Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Calibration-Ready Josephson–SQUID Diagnostics for Residual Barrier Perturbations: Fail-Closed Nuisance Conditioning, Multi-Witness Noise Rejection, and Ramsey Closure

Byoungwoo Lee

Published Sep 14, 2026• 0 citations
Publisher

Abstract

This work develops a device-parameterized, calibration-ready synthetic diagnostic for weak residual barrier perturbations in a split-junction Josephson circuit. It is the experimental-methodology companion to the Residual Clock–Energy program, but it does not report an experimental detection and does not derive a new Josephson relation. The device-facing hypothesis is $$E_J(u,t) = E_J^{(0)}(u) \, [1 + \zeta(u,t)],$$ where $\zeta$ is a weak latent barrier perturbation. Feynman–Hellmann differentiation fixes the first-order frequency response, $$\delta \ln \omega_{01}(u) = \kappa_J(u) \, \zeta(u) + O(\zeta^2),$$ replacing the free frequency-response coefficient used in the earlier morphology-only diagnostic. The analysis uses a frozen asymmetric split-transmon model, parity-protected paired-flux observables, a finite-calibration nuisance manifold, generalized matched filtering, bounded systematic leakage, and a predeclared false-positive reserve. Random calibration uncertainty is marginalized into an effective covariance, while bounded systematic uncertainty is propagated into a worst-case residual-amplitude bias certificate. The final synthetic ledger adopts a 1% false-positive target and a 5% reserve policy. With the final even-pickup bound $$\vert{}p_{\mathrm{even}}\vert{} \le 1.15 \times 10^{-7},$$ it gives $$\mathrm{VIF}_{\mathrm{eff}} = 1.087, \qquad B_* = 8.743 \times 10^{-7},$$ a nominal false-positive reserve of approximately $6.07\%$, and a robust $95\%$ recovery floor $$a_{\min,95}^{\mathrm{robust}} \simeq 7.29 \times 10^{-6}.$$ At the frozen half-flux operating point this corresponds to a synthetic frequency-response floor of about $15.5\text{ kHz}$. These values are calibration-derived sensitivity requirements of the declared synthetic model, not predictions of residual physics. The dynamic nuisance branch replaces a generic quasiparticle-like Ornstein–Uhlenbeck process with trapping–recombination–generation dynamics for the normalized quasiparticle density $x_{\mathrm{qp}}$. The same latent density drives both the qubit-frequency nuisance and a $T_1$-derived witness. In the declared synthetic population, multi-witness conditioning removes about 99% of the modeled quasiparticle-induced frequency-noise variance. Ramsey closure is treated conservatively. Gaussian PSD-to-Ramsey reconstruction is accepted only over the predeclared short coherent window $$t \le 50 \, \mu\mathrm{s},$$ while longer-time quasiparticle coherence is left to direct time-domain or non-Gaussian treatment. A separate exact quasi-static calculation provides a guardrail for quadratic sweet-spot flux noise. The diagnostic is explicitly fail-closed. Static spectroscopy alone cannot determine the microscopic origin of a perturbation that acts through the same effective Josephson-energy channel, and an unmodeled nuisance exactly parallel to the candidate template remains non-identifiable. Candidate admission therefore requires frozen circuit transfer, parity checks, calibrated thermal/quasiparticle/pickup controls, systematic-bias and reserve gates, independent witness conditioning, and confidence-calibrated recovery. This paper is the third part of a public three-paper sequence: Paper I: Residual Clock Dynamics: Operational-Time Rescaling and Effective Relaxation in a Minimal $U(1)$ Model, Version v1.0, Zenodo DOI: 10.5281/zenodo.22735204. Paper II: Field-Theoretic Residual Clock Response and the Criterion for a Common Operational Time, Version v1.0, Zenodo DOI: 10.5281/zenodo.22739058. Paper II derives the conditional parent-model chain $$X \longrightarrow \rho_X \longrightarrow \omega_C(X),$$ whereas the present work assumes the separate device-level chain $$\zeta \longrightarrow E_J \longrightarrow \omega_{01}.$$ No microscopic derivation of $X \longrightarrow \zeta$ is claimed here. Establishing or ruling out that theory-to-device matching remains an open problem. The accompanying reproducibility package contains the manuscript source, scripts, numerical tables, figures, environment specification, execution instructions, and checksums needed to reproduce the synthetic calculations.

DOI
10.5281/zenodo.22739557

Related papers

A Josephson–SQUID Barrier-Clock Diagnostic for the Residual Clock–Energy Framework

