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
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
═══════════════════════════════════════════════════════════════ 📦 VERSION 1 (Ring Topology, IBM Hardware) — ARCHIVED ═══════════════════════════════════════════════════════════════ This OSF package constitutes Version 1 of the TCR experimental record. No additional data or analyses will be added to this registration. USPTO Provisional Patent: 63/960,327 (Filed January 14, 2026) ═══════════════════════════════════════════════════════════════ This project investigates whether optimal continuous gate parameters in quantum circuits are determined by the topological structure of the circuit’s interaction graph, rather than by empirical tuning alone. We study a family of ring-entangled quantum circuits (TICE architecture) implemented on real IBM Quantum hardware and test the hypothesis that certain cyclotomic angles (e.g., sin(π/11), sin(π/9)) produce systematically improved performance compared to a nearby empirically derived baseline parameter (λ_Q ≈ 0.341635). To rigorously control for temporal drift, hardware calibration variation, and compilation artifacts, we employ a preregistered ABBA experimental design, in which baseline (A) and candidate (B) circuits are interleaved in a balanced sequence (A→B→B→A) across multiple blocks, backends, and measurement bases. All circuits are executed with fixed qubit mappings, fixed transpiler seeds, and identical compilation constraints. Primary outcomes are evaluated using measurement distribution purity (MDP = Σ p²), with secondary analyses including alternative measurement bases (X vs Z) and paired statistical tests. All raw job IDs, measurement counts, circuit definitions, and analysis scripts are preserved to enable full reproducibility. This OSF project serves as the preregistered confirmatory record for testing an architecture-dependent cyclotomic resonance hypothesis in quantum circuit control. Exploratory results motivating this preregistration are clearly distinguished from confirmatory analyses conducted under the ABBA protocol
We report the discovery of Topological Cyclotomic Resonance (TCR), a phenomenon where quantum circuits on ring topologies exhibit optimal fidelity at a rotation parameter λ* = sin(π/11). Using IBM Quantum hardware (ibm_fez, ibm_torino) with 960,000 total shots and rigorous ABBA drift-cancellation protocols, we observe the predicted resonance with 8.4σ significance (p < 10⁻¹⁶). The constant generalizes to λ*_V = sin(π/(2V+1)) for V-qubit rings, connecting quantum computing to cyclotomic field theory. All data, code, and preregistration documents are publicly available.
GadIR artifact evaluation This self-contained directory reproduces Figures 10--15, 17, and 18(d) from the packaged Hamiltonians and generated random instances. It contains one GadIR frontend, four architecture backends, the two analysis workflows, and the baseline code used by the experiments. Full reproduction regenerates the result tables from the raw benchmarks. The bundled Figure 15 table supports plot-only validation and is overwritten by reproduce. Repository: https://github.com/xiyurain/GadIR Archive: https://doi.org/10.5281/zenodo.21550065 Requirements Use a machine with Bash, Git, Conda, a C/C++ toolchain, and stable Rust/Cargo. Intel, AMD, and Apple CPUs are supported. The experiments are CPU-only; at least 16 CPU cores, 32 GB RAM, and 20 GB of free disk are recommended. No GPU or quantum hardware is required. Network access is needed only while installing the environments. Install Miniconda (or Anaconda), Git, and the host compiler first. On Ubuntu/Debian, the host packages can be installed with: sudo apt-get update sudo apt-get install -y build-essential curl git Install Rust with rustup: curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh source "$HOME/.cargo/env" conda --version git --version rustc --version cargo --version Installation Clone the public repository (or unpack the Zenodo archive), enter this directory, and run the installation script: git clone git@github.com:xiyurain/GadIR.git cd GadIR/GadIR_AE ./prepare.sh prepare.sh creates three pinned environments under .envs/: analysis: Python 3.10, Qiskit 1.4.3, Qiskit Aer 0.17.1, PyZX 0.9.0, NumPy, pandas, SciPy, matplotlib, Stim/sinter 1.15.0, PyMatching 2.3.0, TQEC, GraphiQ 0.1.1, and Jupyter Notebook; quclear: Python 3.10 and Qiskit 1.1.1. 