This study validates the TCR formula λ*(V) = sin(π/(2V+1)) across five circuit topologies (ring, star, mesh, tree, line) and three qubit counts (V=10, 15, 20) using IBM Quantum hardware. We use ABBA interleaved blocks to control for temporal drift and compare TCR-optimized parameters against a baseline λ=0.3.
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
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.
═══════════════════════════════════════════════════════════════ 📦 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
Abstract Circuit topology—the pattern of two-qubit entangling gates—determines noise propagation paths in variational quantum circuits (VQCs). Using the normalized rank-displacement diagnostic D(ε) across 26 experiment configurations spanning five topologies and five CPTP noise types, plus 135 IBM ibm fez hardware circuits, we show that topology accounts for 48.9% of explainable D(0.05) variance under ω 2 decomposition (Cohen’s d = 2.66 between ring and star; permutation p = 7.1×10−12). The ranking hierarchy (star>grid≈linear>ring, where lower D indicates better ranking preservation) is invariant across the four nondepolarizing noise types (Kendall τ = 1.0 over four ranked lists, p = 0.017 by exact permutation test) but collapses under depolarizing noise. On IBM hardware, the qualitative ranking survives transpilation, though effect magnitude attenuates ∼ 10×. A Heisenberg-picture analytical model qualitatively predicts the τ (n, L) ranking from circuit structure alone (r = 0.645, p = 0.013; R2 = 0.35), providing a theoretical basis for topology-dependent noise sensitivity. We find that classical ML systems (MLP, XGBoost) achieve comparable D(0.05) values, showing that the τ -D functional form is consistent across classical and quantum computation, suggesting a shared noise-response structure. Practical design heuristics are provided
We report systematic experimental observation of coherent, topology-dependent inter-horizon correlations in thermofield double (TFD) states implemented on IBM quantum processors. Using a 100-qubit ladder geometry mapped onto the heavy-hex topology of ibm_fez (156 qubits, Heron r2 architecture), we demonstrate signal ratios R_fit spanning 1.2–202.7 across runs/seeds, with best single-seed R_fit = 23.93 (Run #11) and record multi-seed median R_fit = 102.7 (Run #2, 5 seeds, range 63.5–202.7), validated by pre-registered GO/NO-GO criteria across 14 experimental runs spanning January 24-30, 2026. Our experimental framework incorporates two rigorous anti-artifact controls (see Fig. 6-7): (1) SCRAMBLE control applies identical circuit depth with incorrect topology, destroying the signal (reduction factor > 10×); (2) ECHO control (Loschmidt reversal) applies the coupling layer twice, annihilating coherent contributions (reduction factor 8.6-50.5×, consistent with expected finite-size echo saturation for N~50 effective subsystems (see Gorin et al. [14] for saturation plateau theory)). Both controls maintain > 95% local fringe retention, confirming they do not trivially destroy coherence. A critical discovery emerged from our January 30, 2026 validation campaign (see Fig. 5): quantum processor calibration drift can cause signal collapse within less than one hour on hardware with identical offline calibration snapshots. Runs #11-#12 achieved R_fit = 23.93 and 18.4 respectively (GO-1 PASS, GO-3 PASS), while Run #13 executed only 53 minutes later on the same backend collapsed to R_fit = 1.20 (GO-1 FAIL). This finding establishes that offline Health Scores do not reliably predict experimental success, and defines an operational envelope requiring Health > 80% (Grade B or better) for empirically associated with high-probability signal stability. The observed second-harmonic (2ω) dominance in the phase-dependent signal (A₂ω/A₁ω > 40×, R² > 0.99, see Fig. 9) is consistent with theoretical predictions for bilinear left-right correlations. A stride sweep (s = 2-5, see Fig. 4) reveals a signal-coherence trade-off, with s = 3 identified as optimal. Total quantum processor time across all 14 runs: approximately 45 minutes. These results establish a validated, falsifiable experimental framework for probing analog quantum gravity signatures on NISQ hardware, with explicit calibration-conditional bounds. The methodology may provide a validated framework applicable to analog Hawking radiation platforms where topology-controlled correlations play a central role (see Section 5.4). Note: Results demonstrated primarily on IBM ibm_fez; multi-device validation on additional backends is recommended to establish cross-platform generalizability.
Universal Fault Tolerance remains the grand challenge of quantum computing. In this work, we present empirical evidence for a passive error suppression protocol based on a topological geometric phase constraint, Y = π²/φ ≈ 6.0998 rad. Through controlled A/B testing on IBM Quantum processors (127-qubit 'Eagle' and 133-qubit 'Heron'), we report a consistent fidelity improvement of ~ 7% in the generation of Bell States compared to standard circuit implementations. These findings suggest that topological phase engineering acts as a "Zero-Overhead" stabilization layer suitable for NISQ-era hardware.