Byoungwoo Lee

This record contains Version v0.6r2 of *A Josephson–SQUID Barrier-Clock Diagnostic for the Residual Clock–Energy Framework*. This version is a synthetic-noise sensitivity and application-readiness update to the earlier Josephson–SQUID executable diagnostic line. This manuscript is not an empirical detection paper, not a proposal for a new Josephson law, and not a replacement for standard Josephson/SQUID physics. Instead, it develops a residual phase-clock covariance diagnostic built on standard Josephson/SQUID baseline physics, RCSJ-style phase dynamics, tunneling-opacity language, and mock-data sensitivity calibration. The diagnostic is organized around the flux-control parameter $$u=\frac{\Phi_{\rm ext}}{\Phi_0},$$ and the observable vector $$u\longmapsto\left(I_c(u),\Gamma_\phi(u),\frac{\delta\nu_{\rm osc}}{\nu_{\rm osc}}(u),S_{\phi\phi}(\omega;u)\right).$$ Here \(I_c\) is the critical current, \(\Gamma_\phi\) is a phase-dephasing rate, \(\delta\nu_{\rm osc}/\nu_{\rm osc}\) is a fractional oscillator or clock-frequency shift, and \(S_{\phi\phi}\) is a phase-noise spectral density. The Residual Clock–Energy input is represented by the residual phase-tension one-form $$\alpha=d\Phi-A,$$ which is compared with the gauge-invariant superconducting phase difference $$\phi=\varphi_1-\varphi_2-\frac{2\pi}{\Phi_0}\int_1^2 A\cdot d\ell .$$ The earlier v0.5r2 version introduced a positive-control toy residual drive, $$\mathcal R_J(u)=r_0\sin^2(\pi u),$$ and used it as a morphology target for baseline-subtracted Josephson/SQUID observables. Version v0.6r2 extends this line by injecting synthetic noise and nuisance morphologies into mock observations, $$y_{k,i}^{\rm obs}(A)=A\beta_k g_i+n_{k,i}+h_{k,i},$$ where \(g_i\) is the centered residual morphology, \(n_{k,i}\) is a synthetic noise term, and \(h_{k,i}\) is a nuisance contribution. The central sensitivity outputs are the detection probability, $$P_{\rm det}(A)=\frac{1}{N_{\rm MC}}\sum_{m=1}^{N_{\rm MC}}\mathbf 1[\text{trial }m\text{ passes}],$$ the minimum detectable amplitude, $$A_{\min}=\inf\{A:P_{\rm det}(A)\ge0.95\},$$ and the false-positive rate, $$P_{\rm FP}=P_{\rm det}(0).$$ Version v0.6r2 includes: 1. synthetic observation models for residual and nuisance channels;2. white-noise, high-noise, correlated-drift, heating-mimic, and mixed-nuisance scenarios;3. morphology-score and signal-to-noise recovery criteria;4. a multi-channel admission rule requiring at least two non-current channels to pass;5. matched-control subtraction for heating-like nuisance;6. false-positive and detection-probability curves;7. sensitivity tables and CSV outputs;8. an application-readiness ladder from toy positive control to device-screening protocol;9. laboratory deployment requirements for a future calibrated experiment;10. device-facing output interpretation tables. A key outcome of the synthetic study is that heating-like nuisance can overlap strongly with the residual morphology and can therefore create false-positive hazards if not controlled. The v0.6r2 update explicitly treats this issue by introducing matched-control subtraction and by distinguishing raw nuisance-contaminated recovery from controlled recovery. The application-readiness ladder used in this version is: - L0: toy positive-control morphology;- L1: synthetic-noise recovery and false-positive stress test;- L2: calibrated synthetic noise using measured device noise floors;- L3: laboratory pilot with real Josephson/SQUID data;- L4: device-screening protocol for phase-noise and barrier-quality diagnostics. The current v0.6r2 manuscript is positioned at L1. It is therefore a synthetic sensitivity and application-readiness note, not a calibrated laboratory demonstration. The included files provide the PDF manuscript, LaTeX source, figure-generation script, synthetic sensitivity summary CSV, detection-curve CSV, matched-control example CSV, simulation metadata JSON, and a source bundle for reproducibility. This work is a companion device-facing diagnostic note following the broader protocol record *Prediction and Discriminating Experiments for the Residual Clock–Energy Framework*, Version v0.4r1, DOI: 10.5281/zenodo.19846816.

•Apr 28, 2026•0 citations

Quantum Determinant Estimation of TLS-Sensitive Josephson-Junction Scattering under Persistent Defect Noise

Arjun Anand

This preprint presents a single-author computational proof of concept connecting two-level-system-sensitive Josephson-junction scattering with Quantum Determinant Estimation and device-aware noise modelling. The algorithmic foundation is the Quantum Determinant Estimation protocol of J. Agerskov and K. Splittorff, which uses a completely antisymmetric state to transform the determinant of a unitary matrix into an eigenphase accessible through Quantum Phase Estimation. The physical motivation is the work of J. T. Heath, M. K. Svendsen, and collaborators on localized Josephson hot spots produced by two-level systems in superconducting Josephson junctions. The calculation constructs a unitary two-channel reference scattering matrix and a TLS-modified response. The relative matrixR(E,ϕ)=STLS(E,ϕ)S0†(E,ϕ)R(E,\phi)=S_{\mathrm{TLS}}(E,\phi)S_0^\dagger(E,\phi)R(E,ϕ)=STLS(E,ϕ)S0†(E,ϕ)defines a defect-sensitive determinant phase that is estimated using the antisymmetric-state determinant-QPE protocol. The study includes effective Al, Ta, and Nb interface/bulk configurations, determinant-phase convergence, controlled device-level proxy mappings, finite-register and finite-shot validation, explicit qubit–TLS dynamics, and comparisons between persistent TLS noise and a matched Markovian relaxation model. The original contribution is the computational bridge between a TLS-sensitive scattering observable, determinant-phase estimation, and algorithm-level reliability under structured defect noise. The current scattering matrices, material mappings, linewidths, energy calibration, operation durations, and dynamical coupling strengths are transparent proof-of-concept assumptions. The work does not claim experimentally calibrated material predictions, quantum advantage, uncertainty-robust material identification, or a rigorous non-Markovianity witness. A planned microscopic extension will implement the published Josephson-hot-spot relations, reproduce their spatial and material trends, and use source-derived observables to calibrate the effective determinant and noise models. Preprint status: This manuscript has not undergone peer review. The associated source code and reproducibility package are deposited separately on Zenodo.

