097), PCA, and polynomial Koopman lifting. 3. Inter-Processor Coherence Sensing (ρ = −0.76) — The relative Witten index ν_ij correlates with T₁ relaxation-time differences between processors at Spearman ρ = −0.76, sensing intrinsic hardware coherence rather than calibrated gate parameters. Additional finding: A semiclassical phase boundary at ℏ_eff ≈ 0.42 where Z(β) diverges, consistent with a phase transition in the Witten Laplacian observable on real IBM Kawasaki hardware. This deposit includes the theoretical framework (CST v13/v14), the PRX Quantum manuscript draft, all analysis code (reproducible in ~60 seconds with pip install qiskit-ibm-runtime), and complete numerical results. Code repository: https://github.com/davidangularme/cst Keywords: Witten Laplacian, superconducting qubits, transmon, spectral universality, quantum computing, IBM Quantum, configuration space, spectral diagnostics, heat kernel, decoherence License: CC BY 4.0 Files to upload: prx_quantum_draft.docx (manuscript) Configuration_Space_Temporality_v13.pdf Configuration_Space_Temporality_v14.pdf witten_transmon_paper.pdf nu_ij_witten.py phase2_benchmark.py phase2_results.json nu_ij_results.json spectral_collapse.png phase2_results.png Response to Methodological Review Document: Response to Methodological Review — Algebraic Coherence, Discretization Artifacts, and Interventional Diagnostics Authors: Frédéric David Blum, Claude (Anthropic), Catalyst AI Date: February 26, 2026 Target manuscript: Spectral Diagnostics of Superconducting Quantum Circuits via the Witten Laplacian on Configuration Space (Draft PRX Quantum) Summary This document responds to a structured methodological review identifying four revision requirements (R1–R4) for the PRX Quantum draft. The review's central thesis — that a discretization producing λ₀ < 0 constitutes a category error, not a numerical imperfection — is accepted in full. The companion paper Spectral Fidelity of the Discrete Witten Laplacian on S¹ (v3) independently establishes the diagnosis (96/96 violation rate under standard stencil) and the remedy (factored dW†dW / FEEC schemes). Response to Revision Requirements Req. Reviewer Demand Response Status R1 λ₀ ≥ 0 as identity test Adopt factored scheme as primary pipeline COMMITTED R2 Inter-scheme replication Full 772-pair recomputation; 2×2 outcome matrix COMMITTED R3 Suspend Z(β) interpretation All claims conditional until λ₀ ≥ 0 guaranteed ACCEPTED R4 Break E_{J,c} circularity Phase IV fingerprinting elevated; sensitivity sweep ACCEPTED The 2×2 Outcome Matrix The recomputation (R2) tests spectral universality (U) and orthogonal information content (O) independently: (O) r ≈ 0.205 SURVIVES (O) r ≈ 0.205 FAILS (U) CV ≈ 0.014 SURVIVES Quadrant A: Full validation. Microscope works. Quadrant B: Universal structure, no ML surplus. (U) CV ≈ 0.014 FAILS Quadrant C: No universality, but useful tool. Quadrant D: Full falsification of PRX claims. We commit to publishing whichever quadrant materializes. Post-Review Dialogue Refinements "Indécidable" → "Non tranché": The Z(β) interpretation is not fundamentally undecidable — it is unresolved pending recomputation under a structure-preserving scheme. Separate (U) from (O): Spectral universality and orthogonal information content are vulnerable to different artifact mechanisms and must be tested independently. Files response_to_methodological_review_prx_quantum.docx — Full formatted response document RESPONSE_REVIEW.md — This summary Related PRX Quantum draft: DOI 10.5281/zenodo.18779189 CST v14: DOI 10.5281/zenodo.18776120 Code: github.com/davidangularme/sdsq
