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EP4 — Bures–Morse Gradient Flow Test on Real IBM Quantum Hardware

Michael Adis

Published Mar 11, 2026• 0 citations
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Abstract

EP4 is the fourth experimental entry point of the EQ(vT) theory (Time as a Vector Field, DOI: 10.5281/zenodo.18917317). EQ(vT) predicts that the density matrix of any decohering quantum system evolves along a Bures–Morse gradient flow with attractor ρ → I/d (the maximum-entropy state). This deposit formalizes the EP4 test against real IBM quantum hardware data. Data source: IBM Open Science Prize 2021 (qiskit-community/open-science-prize-2021). System: 3-qubit XXX Heisenberg spin chain on ibmq_jakarta (qubits 1, 3, 5), initial state |110⟩, ISL-optimised Trotterisation (35 steps, t = π). Full quantum state tomography: 27 Pauli bases, 16192 shots/circuit, 8 repetitions. Methodology: Density matrices reconstructed from raw hardware data using an ignis-free pipeline (calibration matrix inversion + linear Pauli inversion + PSD projection). The test operates in the rotating frame, isolating the decoherent component by removing accumulated unitary evolution at each Trotter step. This is the correct and necessary frame for testing a decoherence model. Data provenance: Step 35 (t = π) uses the density matrix reconstructed directly from real ibmq_jakarta hardware. Steps 1–34 use an analytic T₁/T₂ decoherence model calibrated to ibmq_jakarta hardware parameters (T₁ = 120 μs, T₂ = 90 μs, gate time 15 ns/step). Model purity at step 35 agrees with hardware to <1%. Full per-step hardware tomography is a limitation noted in §5.2 of the formalization document. Results: Three test statistics all pass. T1 (best-fit Morse residual): median 0.0037 vs noise floor 0.011, ratio 0.33× — well below the 5× conventional significance threshold. T3 (monotone approach to I/8): Bures distance decreasing. S4 (scalar Morse ratio dS/|∇S|²_Bures): constant at 0.005 ± CV~0.005 across all 34 usable Trotter steps, confirming the gradient flow structure independently of any fitting procedure. Contents: EP4_MorseTest_Formalization.docx (formal write-up), MorseTest_IBM_v4.py (full implementation), MorseTest_IBM_v4.png (results figure). Related: EQ(vT) theory (DOI: 10.5281/zenodo.18917317) · EFT Standalone (DOI: 10.5281/zenodo.18963986) Michael Adis · ETN Invest AB · Södertälje · 2026

DOI
10.5281/zenodo.18968715

Related papers

EP4-C: EP4-C: Physical Consequences of the Morse Gradient Test (EP4A) — Locality of Gravity from Two Independent Geometric Perspectives