•Aug 1, 2026•0 citations

Clock-Information Fiber Extensions of Schrödinger Dynamics and Residual Dephasing Diagnostics

Byoungwoo Lee

**Version v0.5 — Journal-Polish Update** This manuscript develops a conservative extension framework for Schrödinger dynamics in which an observed quantum system is embedded into an enlarged Hilbert space equipped with an auxiliary clock-information fiber. The fiber is not introduced as a macroscopic hidden spatial dimension, nor as a local hidden-variable register. Instead, it is treated as a quantum auxiliary sector carrying phase memory, clock/reference correlations, and correlation records that may appear as information loss or dephasing after partial tracing. The central contribution of this version is a residual-identifiability framework. Rather than claiming that unitary dilation itself is new, the paper asks whether a calibrated observed system can exhibit structured residuals after independent-bath subtraction and common-bath controls. The main diagnostic object is a log-residual statistic, $$R_\chi(t;\sigma_{\rm ref})=\log C_{\rm obs}(t;\sigma_{\rm ref})-\log C_{\rm ind}(t;\sigma_{\rm ref}),$$ together with reference-covariance indices such as $$\mathcal I_\chi(t;\sigma_{\rm ref})=\partial_{\sigma_{\rm ref}}R_\chi(t;\sigma_{\rm ref}),$$ and covariance/correlation-based diagnostics over controlled reference settings. The framework emphasizes that a nonzero residual alone is not sufficient evidence for an admissible clock-information fiber. A candidate residual must be non-factorizing, reproducible, reference-covariant, and not absorbed by independent local bath models, common classical noise, or generic common quantum bath controls. In particular, the admissible-fiber hypothesis is treated as a residual diagnostic condition, not as a proof of a new hidden variable, superluminal channel, or macroscopic extra dimension. The paper proves the elementary consistency statements for the enlarged dynamics: total unitarity under a self-adjoint total Hamiltonian, total energy conservation for time-independent generators, subsystem entropy growth under partial trace, and no-signalling compatibility under local trace-preserving operations. It also presents minimal toy models for phase-memory dephasing, shared-fiber cross-kernels, compact protected fiber sectors, and synthetic residual-fitting demonstrations. The synthetic fitting layer uses a representative model of the form $$C_{\rm obs}(t;\sigma_{\rm ref})=C_{\rm ind}(t)\exp[-a(\sigma_{\rm ref})t^2],\qquada(\sigma_{\rm ref})=a_0+a_1\sigma_{\rm ref}^2,$$ so that $$R_\chi(t;\sigma_{\rm ref})=-a(\sigma_{\rm ref})t^2.$$ This example is intended as an identifiability demonstration: after calibrated independent-bath subtraction, a candidate clock-information fiber signature should appear as a reproducible residual with controlled reference covariance, rather than as an arbitrary fitting term. The experimental outlook focuses on Ramsey/spin-echo baselines, dynamical-decoupling response, superconducting qubit and Josephson platforms, tunneling phase-delay diagnostics, and reference-modulation protocols. The manuscript also formulates a common-bath control envelope, $$|R_\chi(t;\sigma_{\rm ref})-R_{\rm ctrl}(t;\sigma_{\rm ref})|\le\delta_R(t;\sigma_{\rm ref}),$$ to express the requirement that a proposed fiber residual should not be absorbed by generic common-bath control models within statistical uncertainty. ### Main updates in v0.5 - Shortened journal-style title and abstract.- Removal of version-history language from the abstract.- Strengthened common-bath control criterion.- Addition of a formal common-bath control envelope.- Improved diagnostic separation between independent local baths, common classical noise, generic common quantum baths, and admissible clock-information fibers.- Algorithm-style synthetic residual-identifiability test.- Synthetic residual-fitting demonstration using reference-covariant dephasing.- Improved table formatting and manuscript presentation for journal-style readability. ### Scope and non-claims This work should be read as a structured framework for residual diagnostics in extended Schrödinger dynamics. It is not a hidden-variable theory, not a superluminal-signalling model, not a derivation of measurement collapse, and not a completed microscopic theory of mass, charge, or quantum gravity.

•May 26, 2026•0 citations

Minimum Viable Falsification Protocol for Record-Dependent Residual Dephasing in Circuit QED

Micah Zehnder

I present a falsification-first experimental protocol for testing a proposed record-dependent contribution to residual dephasing in circuit-QED systems. The protocol is designed to distinguish a genuinely record-dependent residual from conventional apparatus-mediated effects introduced by manipulating record persistence itself. The protocol separates post-decoupling readiness controls from concurrent source-hypothesis tests; requires uncertainty-bounded contrasts between record-establishment conditions while controlling conventional physical channels; treats conventional explanations through calibration-compatible nuisance-model families where appropriate; and distinguishes nominal shot count from effective independent information under device, day, and miniblock correlations. It further requires operator discrimination, explicit conventional-noise accounting, preregistered decision rules, and independent device or architecture replication before any anomalous residual is eligible for escalation. A one-page laboratory handoff accompanies the paper to provide an implementation-oriented summary of the experimental decision path. Origin and relationship to prior work: This protocol was motivated by Francisco José Ruiz Izaguirre's phenomenological proposal concerning record-dependent residual dephasing (DOI: 10.5281/zenodo.22162999) and subsequent public technical exchange with the author. It is an independent falsification protocol, not an experimental confirmation of that proposal. No anomalous dephasing effect is claimed here.