Title: Spectral Diagnostics of Superconducting Quantum Circuits via the Witten Laplacian on Configuration Space Authors: Frédéric David Blum (Catalyst AI); Claude (Anthropic) continue work : https://zenodo.org/records/18776120 email : dvid75113@gmail.com We construct the Witten Laplacian on the configuration torus T² of coupled transmon qubits and compute it for 772 qubit pairs across six IBM Quantum processors (Sherbrooke, Brisbane, Osaka, Kawasaki, Kyiv, Quebec — real calibration snapshots via Qiskit FakeProvider). Three principal findings: 1. Spectral Universality (CV = 1.4%) — Rescaled eigenvalue ratios collapse across all processors with sub-percent coefficient of variation. The Witten spectrum possesses a universal structure independent of fabrication and noise environment. 2. Orthogonal Information Content (r = 0.205, p < 10⁻³) — After removing all variance explained by 10 raw calibration parameters, Witten spectral features still predict gate-length residuals with r = 0.205. The spectral transform extracts information invisible to standard characterization. In a rigorous 5-fold cross-validated benchmark, Witten features (R² = 0.134) outperform raw features (R² = 0.097), PCA, and polynomial Koopman lifting. 3. Inter-Processor Coherence Sensing (ρ = −0.76) — The relative Witten index ν_ij correlates with T₁ relaxation-time differences between processors at Spearman ρ = −0.76, sensing intrinsic hardware coherence rather than calibrated gate parameters. Additional finding: A semiclassical phase boundary at ℏ_eff ≈ 0.42 where Z(β) diverges, consistent with a phase transition in the Witten Laplacian observable on real IBM Kawasaki hardware. This deposit includes the theoretical framework (CST v13/v14), the PRX Quantum manuscript draft, all analysis code (reproducible in ~60 seconds with pip install qiskit-ibm-runtime), and complete numerical results. Code repository: https://github.com/davidangularme/cst Keywords: Witten Laplacian, superconducting qubits, transmon, spectral universality, quantum computing, IBM Quantum, configuration space, spectral diagnostics, heat kernel, decoherence License: CC BY 4.0 Files to upload: prx_quantum_draft.docx (manuscript) Configuration_Space_Temporality_v13.pdf Configuration_Space_Temporality_v14.pdf witten_transmon_paper.pdf nu_ij_witten.py phase2_benchmark.py phase2_results.json nu_ij_results.json spectral_collapse.png phase2_results.png Response to Methodological Review Document: Response to Methodological Review — Algebraic Coherence, Discretization Artifacts, and Interventional Diagnostics Authors: Frédéric David Blum, Claude (Anthropic), Catalyst AI Date: February 26, 2026 Target manuscript: Spectral Diagnostics of Superconducting Quantum Circuits via the Witten Laplacian on Configuration Space (Draft PRX Quantum) Summary This document responds to a structured methodological review identifying four revision requirements (R1–R4) for the PRX Quantum draft. The review's central thesis — that a discretization producing λ₀ < 0 constitutes a category error, not a numerical imperfection — is accepted in full. The companion paper Spectral Fidelity of the Discrete Witten Laplacian on S¹ (v3) independently establishes the diagnosis (96/96 violation rate under standard stencil) and the remedy (factored dW†dW / FEEC schemes). Response to Revision Requirements Req. Reviewer Demand Response Status R1 λ₀ ≥ 0 as identity test Adopt factored scheme as primary pipeline COMMITTED R2 Inter-scheme replication Full 772-pair recomputation; 2×2 outcome matrix COMMITTED R3 Suspend Z(β) interpretation All claims conditional until λ₀ ≥ 0 guaranteed ACCEPTED R4 Break E_{J,c} circularity Phase IV fingerprinting elevated; sensitivity sweep ACCEPTED The 2×2 Outcome Matrix The recomputation (R2) tests spectral universality (U) and orthogonal information content (O) independently: (O) r ≈ 0.205 SURVIVES (O) r ≈ 0.205 FAILS (U) CV ≈ 0.014 SURVIVES Quadrant A: Full validation. Microscope works. Quadrant B: Universal structure, no ML surplus. (U) CV ≈ 0.014 FAILS Quadrant C: No universality, but useful tool. Quadrant D: Full falsification of PRX claims. We commit to publishing whichever quadrant materializes. Post-Review Dialogue Refinements "Indécidable" → "Non tranché": The Z(β) interpretation is not fundamentally undecidable — it is unresolved pending recomputation under a structure-preserving scheme. Separate (U) from (O): Spectral universality and orthogonal information content are vulnerable to different artifact mechanisms and must be tested independently. Files response_to_methodological_review_prx_quantum.docx — Full formatted response document RESPONSE_REVIEW.md — This summary Related PRX Quantum draft: DOI 10.5281/zenodo.18779189 CST v14: DOI 10.5281/zenodo.18776120 Code: github.com/davidangularme/sdsq
