Spectral Diagnostics of Superconducting Quantum Circuits via the Witten Laplacian on Configuration Space

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 : [email protected] 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