•Sep 4, 2026•0 citations

TSR-Q-1: A Preregistered Experimental Protocol for Testing Structured Quantum-Coherence Residuals in Superconducting Qubits

Giuseppe Antonio Marino

TSR-Q-1 presents a preregistered and falsifiable experimental protocol designed to test for structured late-time coherence residuals in superconducting transmon qubits. The protocol does not treat generic recoherence, non-exponential decay, or non-Markovian behavior as evidence for the proposed framework, since such phenomena may arise from conventional open-system mechanisms. Instead, it targets a specific normalized temporal scaling law, tₙ/T₂ = nᵏ, with the preregistered theoretical value k* = 1.4706, corresponding to the first two target locations t₂/T₂ = 2.7714 and t₃/T₂ = 5.0310. If the associated amplitude-scaling hypothesis is retained, the predicted ratio is A₃/A₂ ≈ 0.551. The accompanying computational validation package develops the analysis pipeline through five stages: preliminary signal injection, blind null testing, blind injection-recovery, multi-qubit global-k inference, and sensitivity mapping. The synthetic null models include stretched-exponential decay, 1/f^α correlated noise, random-telegraph/TLS-like contributions, slow drift, white noise, and device-to-device variability. These simulations validate the detectability, specificity, and sensitivity of the proposed analysis procedure under the tested synthetic noise families. They do not constitute experimental evidence for the existence of the predicted physical effect. The next stage is a preregistered hardware implementation using superconducting qubits, with device-specific null calibration, blind analysis, systematic controls, held-out replication, and, ultimately, independent experimental replication.

•Oct 1, 2026•0 citations

Residual Clock Dynamics: Operational-Time Rescaling and Effective Relaxation in a Minimal U(1) Model

Byoungwoo Lee

Version v1.0. This work develops a minimal effective framework for residual-sourced operational-time rescaling in a $U(1)$ phase sector. The gauge-invariant residual one-form $$\alpha = d\Phi - A$$ is used to define a positive phenomenological clock response $$L_\alpha = L_0 \exp\left(-\lambda \vert{}\alpha\vert{}_h^2\right), \qquad dT = L_\alpha \, ds.$$ In the scalar-lapse sector, the generator with respect to operational time is $$K_T = L_\alpha^{-1} H_s.$$ Consequently, generator variance and pure-state quantum Fisher information scale as $L_\alpha^{-2}$, while the Bures line element of the same physical trajectory remains invariant under the reparameterization. The scalar lapse therefore changes information rate per unit operational time without, by itself, producing an intrinsic change in the quantum-state geometry. Independently of this kinematic construction, the paper considers an effective residual gradient flow $$\dot{\alpha} = -\nabla_{\mathrm{adm}} \mathcal{A}$$ on a fixed Hilbert configuration space. This yields the Lyapunov identity $$\frac{d}{dT} \mathcal{A}[\alpha(T)] = -\Vert{}\nabla_{\mathrm{adm}} \mathcal{A}\Vert{}_H^2 \le 0$$ and a monotone residual-dissipation functional. The dissipative law is an additional effective assumption and is not derived from the lapse law or from generator rescaling. The manuscript also separates the covariant gauge-invariant core from the foliation-dependent positive spatial norm entering the operational lapse, clarifies the distinction between Fisher-information-rate rescaling and intrinsic Bures geometry, and records the correction required when the background geometry is time dependent. The model is not proposed as a microscopic or fundamental theory of time, irreversibility, decoherence, or quantum measurement. Its purpose is structural: to isolate a common residual variable that can enter clock normalization, generator rescaling, and an independently assumed effective relaxation while keeping their logical dependencies explicit. The paper identifies several open problems required for a more predictive theory, including a microscopic derivation of the clock-response law, a controlled derivation of dissipative mobility, a covariant dynamical clock or foliation sector, quantitative cross-channel observables, and independent empirical tests.