Qubit layout selection determining which physical qubits a logical circuit occupies on a superconducting processor is fundamentally a noise-field sampling problem. On IBM Heron r1 and Heron r2 devices, two-qubit gate error varies by nearly one order of magnitude (7– $9\times $ ) across qubit pairs on the same chip, causing measured fidelity differences up to 0.903 from layout choice alone. We introduce the Gate Noise Sensitivity Index (GNSI), a calibration-weighted linear combination of per-qubit readout error and per-edge two-qubit gate error, derived analytically as a first-order approximation of circuit fidelity under independent, heterogeneous noise channels. For 12 backend–circuit combinations on three IBM processors (133-qubit Heron r1 and 156-qubit Heron r2), GNSI scores are computed for the full pool of 1,320 computationally enumerated candidate layouts; the top-ranked (GNSI-BEST) and bottom-ranked (GNSI-WORST) layouts are then executed on hardware. GNSI-BEST ranks first by score in all 12 instances (Hit@1 = 100% within the enumerated candidate pool) and consistently achieves higher measured fidelity than GNSI-WORST, with Spearman rank correlation ρ=0.926±0.016 and statistically significant fidelity separation in 9 of 12 paired tests. Initial hardware comparisons on ibm_fez ( n=5 ) show GNSI-BEST matching or exceeding SABRE-selected fidelity. We further identify a depth-dependent regime transition: gate-error heterogeneity appears to govern ranking in shallow circuits (depth ≤15 ), while qubit-specific T1 variation may dominate for deeper circuits (depth ≥20 ). The analytic regime boundary d∗(b) , computable from calibration data alone, shows agreement within ±2 depth layers across all three backends in initial comparisons; GNSI-Extended incorporating the decoherence term receives an initial hardware comparison on two circuits, with full validation left to future work. These results suggest that layout-dependent fidelity variation may be governed by a calibration-predictable noise field, with direct implications for compiler design and noise-adaptive quantum circuit execution.
We derive analytically that the optimal feedforward phase for ZZ-coupling correction in superconducting qubits is given by the argument of the first circular moment of the accumulated phase distribution: φ* = arctan(S/C), where C = ⟨cos φ⟩ and S = ⟨sin φ⟩. A negative second derivative proves this is always a maximum. We measure GPS = P_ff − P_ref on IBM Heron r2 processors (ibm_kingston, ibm_marrakesh; five qubit pairs) and IQM Garnet (Crystal 20). A robust empirical invariant is observed: π ν_ZZ τ* ≈ const ≈ 0.873 rad, confirmed across five independent IBM configurations (π ν_ZZ τ* = 0.873 ± 0.001 rad). A preliminary τ-scan on IQM Garnet shows a GPS sign reversal consistent with a zero-crossing near φ = 0.873 rad. The result establishes a robust empirical invariant within superconducting architectures, enabling feedforward calibration without full phase tomography. Related work:- EEDT Protocol: https://doi.org/10.5281/zenodo.19029431- Bell Decay Clock: https://doi.org/10.5281/zenodo.19367565- Software (Quantum-6502): https://doi.org/10.5281/zenodo.19160835
This deposit contains a reproducible replication package and raw results for a multi-topology hardware validation of Topological Cyclotomic Resonance (TCR) on IBM Quantum backends ibm_fez and ibm_torino. We test the closed-form parameter ruleλ*(V) = sin(π/(2V+1))across five circuit topologies (ring, star, mesh, tree, line) and three problem sizes (V=10, 15, 20), using an ABBA interleaved design for drift control. The package includes raw and summary JSON outputs, a SHA256 manifest, analysis tables, and code/configuration needed to reproduce the experiment (tokens are not included; IBM credentials are provided via environment variables).DOI: 10.5281/zenodo.18357071 | OSF: https://osf.io/xuebt/ | ORCID: https://orcid.org/0009-0007-7286-3373