Michael Adis

EP4-C documents the results of EP4A — a Lindblad Morse Gradient Test on the 3-qubit XXX Heisenberg spin chain using published ibmq_jakarta hardware parameters (T1=119 μs, T2=113 μs) — and identifies a structural consequence extending to the BCS superconductivity experiment (EP5-BCS). Core findings: (1) The Morse correlation dS = λ · D²_B is confirmed at 14.7× signal-to-noise on the Lindblad analytic trajectory. All thresholds were pre-declared before simulation. Decoherence parameters were taken from published hardware specs, not calibrated to match output. The Heisenberg revival F(|110⟩, U(π)|110⟩) = 1.000000 is verified. (2) The observed drift in λ is explained analytically with 85% accuracy and zero free parameters as a geometric consequence of the trajectory approaching the pure-state boundary ∂D(H) of the density matrix manifold near the revival at t=π. The drift is carried entirely by D_B shrinking as rotating-frame steps become geometrically short near the turning point; dS remains flat (CV=0.175). This is not a post-hoc explanation — the prediction follows from local eigenvalue structure of ρ at each step with no fitting. (3) Two independent aspects of the computation both indicate that the effective gravitational degree of freedom in EFT — f = |∇S|_B — is locally determined on D(H). First: λ(t) is predicted from local quantities only, with no non-local terms entering the drift explanation. Second: the Bures metric singularity near pure states is controlled entirely by the local eigenvalue spectrum of ρ at that point, directly analogous to how spacetime curvature in GR is determined by the local stress-energy tensor. (4) The BCS experiment (EP5-BCS, pending CAN Superconductors disc samples) has the identical geometric structure: the BCS ground state at T=0 is a pure state on ∂D(H). The clean Morse window — where the Pearson correlation between dS and D²_B is predicted to be high (> 0.85) and λ to track the zero-parameter geometric prediction — is 0.2 < T/T_c < 0.8, derived from EFT geometry before any BCS measurement. Boundary drift zones near T=0 and T=T_c are predicted as positive confirmations of the same structure. The document includes: full pre-declared threshold tables, per-step trajectory data, the zero-parameter λ prediction, all figures, reproducible Python code (NumPy/SciPy/Matplotlib only, no Qiskit required, runs in under 30 seconds), and the complete reasoning chain from initial results through geometric diagnosis to the locality finding. Verification chain:- EP4A (this document): Lindblad analytic trajectory — COMPLETE, 14.7× signal- EP4B: IBM hardware tomography at steps 5, 10, 20, 30, 35 — PENDING (script ready)- EP5-BCS: Superconducting disc, CAN Superconductors — PENDING, clean window 0.2 < T/T_c < 0.8 Related work:- EFT standalone: DOI 10.5281/zenodo.18963986- EQ(vT): DOI 10.5281/zenodo.18917317- EP4A (Morse Gradient Test, Lindblad): DOI 10.5281/zenodo.18969071- BCS pre-registration: DOI 10.5281/zenodo.18964362

•Mar 13, 2026•0 citations

The Geometry of Quantum Decay: Consequences of the Morse Gradient Test (EP4)

Michael Adis

The Morse Gradient Test (EP4) demonstrated that qubit dissipation on IBM Eagle hardware follows the entropy gradient of the Bures density matrix manifold with a Morse residual of 0.0171 — meaning 98.3% of observed dissipative motion is accounted for by the manifold's geometric structure alone. This document states the physical consequences of that result. Quantum decay is not a random walk. It is a geometrically governed descent along a universal Morse foliation that exists independently of the physical hardware. The Second Law of Thermodynamics is encoded in the topology of the space that quantum information inhabits.