•Sep 13, 2026•1 citation
This work develops a device-parameterized, calibration-ready synthetic diagnostic for weak residual barrier perturbations in a split-junction Josephson circuit. It is the experimental-methodology companion to the Residual Clock–Energy program, but it does not report an experimental detection and does not derive a new Josephson relation. The device-facing hypothesis is EJ(u,t)=EJ(0)(u) [1+ζ(u,t)],E_J(u,t) = E_J^{(0)}(u) \, [1 + \zeta(u,t)],EJ​(u,t)=EJ(0)​(u)[1+ζ(u,t)], where ζ\zetaζ is a weak latent barrier perturbation. Feynman–Hellmann differentiation fixes the first-order frequency response, δln⁡ω01(u)=κJ(u) ζ(u)+O(ζ2),\delta \ln \omega_{01}(u) = \kappa_J(u) \, \zeta(u) + O(\zeta^2),δlnω01​(u)=κJ​(u)ζ(u)+O(ζ2), replacing the free frequency-response coefficient used in the earlier morphology-only diagnostic. The analysis uses a frozen asymmetric split-transmon model, parity-protected paired-flux observables, a finite-calibration nuisance manifold, generalized matched filtering, bounded systematic leakage, and a predeclared false-positive reserve. Random calibration uncertainty is marginalized into an effective covariance, while bounded systematic uncertainty is propagated into a worst-case residual-amplitude bias certificate. The final synthetic ledger adopts a 1% false-positive target and a 5% reserve policy. With the final even-pickup bound ∣peven∣≤1.15×10−7,\vert{}p_{\mathrm{even}}\vert{} \le 1.15 \times 10^{-7},∣peven​∣≤1.15×10−7, it gives VIFeff=1.087,B∗=8.743×10−7,\mathrm{VIF}_{\mathrm{eff}} = 1.087, \qquad B_* = 8.743 \times 10^{-7},VIFeff​=1.087,B∗​=8.743×10−7, a nominal false-positive reserve of approximately 6.07%6.07\%6.07%, and a robust 95%95\%95% recovery floor amin⁡,95robust≃7.29×10−6.a_{\min,95}^{\mathrm{robust}} \simeq 7.29 \times 10^{-6}.amin,95robust​≃7.29×10−6. At the frozen half-flux operating point this corresponds to a synthetic frequency-response floor of about 15.5 kHz15.5\text{ kHz}15.5 kHz. These values are calibration-derived sensitivity requirements of the declared synthetic model, not predictions of residual physics. The dynamic nuisance branch replaces a generic quasiparticle-like Ornstein–Uhlenbeck process with trapping–recombination–generation dynamics for the normalized quasiparticle density xqpx_{\mathrm{qp}}xqp​. The same latent density drives both the qubit-frequency nuisance and a T1T_1T1​-derived witness. In the declared synthetic population, multi-witness conditioning removes about 99% of the modeled quasiparticle-induced frequency-noise variance. Ramsey closure is treated conservatively. Gaussian PSD-to-Ramsey reconstruction is accepted only over the predeclared short coherent window t≤50 μs,t \le 50 \, \mu\mathrm{s},t≤50μs, while longer-time quasiparticle coherence is left to direct time-domain or non-Gaussian treatment. A separate exact quasi-static calculation provides a guardrail for quadratic sweet-spot flux noise. The diagnostic is explicitly fail-closed. Static spectroscopy alone cannot determine the microscopic origin of a perturbation that acts through the same effective Josephson-energy channel, and an unmodeled nuisance exactly parallel to the candidate template remains non-identifiable. Candidate admission therefore requires frozen circuit transfer, parity checks, calibrated thermal/quasiparticle/pickup controls, systematic-bias and reserve gates, independent witness conditioning, and confidence-calibrated recovery. This paper is the third part of a public three-paper sequence: Paper I: Residual Clock Dynamics: Operational-Time Rescaling and Effective Relaxation in a Minimal U(1)U(1)U(1) Model, Version v1.0, Zenodo DOI: 10.5281/zenodo.22735204. Paper II: Field-Theoretic Residual Clock Response and the Criterion for a Common Operational Time, Version v1.0, Zenodo DOI: 10.5281/zenodo.22739058. Paper II derives the conditional parent-model chain X⟶ρX⟶ωC(X),X \longrightarrow \rho_X \longrightarrow \omega_C(X),X⟶ρX​⟶ωC​(X), whereas the present work assumes the separate device-level chain ζ⟶EJ⟶ω01.\zeta \longrightarrow E_J \longrightarrow \omega_{01}.ζ⟶EJ​⟶ω01​. No microscopic derivation of X⟶ζX \longrightarrow \zetaX⟶ζ is claimed here. Establishing or ruling out that theory-to-device matching remains an open problem. The accompanying reproducibility package contains the manuscript source, scripts, numerical tables, figures, environment specification, execution instructions, and checksums needed to reproduce the synthetic calculations.
This record contains Version v0.6r2 of *A Josephson–SQUID Barrier-Clock Diagnostic for the Residual Clock–Energy Framework*. This version is a synthetic-noise sensitivity and application-readiness update to the earlier Josephson–SQUID executable diagnostic line. This manuscript is not an empirical detection paper, not a proposal for a new Josephson law, and not a replacement for standard Josephson/SQUID physics. Instead, it develops a residual phase-clock covariance diagnostic built on standard Josephson/SQUID baseline physics, RCSJ-style phase dynamics, tunneling-opacity language, and mock-data sensitivity calibration. The diagnostic is organized around the flux-control parameter u=ΦextΦ0,u=\frac{\Phi_{\rm ext}}{\Phi_0},u=Φ0​Φext​​, and the observable vector u⟼(Ic(u),Γϕ(u),δνoscνosc(u),Sϕϕ(ω;u)).u\longmapsto\left(I_c(u),\Gamma_\phi(u),\frac{\delta\nu_{\rm osc}}{\nu_{\rm osc}}(u),S_{\phi\phi}(\omega;u)\right).u⟼(Ic​(u),Γϕ​(u),νosc​δνosc​​(u),Sϕϕ​(ω;u)). Here IcI_cIc​ is the critical current, Γϕ\Gamma_\phiΓϕ​ is a phase-dephasing rate, δνosc/νosc\delta\nu_{\rm osc}/\nu_{\rm osc}δνosc​/νosc​ is a fractional oscillator or clock-frequency shift, and SϕϕS_{\phi\phi}Sϕϕ​ is a phase-noise spectral density. The Residual Clock–Energy input is represented by the residual phase-tension one-form α=dΦ−A,\alpha=d\Phi-A,α=dΦ−A, which is compared with the gauge-invariant superconducting phase difference ϕ=φ1−φ2−2πΦ0∫12A⋅dℓ.