2qan: Python 3.9 and Qiskit Terra 0.20.2 (Qiskit 0.36.2). The script also builds and installs the packaged Rustiq Python extension into the analysis environment and installs Tweedledum 1.1.1 without build isolation before Qiskit Terra 0.20.2 in the 2QAN environment. TQEC and GraphiQ are installed at the exact revisions recorded in environments/analysis.yml. GraphiQ is retained for compatibility with the submitted installation check and is installed from the bundled wheel built at the recorded revision without its obsolete Qiskit 0.38 dependency; the Figure 15 workflow uses the packaged GSSynth backend. Manual environment activation is unnecessary. An installation can be checked with: ./.envs/analysis/bin/python -c "import qiskit, pyzx, rustiq, stim, sinter, pymatching, tqec, graphiq" ./.envs/quclear/bin/python -c "import qiskit" ./.envs/2qan/bin/python -c "import qiskit" If SSH access to GitHub is unavailable, download the Zenodo archive instead of cloning. The pinned TQEC revision still requires network access during prepare.sh. Running the artifact All commands are run from GadIR_AE/: ./run.sh smoke ./run.sh reproduce ./run.sh plot smoke runs one small input for each architecture backend and reduced-size Figure 17/18(d) analyses. reproduce compiles all selected benchmarks, writes fresh tables under results/, and draws all eight figures. plot only redraws from the tables already generated under results/. To generate all paper figures from completed AE results, use the provided plot-only notebook: ./.envs/analysis/bin/jupyter notebook generate_all_figures.ipynb The notebook draws Figures 10--15, 17, and 18(d) into output/; run ./run.sh reproduce first. The submitted artifact appendix refers to Figure 18(c) in this sentence. This is a labeling typo: the included analysis and notebook reproduce Figure 18(d). The workflows run in this order: superconducting, neutral atom, FTQC, MBQC, and analysis. Full reproduction is intentionally long: FTQC sampling and all 84 Figure 15 compiler jobs can take hours to days. smoke also executes real compiler/simulator paths and can take tens of minutes. The expected figure files are: output/figure10.pdf output/figure10_full_range.pdf output/figure11.pdf output/figure11_full_range.pdf output/figure12.pdf output/figure13.pdf output/figure14.pdf output/figure15.pdf output/figure17.pdf output/figure18d.pdf Figure 17 generates 1000 random instances at each term count with fixed seed 7. Figure 18(d) evolves the packaged Hamiltonians with four product-formula steps at times 0.4, 0.8, and 1.0, then reports the maximum bipartite entropy over every MPS prefix cut. Because the packaged structural Hamiltonians contain Pauli strings without numeric coefficients, every input term uses coefficient Open markers are the dimension-derived bound S_MPS <= floor(n_qubits / 2). The tables are written to results/analysis/figure17.csv and results/analysis/figure18d.csv. Layout benchmarks/ source Hamiltonians hardware/ superconducting and neutral-atom architectures src/gadir_frontend/ architecture-independent GadIR frontend src/superconducting/ Figures 10--11 backend src/neutral_atom/ Figure 12 backend src/ftqc/ Figures 13--14 backend src/mbqc/ Figure 15 backend src/analysis/ Figures 17 and 18(d) workflows baselines/ baseline implementations or dependency records environments/ pinned Conda specifications results/ generated tables and intermediate circuits output/ generated PDFs GadIR licensing is not declared by a new license file in this AE directory. Redistributed third-party code retains its upstream notice in baselines/<method>/LICENSE; TQEC is an installed dependency pinned in environments/analysis.yml.