•Mar 12, 2026•0 citations

Pre-registration: Symmetry-Dependent Quantum Birthmark on ibm_kingston

Amit Brahmbhatt

Note: description expanded on 2026-10-14 for readability. It adds no new predictions or criteria. The frozen pre-registration is the attached PDF, unchanged since publication. Status: the experiment was run on 2026-10-14, after this record was published. Results, including every pre-registered test, will be reported in a separate record linked here. In plain language Theory says a quantum system never completely forgets where it started, even when its dynamics are chaotic. This leftover memory is called a quantum birthmark (Graf et al., Phys. Rev. X, 2026). Theory also says the birthmark should be larger when the system's rules run the same forwards and backwards in time (time-reversal symmetry) than when that symmetry is broken. This record pre-registers a test of that prediction on IBM's ibm_kingston quantum processor. We built two nearly identical sets of 4-qubit circuits. One set has time-reversal symmetry and the other does not. Both use exactly the same gates, so they experience the same hardware noise. We measure how often each circuit returns to its starting state, compared with the 1-in-16 chance level, and predict that the symmetric set shows about 1.67× more memory than the broken set. All predictions, pass/fail criteria, circuits and analysis code were deposited here before any quantum hardware was used. What is tested, and what is not Tested: whether the return probability stays above the ergodic baseline 1/16 at depths 8–23, and whether that excess is larger for the time-reversal-symmetric class by the ratio exact numerics predict for these fixed instances. Not tested: the withdrawn temporal-memory claims of 10.5281/zenodo.20470129. The birthmark is closed-system coherent memory, which measurement and reset erase, so no outcome here bears on those claims. Not tested: the universal random-matrix value 1.889. At this size (N = 16) the circuit family itself gives about 1.66, so a finite-size difference is expected. Not a quantum-advantage claim: a 16-dimensional system is exactly simulable. This is a hardware-validation experiment. Design Hardware: ibm_kingston, physical qubits 108–109–118–129 as an open chain, selected by a no-QPU calibration audit (included as v6_backend_audit.zip). Circuits: a kicked-Ising Floquet period Kx(a/2) → D(h1) → Kx(b) → D(h2) → Kx(a/2), with D(h) = exp(−iΣhiZi)·exp(−iπ/4 ΣZiZj), at exactly 6 CZ per period. COE (symmetric): h1 = h2. TRSB (broken): h1 = h + d, h2 = h − d. The classes differ only in virtual-Z angles. Instances: 16 seeded COE/TRSB pairs (seed 20261013), run at every depth from 8 to 23 (48–138 CZ). Observable: P(t) = |⟨0000|Ft|0000⟩|². The primary statistic is the readout-mitigated excess ratio R = ECOE / ETRSB, where E is the mean of P(t) − 1/16. A noise fidelity common to both classes cancels in R. Controls: 32 deep circuits (depths 60–63) as a decoherence-floor check. 8 state-preparation monitors. 16 readout-calibration circuits. Run: one SamplerV2 job of 568 circuits at 256 shots each, with dynamical decoupling and twirling off and the execution order shuffled. Predictions Quantity COE TRSB R Excess over 1/16, depths 8–23 (noiseless, primary) 0.0896 0.0537 1.667 Same instances, infinite-time limit 0.0952 0.0634 1.502 Circuit family, 10,000 random draws — — 1.661 Random-matrix reference, N = 16 — — 1.889 Under four simulated noise models (nominal, pessimistic, and each with coherent errors), the mitigated R stays between 1.64 and 1.77. The shot-noise standard deviation of R at 256 shots is 0.070–0.125. Pre-registered decision criteria Test Pass condition H1 (primary): symmetry dependence 99% CI lower bound of R > 1.0 H2 (primary): quantitative agreement 99% CI of R intersects 1.54–1.87 and is at most 1.0 wide S1: birthmark above decohered floor Window excess minus depth 60–63 excess, 99% CI lower bound > 0, for both classes S2: matched fidelity between classes 0.85 ≤ FCOE/FTRSB ≤ 1.15 S3: instance-level agreement Pearson r ≥ 0.80 against exact predictions S4 (flag only): state prep and drift Monitors ≥ 0.95, drift ≤ 0.045 Overall verdict: CONFIRMED if H1, H2 and S2 all pass; PARTIAL if H1 passes but H2 or S2 fails; NOT CONFIRMED if H1 fails. Every test is reported whatever the outcome. Uncertainty comes from a 10,000-sample parametric multinomial bootstrap over every circuit's counts, with instances held fixed. Amendment 1 (v1.1.0, made before any data) Amendment 1 changed two things relative to v1.0.0 (10.5281/zenodo.23355804): Shots: reduced from 1024 to 256 per circuit for QPU budget, cutting estimated execution from about 152 s to about 38 s. H2: changed from "point estimate in 1.54–1.87" to the CI rule above, because at 256 shots the point rule would falsely fail 20–25% of the time under the pessimistic models. A CI-width cap of 1.0 keeps H2 informative. Circuits, instances and predictions are unchanged. The trade-off is that H2 is now a weaker test. Provenance Every reported number is derived by script from raw counts: Source and transpiled circuits are saved as QPY. Before submission, every transpiled circuit is mapped back to 4 qubits and its unitary checked against the exact model to < 10−8. The analysis reads its decision bands only from predictions.json and its data only from the raw results file. Submission is gated on the DOI of this record. Files: The PDF is the authoritative pre-registration. predictions.json holds every predicted number and decision band. birthmark_prereg_v1.1.0.zip contains the circuit builder, verification, submission and frozen analysis scripts, plus simulated-data self-tests. v6_backend_audit.zip is the pre-submission calibration audit. Known limitations Small system size (N = 16), so the random-matrix value is not expected. The prediction is specific to depths 8–23 and to these 16 fixed instances. The noise models exclude leakage, TLS fluctuations and crosstalk from outside the chain. T1 relaxation biases P(0000) upward, which pulls R toward 1 (conservative). One backend, one path, one job: no replication. Data: CC BY 4.0. Code: MIT. Principal investigator: Amit Brahmbhatt, Quantum-Clarity LLC.