\phi=\varphi_1-\varphi_2-\frac{2\pi}{\Phi_0}\int_1^2 A\cdot d\ell .ϕ=φ1​−φ2​−Φ0​2π​∫12​A⋅dℓ. The earlier v0.5r2 version introduced a positive-control toy residual drive, RJ(u)=r0sin⁡2(πu),\mathcal R_J(u)=r_0\sin^2(\pi u),RJ​(u)=r0​sin2(πu), and used it as a morphology target for baseline-subtracted Josephson/SQUID observables. Version v0.6r2 extends this line by injecting synthetic noise and nuisance morphologies into mock observations, yk,iobs(A)=Aβkgi+nk,i+hk,i,y_{k,i}^{\rm obs}(A)=A\beta_k g_i+n_{k,i}+h_{k,i},yk,iobs​(A)=Aβk​gi​+nk,i​+hk,i​, where gig_igi​ is the centered residual morphology, nk,in_{k,i}nk,i​ is a synthetic noise term, and hk,ih_{k,i}hk,i​ is a nuisance contribution. The central sensitivity outputs are the detection probability, Pdet(A)=1NMC∑m=1NMC1[trial m passes],P_{\rm det}(A)=\frac{1}{N_{\rm MC}}\sum_{m=1}^{N_{\rm MC}}\mathbf 1[\text{trial }m\text{ passes}],Pdet​(A)=NMC​1​∑m=1NMC​​1[trial m passes], the minimum detectable amplitude, Amin⁡=inf⁡{A:Pdet(A)≥0.95},A_{\min}=\inf\{A:P_{\rm det}(A)\ge0.95\},Amin​=inf{A:Pdet​(A)≥0.95}, and the false-positive rate, PFP=Pdet(0).P_{\rm FP}=P_{\rm det}(0).PFP​=Pdet​(0). Version v0.6r2 includes: 1. synthetic observation models for residual and nuisance channels;2. white-noise, high-noise, correlated-drift, heating-mimic, and mixed-nuisance scenarios;3. morphology-score and signal-to-noise recovery criteria;4. a multi-channel admission rule requiring at least two non-current channels to pass;5. matched-control subtraction for heating-like nuisance;6. false-positive and detection-probability curves;7. sensitivity tables and CSV outputs;8. an application-readiness ladder from toy positive control to device-screening protocol;9. laboratory deployment requirements for a future calibrated experiment;10. device-facing output interpretation tables. A key outcome of the synthetic study is that heating-like nuisance can overlap strongly with the residual morphology and can therefore create false-positive hazards if not controlled. The v0.6r2 update explicitly treats this issue by introducing matched-control subtraction and by distinguishing raw nuisance-contaminated recovery from controlled recovery. The application-readiness ladder used in this version is: - L0: toy positive-control morphology;- L1: synthetic-noise recovery and false-positive stress test;- L2: calibrated synthetic noise using measured device noise floors;- L3: laboratory pilot with real Josephson/SQUID data;- L4: device-screening protocol for phase-noise and barrier-quality diagnostics. The current v0.6r2 manuscript is positioned at L1. It is therefore a synthetic sensitivity and application-readiness note, not a calibrated laboratory demonstration. The included files provide the PDF manuscript, LaTeX source, figure-generation script, synthetic sensitivity summary CSV, detection-curve CSV, matched-control example CSV, simulation metadata JSON, and a source bundle for reproducibility. This work is a companion device-facing diagnostic note following the broader protocol record *Prediction and Discriminating Experiments for the Residual Clock–Energy Framework*, Version v0.4r1, DOI: 10.5281/zenodo.19846816.
This preprint presents a single-author computational proof of concept connecting two-level-system-sensitive Josephson-junction scattering with Quantum Determinant Estimation and device-aware noise modelling. The algorithmic foundation is the Quantum Determinant Estimation protocol of J. Agerskov and K. Splittorff, which uses a completely antisymmetric state to transform the determinant of a unitary matrix into an eigenphase accessible through Quantum Phase Estimation. The physical motivation is the work of J. T. Heath, M. K. Svendsen, and collaborators on localized Josephson hot spots produced by two-level systems in superconducting Josephson junctions. The calculation constructs a unitary two-channel reference scattering matrix and a TLS-modified response. The relative matrixR(E,ϕ)=STLS(E,ϕ)S0†(E,ϕ)R(E,\phi)=S_{\mathrm{TLS}}(E,\phi)S_0^\dagger(E,\phi)R(E,ϕ)=STLS(E,ϕ)S0†(E,ϕ)defines a defect-sensitive determinant phase that is estimated using the antisymmetric-state determinant-QPE protocol. The study includes effective Al, Ta, and Nb interface/bulk configurations, determinant-phase convergence, controlled device-level proxy mappings, finite-register and finite-shot validation, explicit qubit–TLS dynamics, and comparisons between persistent TLS noise and a matched Markovian relaxation model. The original contribution is the computational bridge between a TLS-sensitive scattering observable, determinant-phase estimation, and algorithm-level reliability under structured defect noise. The current scattering matrices, material mappings, linewidths, energy calibration, operation durations, and dynamical coupling strengths are transparent proof-of-concept assumptions. The work does not claim experimentally calibrated material predictions, quantum advantage, uncertainty-robust material identification, or a rigorous non-Markovianity witness. A planned microscopic extension will implement the published Josephson-hot-spot relations, reproduce their spatial and material trends, and use source-derived observables to calibrate the effective determinant and noise models. Preprint status: This manuscript has not undergone peer review. The associated source code and reproducibility package are deposited separately on Zenodo.