Configuration Space Temporality — Complete Research Archive v33Corrections, a Resolution Law, and the foundations of CST among timeless formulations Frédéric David Blum · Catalyst AI Research · Haifa, Israel · DOI: 10.5281/zenodo.18859602 · October 2026Computations and drafting assisted by Claude (Anthropic). What is CST?Configuration Space Temporality (CST) is a framework in which time is not a background parameter: it emerges as the accumulated cost of energy-driven transitions between configurations of a physical system. Three axioms (configuration uniqueness, energy-driven transition, bounded transition rate) define a tensor of transition G on configuration space (the Bures metric on quantum configurations, with the Umegaki relative entropy as potential), a transport distance d_CST satisfying the Carlen–Maas axioms of a quantum Wasserstein distance, the Witten Laplacian H_W whose thermodynamic limit is a Lindblad generator, and the cascade number κ = ΔE·Δτ/(ħ ln 2). STATUS — October 2026Every claim in this archive that the Riemann Hypothesis has been proved, reduced to a single assumption, or approached through the Bost–Connes Hamiltonian, the Fisher–Rao action functional, the rigidity matrix or the confinement constant α is WITHDRAWN. The physical framework is kept, placed on its exact foundations, and given one law. What's new in v33 Corrections. A re-audit with every number recomputed found four errors. (i) The Fisher pole identity |I(s)|·|s−ρ|² = 1 holds at every simple zero of every analytic function, on or off the critical line; it is not a quantization condition and carries no information about RH. (ii) The rigidity matrix R has an exact zero eigenvalue (its rows sum to zero), so α = μ₁/μ₀ is undefined; the collinear configuration is a transverse maximum of the log-gas energy, not a minimum; and R is built from ordinates already on the line, so no property of R can be equivalent to RH. (iii) Exponential dominance fails: μ₁/μ₀ grows only from 10^6.4 (N = 45) to 10^7.8 (N = 200), α(N) → 0, and GUE, Poisson and evenly spaced control points give the same values as the zeros (the tiny eigenvalues come from the cosine basis, not from arithmetic). (iv) The Bost–Connes Hamiltonian has spectrum {log n}; Assumption A, Assumption B and the "zeros as resolvent poles" claim are withdrawn, and the CMP v25–v27 "complete proof chain" is withdrawn in full. Of 17 RH-related results: 3 hold as stated, 3 hold but are trivial or known, 1 is falsified numerically, 1 stays open (Li positivity, equivalent to RH), 9 are withdrawn. The full audit, with the status of every claim and the superseded files listed, is the document "CST/FDBC Archive v33 — Corrections and a Non-Circular Weil-Form Test". Foundations. CST is placed explicitly on the three established timeless formulations of physics: Jacobi geometry and Barbour's relational dynamics (G is a Jacobi metric, CST time is the Jacobi arc length, i.e. the Maupertuis action, and κ_cl = S₀/(ħ ln 2)); Wheeler–DeWitt and the Page–Wootters mechanism (time as clock correlation); and the thermal time of Connes–Rovelli (time as the modular flow of the state — the correct use of the KMS machinery in CST). These formulations are empirically equivalent to their timed counterparts; a new law must therefore live where state-based and timed descriptions differ. The Resolution Law (new). For a quantum trajectory ψ(t) = e^{−iHt/ħ}ψ of duration Δτ whose energy distribution is flat on a band of width Ω_E, the number of modes of the trajectory distinguishable at level ε isd_ε = Ω_E Δτ/h + (1/π²) ln(Ω_E Δτ/4ħ) · ln((1−ε)/ε) + o(ln c),and no mode beyond twice the Slepian parameter c = Ω_EΔτ/4ħ is distinguishable above e^{−1.5c}. The leading term is the Landau count (the action budget in units of h), of the same kind as the Margolus–Levitin and Mandelstam–Tamm speed limits and identifying the cascade number (κ = (2π/ln 2) × Landau count); the second term is a universal logarithmic "soft horizon" (Landau–Widom plunge); the cutoff is a rigorous non-asymptotic bound. The law is proved as a theorem of time–band limiting — the Gram operator of a quantum trajectory is Slepian's time–band limiting operator with the energy distribution as symbol — with two-sided bounds for bounded energy densities, verified numerically (prolate