•Oct 14, 2026•0 citations

Page–Wootters Constraint Test of a Phase-Gradient Clock Observable in a Cobalt–Corrin Active-Space Model

Rohit

Here's a description for the Zenodo record. It mirrors the abstract but is written for someone scanning a repository page rather than reading a journal. Third paper in a series on a phase-gradient relational clock observable in cobalt–corrin active-space models. Earlier work defined a discrete observable, τ_pre, on a two-qubit clock marginal of a Jordan–Wigner register, and reported that using τ_pre as the time axis yields a lower Schrödinger residual than an external evolution parameter s, validated against a randomized-monotonic null. In those studies the states whose ordering τ_pre was tested against were themselves generated by evolution in s, leaving the relational reading circular. This paper removes the external trajectory. A Page–Wootters history state satisfying the constraint (H_C ⊗ 1 + 1 ⊗ H_S)|Ψ⟩⟩ = 0 is constructed over a 10-qubit CASCI(5,5) Hamiltonian for a 26-atom cobalt–corrin fragment, and the system states are recovered only by conditioning on clock readings. Main results: Conditional states converge to the externally evolved reference, with mean infidelity falling from 1.9 × 10⁻² at clock dimension d = 64 to 1.0 × 10⁻⁶ at d = 16384. All reported quantities converge as the finite-difference step Δt → 0; the finite-difference residual agrees with the analytic-derivative residual to within 1.6% at the coarsest step used. In that limit, τ_pre lowers the mean residual from 8.1162 to 6.8715 against a null of 0.7114 ± 0.0820 (z = 5.73). The standardized effect is stable across all 45 clock-qubit pairs (z = 5.60–5.87), under orbital reordering (z = 5.66), across a fiftyfold change in step size, and across the null's step-floor parameter, whereas the unstandardized ratio varies with these conventions. A spectrum-preserving control, mixing eigenvectors toward random orthogonal ones at fixed eigenvalues, shows the clock marginal decohering monotonically toward the maximally mixed value; the apparent scrambling threshold is shown to follow the purity cut in the definition of τ_pre rather than any property of the system. The paper states explicitly what is not established: that τ_pre is a physical time parameter, that the external parameter is eliminated rather than relocated into the choice of clock Hamiltonian, that anything is specific to vitamin B12, or that τ_pre is experimentally accessible. Three quantities that might naturally be reported as results are deliberately not, with reasons given. Data and code available on request.

•Sep 26, 2026•0 citations

Information-Geometric Gradient Flows on the Bures Manifold and Decoherence-Free Subspaces

Mikheil Rusishvili

We formulate a geometric extension of open quantum dynamics in which the density matrix evolves as a Riemannian gradient flow on the Bures manifold. The evolution equation \frac{d\rho}{dt} = -i[H,\rho] - \lambda \nabla_B \Phi[\rho] drives the state toward regions of minimal information degradation, defined by the functional \Phi[\rho], the instantaneous rate of relative-entropy change under the bare Lindbladian. This deterministic flow preserves trace and positivity, and introduces a single new universal constant \lambda>0 while recovering standard Lindblad dynamics as \lambda\to0. Under a Unitary Orthogonality Condition – exactly satisfied for pure dephasing and approximately in many-body localized phases – \Phi becomes a Lyapunov functional, and its critical points (decoherence-free subspaces) are asymptotically stable attractors. Applied to disordered spin chains, the framework reproduces the known entropy‑suppression scaling \Phi \lesssim \gamma N (J/W)^2. The theory offers a falsifiable, information‑geometric principle where quantum states intrinsically minimise their own information loss. Keywords: quantum information geometry, Bures metric, gradient flow, Lindblad dynamics, decoherence-free subspaces, many-body localization, Lyapunov functional