**Version v0.5 — Journal-Polish Update** This manuscript develops a conservative extension framework for Schrödinger dynamics in which an observed quantum system is embedded into an enlarged Hilbert space equipped with an auxiliary clock-information fiber. The fiber is not introduced as a macroscopic hidden spatial dimension, nor as a local hidden-variable register. Instead, it is treated as a quantum auxiliary sector carrying phase memory, clock/reference correlations, and correlation records that may appear as information loss or dephasing after partial tracing. The central contribution of this version is a residual-identifiability framework. Rather than claiming that unitary dilation itself is new, the paper asks whether a calibrated observed system can exhibit structured residuals after independent-bath subtraction and common-bath controls. The main diagnostic object is a log-residual statistic, Rχ(t;σref)=log⁡Cobs(t;σref)−log⁡Cind(t;σref),R_\chi(t;\sigma_{\rm ref})=\log C_{\rm obs}(t;\sigma_{\rm ref})-\log C_{\rm ind}(t;\sigma_{\rm ref}),Rχ​(t;σref​)=logCobs​(t;σref​)−logCind​(t;σref​), together with reference-covariance indices such as Iχ(t;σref)=∂σrefRχ(t;σref),\mathcal I_\chi(t;\sigma_{\rm ref})=\partial_{\sigma_{\rm ref}}R_\chi(t;\sigma_{\rm ref}),Iχ​(t;σref​)=∂σref​​Rχ​(t;σref​), and covariance/correlation-based diagnostics over controlled reference settings. The framework emphasizes that a nonzero residual alone is not sufficient evidence for an admissible clock-information fiber. A candidate residual must be non-factorizing, reproducible, reference-covariant, and not absorbed by independent local bath models, common classical noise, or generic common quantum bath controls. In particular, the admissible-fiber hypothesis is treated as a residual diagnostic condition, not as a proof of a new hidden variable, superluminal channel, or macroscopic extra dimension. The paper proves the elementary consistency statements for the enlarged dynamics: total unitarity under a self-adjoint total Hamiltonian, total energy conservation for time-independent generators, subsystem entropy growth under partial trace, and no-signalling compatibility under local trace-preserving operations. It also presents minimal toy models for phase-memory dephasing, shared-fiber cross-kernels, compact protected fiber sectors, and synthetic residual-fitting demonstrations. The synthetic fitting layer uses a representative model of the form $$C_{\rm obs}(t;\sigma_{\rm ref})=C_{\rm ind}(t)\exp[-a(\sigma_{\rm ref})t^2],\qquada(\sigma_{\rm ref})=a_0+a_1\sigma_{\rm ref}^2,$$ so that Rχ(t;σref)=−a(σref)t2.R_\chi(t;\sigma_{\rm ref})=-a(\sigma_{\rm ref})t^2.Rχ​(t;σref​)=−a(σref​)t2. This example is intended as an identifiability demonstration: after calibrated independent-bath subtraction, a candidate clock-information fiber signature should appear as a reproducible residual with controlled reference covariance, rather than as an arbitrary fitting term. The experimental outlook focuses on Ramsey/spin-echo baselines, dynamical-decoupling response, superconducting qubit and Josephson platforms, tunneling phase-delay diagnostics, and reference-modulation protocols. The manuscript also formulates a common-bath control envelope, ∣Rχ(t;σref)−Rctrl(t;σref)∣≤δR(t;σref),|R_\chi(t;\sigma_{\rm ref})-R_{\rm ctrl}(t;\sigma_{\rm ref})|\le\delta_R(t;\sigma_{\rm ref}),∣Rχ​(t;σref​)−Rctrl​(t;σref​)∣≤δR​(t;σref​), to express the requirement that a proposed fiber residual should not be absorbed by generic common-bath control models within statistical uncertainty. ### Main updates in v0.5 - Shortened journal-style title and abstract.- Removal of version-history language from the abstract.- Strengthened common-bath control criterion.- Addition of a formal common-bath control envelope.- Improved diagnostic separation between independent local baths, common classical noise, generic common quantum baths, and admissible clock-information fibers.- Algorithm-style synthetic residual-identifiability test.- Synthetic residual-fitting demonstration using reference-covariant dephasing.- Improved table formatting and manuscript presentation for journal-style readability. ### Scope and non-claims This work should be read as a structured framework for residual diagnostics in extended Schrödinger dynamics. It is not a hidden-variable theory, not a superluminal-signalling model, not a derivation of measurement collapse, and not a completed microscopic theory of mass, charge, or quantum gravity.