eigenvalue counts at c = 10, 30, 100), and given a falsification protocol on a many-level system (cavity mode or quantum simulator) through the survival amplitude. It replaces the earlier prediction P2 of a sharp reversibility threshold at κ = 1, and it is the first prediction of CST stated with a theorem behind it. A tested negative. The conjecture that the cascade number is tied to Barbour–Koslowski–Mercati shape complexity by a universal power law was tested on E = 0 three-body solutions: the Janus structure is reproduced, but the exponent is not universal (0.8–1.9); the CST clock is the ephemeris time of the bound pair. Recorded so that it is not tried again. Companion workScale-Resolved Weil Positivity (preprint, DOI 10.5281/zenodo.23229271; code: github.com/davidangularme/scale-resolved-weil-positivity): the positive mathematics that came out of the audit — a prime-side study of the truncated Weil form, with certified positivity on the window [1/2, 2] (margin enclosed between 1.38×10⁻¹³ and 7.6×10⁻¹³; an independent certification, at L = log 2, of a theorem of X. Zhu, arXiv:2608.24827, valid for L ≤ 0.8), certified rigidity of the prime data, the detection and reconstruction laws, and the structure of the minimiser as Riemann's Φ times a window. Nothing there bears on RH beyond the finite scales treated. Validated and untestedValidated: the H_W spectral diagnostic on 768 qubit pairs of six IBM Eagle r3 processors, r = 0.365 after projecting out calibration parameters (a diagnostic correlation; it does not test the Resolution Law). Untested: P6 (no dark-matter particle), P9 (gravity as collective mode), P16, and the Resolution Law itself. Withdrawn: P2 (cascade criticality at κ = 1), IG-P1 to IG-P5. Files added in v33CST_v33_Corrections_and_a_Resolution_Law.pdf (the single document of this version) · cst-fdbc-archive-v33-corrections.pdf (the full audit) · v33_cst_code.zip (prolate.py, lw_check.py, janus.py and results). Earlier files remain for the record; those superseded are listed in the audit document: CMP_Paper_FDBC_v25–v27, FDBC_v2_CMP_Submission, FDBC_v2_Complete_Proof_Chain, FDBC_v2_Proof_Chain_CORRECTED, FDBC_v2_Assumption_B_PROVED (both), FDBC_v2_Spectral_Gap_PROVED, FDBC_v2_No_Gap_Final, Information_Geometric_Confinement_Riemann_Zeros_Blum_2026, blum-claude-weil-minimiser-2026 (its table stands, its conclusions do not). The submission CIMP-D-26-00460 is being withdrawn. Previous versionsv33 (current): corrections and withdrawals; foundations; the Resolution Law; tested negative on complexity. v32: information-geometric confinement (withdrawn in v33). v31: exponential isolation of the Weil minimiser (table stands, conclusions withdrawn). v30: Fourier-side ΨDO identification. v29.1–v25: see the archive. CitationBlum, F. D. (2026). Configuration Space Temporality: Complete Research Archive v33 — Corrections, a Resolution Law, and the foundations of CST among timeless formulations. Zenodo. https://doi.org/10.5281/zenodo.18859602 Keywordsemergent time · configuration space temporality · Jacobi metric · relational dynamics · Page–Wootters · thermal time · quantum optimal transport · Bures metric · Witten Laplacian · cascade number · quantum speed limit · Margolus–Levitin · time–band limiting · prolate spheroidal functions · Landau–Widom · resolution law · transmon qubits · Weil positivity · corrections · retraction
Abstract The development of new superconducting circuits and the improvement of existing ones rely on the accurate modeling of spectral properties which are key to achieving the needed advances in qubit performance. Systematic circuit analysis at the lumped-element level, starting from a circuit network and culminating in a Hamiltonian appropriately describing the quantum properties of the circuit, is a well-established procedure, yet cumbersome to carry out manually for larger circuits. We present work utilizing symbolic computer algebra and numerical diagonalization routines versatile enough to tackle a variety of circuits. Results from this work are accessible through a newly released module of the scqubits package.
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