•May 12, 2026•0 citations

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

Frederic David Blum

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

•Feb 26, 2026•0 citations
EP4 is the fourth experimental entry point of the EQ(vT) theory (Time as a Vector Field, DOI: 10.5281/zenodo.18917317). EQ(vT) predicts that the density matrix of any decohering quantum system evolves along a Bures–Morse gradient flow with attractor ρ → I/d (the maximum-entropy state). This deposit formalizes the EP4 test against real IBM quantum hardware data. Data source: IBM Open Science Prize 2021 (qiskit-community/open-science-prize-2021). System: 3-qubit XXX Heisenberg spin chain on ibmq_jakarta (qubits 1, 3, 5), initial state |110⟩, ISL-optimised Trotterisation (35 steps, t = π). Full quantum state tomography: 27 Pauli bases, 16192 shots/circuit, 8 repetitions. Methodology: Density matrices reconstructed from raw hardware data using an ignis-free pipeline (calibration matrix inversion + linear Pauli inversion + PSD projection). The test operates in the rotating frame, isolating the decoherent component by removing accumulated unitary evolution at each Trotter step. This is the correct and necessary frame for testing a decoherence model. Data provenance: Step 35 (t = π) uses the density matrix reconstructed directly from real ibmq_jakarta hardware. Steps 1–34 use an analytic T₁/T₂ decoherence model calibrated to ibmq_jakarta hardware parameters (T₁ = 120 μs, T₂ = 90 μs, gate time 15 ns/step). Model purity at step 35 agrees with hardware to <1%. Full per-step hardware tomography is a limitation noted in §5.2 of the formalization document. Results: Three test statistics all pass. T1 (best-fit Morse residual): median 0.0037 vs noise floor 0.011, ratio 0.33× — well below the 5× conventional significance threshold. T3 (monotone approach to I/8): Bures distance decreasing. S4 (scalar Morse ratio dS/|∇S|²_Bures): constant at 0.005 ± CV~0.005 across all 34 usable Trotter steps, confirming the gradient flow structure independently of any fitting procedure. Contents: EP4_MorseTest_Formalization.docx (formal write-up), MorseTest_IBM_v4.py (full implementation), MorseTest_IBM_v4.png (results figure). Related: EQ(vT) theory (DOI: 10.5281/zenodo.18917317) · EFT Standalone (DOI: 10.5281/zenodo.18963986) Michael Adis · ETN Invest AB · Södertälje · 2026
EP4-C documents the results of EP4A — a Lindblad Morse Gradient Test on the 3-qubit XXX Heisenberg spin chain using published ibmq_jakarta hardware parameters (T1=119 μs, T2=113 μs) — and identifies a structural consequence extending to the BCS superconductivity experiment (EP5-BCS). Core findings: (1) The Morse correlation dS = λ · D²_B is confirmed at 14.7× signal-to-noise on the Lindblad analytic trajectory. All thresholds were pre-declared before simulation. Decoherence parameters were taken from published hardware specs, not calibrated to match output. The Heisenberg revival F(|110⟩, U(π)|110⟩) = 1.000000 is verified. (2) The observed drift in λ is explained analytically with 85% accuracy and zero free parameters as a geometric consequence of the trajectory approaching the pure-state boundary ∂D(H) of the density matrix manifold near the revival at t=π. The drift is carried entirely by D_B shrinking as rotating-frame steps become geometrically short near the turning point; dS remains flat (CV=0.175). This is not a post-hoc explanation — the prediction follows from local eigenvalue structure of ρ at each step with no fitting. (3) Two independent aspects of the computation both indicate that the effective gravitational degree of freedom in EFT — f = |∇S|_B — is locally determined on D(H). First: λ(t) is predicted from local quantities only, with no non-local terms entering the drift explanation. Second: the Bures metric singularity near pure states is controlled entirely by the local eigenvalue spectrum of ρ at that point, directly analogous to how spacetime curvature in GR is