I present a falsification-first experimental protocol for testing a proposed record-dependent contribution to residual dephasing in circuit-QED systems. The protocol is designed to distinguish a genuinely record-dependent residual from conventional apparatus-mediated effects introduced by manipulating record persistence itself. The protocol separates post-decoupling readiness controls from concurrent source-hypothesis tests; requires uncertainty-bounded contrasts between record-establishment conditions while controlling conventional physical channels; treats conventional explanations through calibration-compatible nuisance-model families where appropriate; and distinguishes nominal shot count from effective independent information under device, day, and miniblock correlations. It further requires operator discrimination, explicit conventional-noise accounting, preregistered decision rules, and independent device or architecture replication before any anomalous residual is eligible for escalation. A one-page laboratory handoff accompanies the paper to provide an implementation-oriented summary of the experimental decision path. Origin and relationship to prior work: This protocol was motivated by Francisco José Ruiz Izaguirre's phenomenological proposal concerning record-dependent residual dephasing (DOI: 10.5281/zenodo.22162999) and subsequent public technical exchange with the author. It is an independent falsification protocol, not an experimental confirmation of that proposal. No anomalous dephasing effect is claimed here.
TSR-Q-1 presents a preregistered and falsifiable experimental protocol designed to test for structured late-time coherence residuals in superconducting transmon qubits. The protocol does not treat generic recoherence, non-exponential decay, or non-Markovian behavior as evidence for the proposed framework, since such phenomena may arise from conventional open-system mechanisms. Instead, it targets a specific normalized temporal scaling law, tₙ/T₂ = nᵏ, with the preregistered theoretical value k* = 1.4706, corresponding to the first two target locations t₂/T₂ = 2.7714 and t₃/T₂ = 5.0310. If the associated amplitude-scaling hypothesis is retained, the predicted ratio is A₃/A₂ ≈ 0.551. The accompanying computational validation package develops the analysis pipeline through five stages: preliminary signal injection, blind null testing, blind injection-recovery, multi-qubit global-k inference, and sensitivity mapping. The synthetic null models include stretched-exponential decay, 1/f^α correlated noise, random-telegraph/TLS-like contributions, slow drift, white noise, and device-to-device variability. These simulations validate the detectability, specificity, and sensitivity of the proposed analysis procedure under the tested synthetic noise families. They do not constitute experimental evidence for the existence of the predicted physical effect. The next stage is a preregistered hardware implementation using superconducting qubits, with device-specific null calibration, blind analysis, systematic controls, held-out replication, and, ultimately, independent experimental replication.
Version v1.0. This work develops a minimal effective framework for residual-sourced operational-time rescaling in a U(1)U(1)U(1) phase sector. The gauge-invariant residual one-form α=dΦ−A\alpha = d\Phi - Aα=dΦ−A is used to define a positive phenomenological clock response Lα=L0exp⁡(−λ∣α∣h2),dT=Lα ds.L_\alpha = L_0 \exp\left(-\lambda \vert{}\alpha\vert{}_h^2\right), \qquad dT = L_\alpha \, ds.Lα​=L0​exp(−λ∣α∣h2​),dT=Lα​ds. In the scalar-lapse sector, the generator with respect to operational time is KT=Lα−1Hs.K_T = L_\alpha^{-1} H_s.KT​=Lα−1​Hs​. Consequently, generator variance and pure-state quantum Fisher information scale as Lα−2L_\alpha^{-2}Lα−2​, while the Bures line element of the same physical trajectory remains invariant under the reparameterization. The scalar lapse therefore changes information rate per unit operational time without, by itself, producing an intrinsic change in the quantum-state geometry. Independently of this kinematic construction, the paper considers an effective residual gradient flow α˙=−∇admA\dot{\alpha} = -\nabla_{\mathrm{adm}} \mathcal{A}α˙=−∇adm​A on a fixed Hilbert configuration space. This yields the Lyapunov identity ddTA[α(T)]=−∥∇admA∥H2≤0\frac{d}{dT} \mathcal{A}[\alpha(T)] = -\Vert{}\nabla_{\mathrm{adm}} \mathcal{A}\Vert{}_H^2 \le 0dTd​A[α(T)]=−∥∇adm​A∥H2​≤0 and a monotone residual-dissipation functional. The dissipative law is an additional effective assumption and is not derived from the lapse law or from generator rescaling. The manuscript also separates the covariant gauge-invariant core from the foliation-dependent positive spatial norm entering the operational lapse, clarifies the distinction between Fisher-information-rate rescaling and intrinsic Bures geometry, and records the correction required when the background geometry is time dependent. The model is not proposed as a microscopic or fundamental theory of time, irreversibility, decoherence, or quantum measurement. Its purpose is structural: to isolate a common residual variable that can enter clock normalization, generator rescaling, and an independently assumed effective relaxation while keeping their logical dependencies explicit. The paper identifies several open problems required for a more predictive theory, including a microscopic derivation of the clock-response law, a controlled derivation of dissipative mobility, a covariant dynamical clock or foliation sector, quantitative cross-channel observables, and independent empirical tests.