This report records and interprets the second real-device execution of the CNC fork experiment in the certifiable T = 2 “binary-clock” design (runner v3), including a software-forensics correction: an obsolete analysis JSON incorrectly reported ν = 1.0 even though all 2-bit clock patterns are legal by construction in T = 2. It also specifies a final replication run (“Test 3”) intended to be maximally robust against the dominant remaining failure mode (near-threshold readout invasiveness on ibm_fez). A conclusive outcome of Test 3 is meaningful regardless of direction, because (as preregistered) the runner only emits a conclusive label after certifying overlap and bounding nuisance effects (mismatch and readout invasiveness). Run metadata (from locked runner output): backend: ibm_fez output created (UTC): 2026-01-10T19:03:16.074947+00:00 IBM Runtime job id: d5ha332gim5s73ahnueg physical layout (C1,C2,S): [1, 2, 3] protocol blocks: ε ∈ {0.40, 0.20} (primary block ε = 0.40) Qiskit versions (recorded by harness): qiskit 2.2.3, qiskit-ibm-runtime 0.43.1 Key certified outputs (primary block, ε = 0.40): D̄ = 0.381793 ν = 0.016503 (≤ ν_max = 0.020) ε_inv = 0.047647 (≤ ε_inv,max = 0.050) δ′ = 0.313209 decision (locked runner): reject hard CNC The Test 3 OSF preregistration is complete and time‑stamped, but remains embargoed until execution; the public link will be added here immediately after the embargo is lifted. Raw run artefacts and outputs to be archived as a separate Zenodo Dataset record by the hardware executor (Morgan Cameron). This report is a forensic note and replication/protocol document.
Fresh IBM Fez platform-lock pre-registration for executing the (Z_2)^3 prediction under the Stage 1c topological gate (DOI 10.5281/zenodo.20404635). Locks: backend ibm_fez, qubits (15, 2, 23), calibration snapshot of 2026-05-27T02:18:29Z (SHA-256 3f69b12d793b7c0cfc1f7cb343b3a0b8c40f04ae3a6239f7e3edd48192dadd1d), analysis script SHA-256 69c5e040c96f8b0f3fd50bc5014a63b4d461129d2e2affb0297f54887d871534, execution parameters (16,000 shots per circuit, 36 circuits total, bootstrap seed 20260526), and outcome reporting commitment.The Stage 1c gate authority (R_gap = (τ - σ_2) / std(σ_2^bootstrap) ≥ 3.0 with m̂_0 = 1) replaces Stage 1b §6.2's union-bound mundane gate. All other Stage 1b provisions (predictions 7/8 vs 8/9, operational f̂ definition, statistical-power requirement, Bayes-factor decision rule) remain in force.This Stage 2c is distinct from Stage 2 (DOI 10.5281/zenodo.20360347) which locked qubits (15, 25, 56) against a 2026-05-23 calibration epoch and yielded the INDETERMINATE Stage 3 outcome (DOI 10.5281/zenodo.20360386) under the old gate. The present Stage 2c lock targets a fresh calibration epoch and a freshly-quality-ranked qubit triple, and the certified execution under this lock will produce a Stage 3c result-of-execution report.Files in this deposit:uct_prediction_2_pregist_stage2c_fez.md — platform pre-registration document (SHA-256: f37062bc98e9429ffe6e92fea135ad6ff729a56c00606337747872d0a4b00dc9, 10320 bytes)ibm_fez_cal_snapshot_2026-05-26.json — locked Fez calibration snapshot (SHA-256: 3f69b12d793b7c0cfc1f7cb343b3a0b8c40f04ae3a6239f7e3edd48192dadd1d, 19485 bytes)Calibration validity window: Fez job to be submitted within 24 hours of snapshot time (by 2026-05-28T02:18:29Z). Beyond that window this Stage 2c is invalidated and a fresh Stage 2 must be deposited.Lock chain:Stage 1: 10.5281/zenodo.20360004Stage 1b: 10.5281/zenodo.20360259Stage 1c: 10.5281/zenodo.20404635 (gate authority)Stage 2: 10.5281/zenodo.20360347 (historical — different qubits and cal epoch)Stage 3: 10.5281/zenodo.20360386 (INDETERMINATE under old gate — preserved as historical record)