determined by the local stress-energy tensor. (4) The BCS experiment (EP5-BCS, pending CAN Superconductors disc samples) has the identical geometric structure: the BCS ground state at T=0 is a pure state on ∂D(H). The clean Morse window — where the Pearson correlation between dS and D²_B is predicted to be high (> 0.85) and λ to track the zero-parameter geometric prediction — is 0.2 < T/T_c < 0.8, derived from EFT geometry before any BCS measurement. Boundary drift zones near T=0 and T=T_c are predicted as positive confirmations of the same structure. The document includes: full pre-declared threshold tables, per-step trajectory data, the zero-parameter λ prediction, all figures, reproducible Python code (NumPy/SciPy/Matplotlib only, no Qiskit required, runs in under 30 seconds), and the complete reasoning chain from initial results through geometric diagnosis to the locality finding. Verification chain:- EP4A (this document): Lindblad analytic trajectory — COMPLETE, 14.7× signal- EP4B: IBM hardware tomography at steps 5, 10, 20, 30, 35 — PENDING (script ready)- EP5-BCS: Superconducting disc, CAN Superconductors — PENDING, clean window 0.2 < T/T_c < 0.8 Related work:- EFT standalone: DOI 10.5281/zenodo.18963986- EQ(vT): DOI 10.5281/zenodo.18917317- EP4A (Morse Gradient Test, Lindblad): DOI 10.5281/zenodo.18969071- BCS pre-registration: DOI 10.5281/zenodo.18964362
The Morse Gradient Test (EP4) demonstrated that qubit dissipation on IBM Eagle hardware follows the entropy gradient of the Bures density matrix manifold with a Morse residual of 0.0171 — meaning 98.3% of observed dissipative motion is accounted for by the manifold's geometric structure alone. This document states the physical consequences of that result. Quantum decay is not a random walk. It is a geometrically governed descent along a universal Morse foliation that exists independently of the physical hardware. The Second Law of Thermodynamics is encoded in the topology of the space that quantum information inhabits.
Note: description expanded on 2026-10-14 for readability. It adds no new predictions or criteria. The frozen pre-registration is the attached PDF, unchanged since publication. Status: the experiment was run on 2026-10-14, after this record was published. Results, including every pre-registered test, will be reported in a separate record linked here. In plain language Theory says a quantum system never completely forgets where it started, even when its dynamics are chaotic. This leftover memory is called a quantum birthmark (Graf et al., Phys. Rev. X, 2026). Theory also says the birthmark should be larger when the system's rules run the same forwards and backwards in time (time-reversal symmetry) than when that symmetry is broken. This record pre-registers a test of that prediction on IBM's ibm_kingston quantum processor. We built two nearly identical sets of 4-qubit circuits. One set has time-reversal symmetry and the other does not. Both use exactly the same gates, so they experience the same hardware noise. We measure how often each circuit returns to its starting state, compared with the 1-in-16 chance level, and predict that the symmetric set shows about 1.67× more memory than the broken set. All predictions, pass/fail criteria, circuits and analysis code were deposited here before any quantum hardware was used. What is tested, and what is not Tested: whether the return probability stays above the ergodic baseline 1/16 at depths 8–23, and whether that excess is larger for the time-reversal-symmetric class by the ratio exact numerics predict for these fixed instances. Not tested: the withdrawn temporal-memory claims of 10.5281/zenodo.20470129. The birthmark is closed-system coherent memory, which measurement and reset erase, so no outcome here bears on those claims. Not tested: the universal random-matrix value 1.889. At this size (N = 16) the circuit family itself gives about 1.66, so a finite-size difference is expected. Not a quantum-advantage claim: a 16-dimensional system is exactly simulable. This is a hardware-validation experiment. Design Hardware: ibm_kingston, physical qubits 108–109–118–129 as an open chain, selected by a no-QPU calibration audit (included as v6_backend_audit.zip). Circuits: a kicked-Ising Floquet period Kx(a/2) → D(h1) → Kx(b) → D(h2) → Kx(a/2), with D(h) = exp(−iΣhiZi)·exp(−iπ/4 ΣZiZj), at exactly 6 CZ per period. COE (symmetric): h1 = h2. TRSB (broken): h1 = h + d, h2 = h − d. The classes differ only in virtual-Z angles. Instances: 16 seeded COE/TRSB pairs (seed 20261013), run at every depth from 8 to 23 (48–138 CZ). Observable: P(t) = |⟨0000|Ft|0000⟩|². The primary statistic is the readout-mitigated excess ratio R = ECOE / ETRSB, where E is the mean of P(t) − 1/16. A noise fidelity common to both classes cancels in R. Controls: 32 deep circuits (depths 60–63) as a decoherence-floor check. 8 state-preparation monitors. 16 readout-calibration circuits. Run: one SamplerV2 job of 568 circuits at 256 shots each, with dynamical decoupling and twirling off and the execution order shuffled. Predictions Quantity COE TRSB R Excess over 1/16, depths 8–23 (noiseless, primary) 0.0896 0.0537 1.667 Same instances, infinite-time limit 0.0952 0.0634 1.502 Circuit family, 10,000 random draws — — 1.661 Random-matrix reference, N = 16 — — 1.889 Under four simulated noise models (nominal, pessimistic, and each with coherent errors), the mitigated R stays between 1.64 and 1.77. The shot-noise standard deviation of R at 256 shots is 0.070–0.125. Pre-registered decision criteria Test Pass condition H1 (primary): symmetry dependence 99% CI lower bound of R > 1.0 H2 (primary): quantitative agreement 99% CI of R intersects 1.54–1.87 and is at most 1.0 wide S1: birthmark above decohered floor Window excess minus depth 60–63 excess, 99% CI lower bound > 0, for both classes S2: matched fidelity between classes 0.85 ≤ FCOE/FTRSB ≤ 1.15 S3: instance-level agreement Pearson r ≥ 0.80 against exact predictions S4 (flag only): state prep and drift Monitors ≥ 0.95, drift ≤ 0.045 Overall verdict: CONFIRMED if H1, H2 and S2 all pass; PARTIAL if H1 passes but H2 or S2 fails; NOT CONFIRMED if H1 fails. Every test is reported whatever the outcome. Uncertainty comes from a 10,000-sample parametric multinomial bootstrap over every circuit's counts, with instances held fixed. Amendment 1 (v1.1.0, made before any data) Amendment 1 changed two things relative to v1.0.0 (10.5281/zenodo.23355804): Shots: reduced from 1024 to 256 per circuit for QPU budget, cutting estimated execution from about 152 s to about 38 s. H2: changed from "point estimate in 1.54–1.87" to the CI rule above, because at 256 shots the point rule would falsely fail 20–25% of the time under the pessimistic models. A CI-width cap of 1.0 keeps H2 informative. Circuits, instances and predictions are unchanged. The trade-off is that H2 is now a weaker test. Provenance Every reported number is derived by script from raw counts: Source and transpiled circuits are saved as QPY. Before submission, every transpiled circuit is mapped back to 4 qubits and its unitary checked against the exact model to < 10−8. The analysis reads its decision bands only from predictions.json and its data only from the raw results file. Submission is gated on the DOI of this record. Files: The PDF is the authoritative pre-registration. predictions.json holds every predicted number and decision band. birthmark_prereg_v1.1.0.zip contains the circuit builder, verification, submission and frozen analysis scripts, plus simulated-data self-tests. v6_backend_audit.zip is the pre-submission calibration audit. Known limitations Small system size (N = 16), so the random-matrix value is not expected. The prediction is specific to depths 8–23 and to these 16 fixed instances. The noise models exclude leakage, TLS fluctuations and crosstalk from outside the chain. T1 relaxation biases P(0000) upward, which pulls R toward 1 (conservative). One backend, one path, one job: no replication. Data: CC BY 4.0. Code: MIT. Principal investigator: Amit Brahmbhatt, Quantum-Clarity LLC.
Here's a description for the Zenodo record. It mirrors the abstract but is written for someone scanning a repository page rather than reading a journal. Third paper in a series on a phase-gradient relational clock observable in cobalt–corrin active-space models. Earlier work defined a discrete observable, τ_pre, on a two-qubit clock marginal of a Jordan–Wigner register, and reported that using τ_pre as the time axis yields a lower Schrödinger residual than an external evolution parameter s, validated against a randomized-monotonic null. In those studies the states whose ordering τ_pre was tested against were themselves generated by evolution in s, leaving the relational reading circular. This paper removes the external trajectory. A Page–Wootters history state satisfying the constraint (H_C ⊗ 1 + 1 ⊗ H_S)|Ψ⟩⟩ = 0 is constructed over a 10-qubit CASCI(5,5) Hamiltonian for a 26-atom cobalt–corrin fragment, and the system states are recovered only by conditioning on clock readings. Main results: Conditional states converge to the externally evolved reference, with mean infidelity falling from 1.9 × 10⁻² at clock dimension d = 64 to 1.0 × 10⁻⁶ at d = 16384. All reported quantities converge as the finite-difference step Δt → 0; the finite-difference residual agrees with the analytic-derivative residual to within 1.6% at the coarsest step used. In that limit, τ_pre lowers the mean residual from 8.1162 to 6.8715 against a null of 0.7114 ± 0.0820 (z = 5.73). The standardized effect is stable across all 45 clock-qubit pairs (z = 5.60–5.87), under orbital reordering (z = 5.66), across a fiftyfold change in step size, and across the null's step-floor parameter, whereas the unstandardized ratio varies with these conventions. A spectrum-preserving control, mixing eigenvectors toward random orthogonal ones at fixed eigenvalues, shows the clock marginal decohering monotonically toward the maximally mixed value; the apparent scrambling threshold is shown to follow the purity cut in the definition of τ_pre rather than any property of the system. The paper states explicitly what is not established: that τ_pre is a physical time parameter, that the external parameter is eliminated rather than relocated into the choice of clock Hamiltonian, that anything is specific to vitamin B12, or that τ_pre is experimentally accessible. Three quantities that might naturally be reported as results are deliberately not, with reasons given. Data and code available on request.
We formulate a geometric extension of open quantum dynamics in which the density matrix evolves as a Riemannian gradient flow on the Bures manifold. The evolution equation \frac{d\rho}{dt} = -i[H,\rho] - \lambda \nabla_B \Phi[\rho] drives the state toward regions of minimal information degradation, defined by the functional \Phi[\rho], the instantaneous rate of relative-entropy change under the bare Lindbladian. This deterministic flow preserves trace and positivity, and introduces a single new universal constant \lambda>0 while recovering standard Lindblad dynamics as \lambda\to0. Under a Unitary Orthogonality Condition – exactly satisfied for pure dephasing and approximately in many-body localized phases – \Phi becomes a Lyapunov functional, and its critical points (decoherence-free subspaces) are asymptotically stable attractors. Applied to disordered spin chains, the framework reproduces the known entropy‑suppression scaling \Phi \lesssim \gamma N (J/W)^2. The theory offers a falsifiable, information‑geometric principle where quantum states intrinsically minimise their own information loss. Keywords: quantum information geometry, Bures metric, gradient flow, Lindblad dynamics, decoherence-free subspaces, many-body localization, Lyapunov functional
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