Quantum Stabilization Dynamics (QSD) is a framework for monitoring and controlling multichannel dynamical systems — quantum processors, solar-wind plasma, gravitational-wave detectors, optical links. It begins with a scalar coherence-field Lagrangian and derives, through four successive layers, a closed-form stability bound: angular error decays geometrically and stays bounded under any external disturbance. The central structural result proves that the TriDelta covariance coordinates are exact algebraic functions of two-node sync-model parameters, and that a unique operating angle θ* = 22.48° emerges from the TriLock balance condition. IBM quantum hardware (ibm_fez, 156-qubit) independently measures θ_source = 22.47° across 9/9 positive-gain passes — within measurement precision of the theoretical value. Validation covers nine real-instrument events across five domains: solar X-rays, solar wind, geomagnetic activity, gravitational waves, and optical links. Heterogeneity is zero (I² = 0%), pooled signal Zθ = +36.2 ± 2.4. Every free parameter is explicitly identified and accounted for.Provisional Patent #64/035,024 (April 10, 2026). GitHub: https://github.com/apmannino-design/qsd-phase-bounded-transport
Quantum Stabilization Dynamics (QSD) is a framework for monitoring and controlling multichannel dynamical systems — quantum processors, solar-wind plasma, gravitational-wave detectors, optical links. It begins with a scalar coherence-field Lagrangian and derives, through four successive layers, a closed-form stability bound: angular error decays geometrically and stays bounded under any external disturbance. The central structural result proves that the TriDelta covariance coordinates are exact algebraic functions of two-node sync-model parameters, and that a unique operating angle θ* = 22.48° emerges from the TriLock balance condition. IBM quantum hardware (ibm_fez, 156-qubit) independently measures θ_source = 22.47° across 9/9 positive-gain passes — within measurement precision of the theoretical value. Validation covers nine real-instrument events across five domains: solar X-rays, solar wind, geomagnetic activity, gravitational waves, and optical links. Heterogeneity is zero (I² = 0%), pooled signal Zθ = +36.2 ± 2.4. Every free parameter is explicitly identified and accounted for.Provisional Patent #64/035,024 (April 10, 2026). GitHub: https://github.com/apmannino-design/qsd-phase-bounded-transport
Experimental measurement data of the QITE formalism (Quantum-Inspired Thermal Equilibrium) on IBM quantum processors of the Heron R2 generation with 156 physical qubits. Altogether 75+ jobs on two different backends (ibm_kingston and ibm_fez), over 830,000 shots, carried out on 8, 10, and 11 April 2026. Seven experiment series: (1) Static phases (R=0.5 / 1.0 / 2.0): three clearly separated Hamming-weight distributions (16.3σ significance), positive ZZ correlations under QITE (+0.318 at R=2.0) versus negative ones in the null experiment (−0.061). Controlled comparison experiment with null hypothesis (identical circuit structure with random parameters). (2) Real-time feedback loop (8 cycles): two targeted perturbations (R=3.0 and R=0.3); the system returns autonomously to equilibrium within 2 cycles. First demonstration of dynamic controllability of a QITE quantum collective on a real quantum computer. (3) Cross-backend reproducibility: identical results on ibm_kingston and ibm_fez — deviations within a few percent. (4) Zero-noise extrapolation (ZNE): circuit folding (1×, 3×, 5×) with Richardson extrapolation. Result: coherence 0.474 → 0.474 extrapolated (improvement: −0.0005). The optimized circuit (depth 13, 120 CZ gates) already operates at the hardware noise floor — ZNE cannot improve it further because the circuit is already near-optimal. (5) Scaling comparison 27 vs. 156 qubits: the 27-qubit version on the same backend (ibm_kingston) shows ZZ correlation of 0.788 against 0.318 at 156 qubits (Δ = +0.470). Circuit depth drops from 13 to 6, CZ gates from 120 to 13. Confirms: the QITE signal scales with gate quality. (6) Extended feedback loop (20 cycles): four extreme perturbations — R=3.0 (excess), R=0.3 (deficit), R=5.0 (5-fold excess), R=0.1 (10-fold deficit). Maximum coherence C=0.785 (highest value ever measured). The system reorganizes itself after each perturbation within 2–4 cycles. Long-term stability demonstrated across 20 cycles and 436 seconds of total runtime. (7) 3-minute stability demonstration (20 cycles, 262.7 seconds): dedicated long-term test with two targeted shocks (R=4.0 and R=0.2). Result: ones_fraction remains between 0.491 and 0.499 over 4.4 minutes (maximum deviation from equilibrium: 0.009). Drift across the entire runtime: +0.003. Complete recovery after both shocks. 18/18 non-shock cycles stable. First demonstration of a self-correcting quantum field on a real quantum computer over several minutes. Circuit optimization relative to 8 April: reduction of circuit depth from 295 to 13 (factor 22×), two-qubit gates from 1,946 to 120, by exclusive use of native Heron R2 gates (CZ, SX, RZ, X) and direct lambda encoding via RY(θ) with θ = 2·arctan(λ₂/λ₁). The system demonstrably produces controllable, correlated, self-organizing quantum states on real hardware — no simulation, no theory, but physical measurement data of a concrete technical system. All 59 IBM job IDs are contained in the raw data and verifiable on quantum.ibm.com. German patent applications Az. 10 2025 003 906.9 (QITE) and Az. 10 2025 004 891.2 (QISE). Final document (12 April 2026) — 21 sections, 9 experiment series, 372 individual quantum measurements. Extensions compared to the previous version: Section 19: 9-minute experiment (209 cycles, 156 qubits, 4096 shots) Phase A: null test (23 cycles, R=1.0) — baseline control measurement Phase B: 8 shocks (R=0.1 to R=8.0) incl. double shock — complete recovery after each shock Section 20: overall summary of all 9 experiment series (8–12 April 2026) Section 21: raw-data appendix with SHA-256 checksums of all 9 JSON files Core results: 372 quantum measurements on IBM Heron R2 (ibm_kingston, ibm_fez) Dynamic range R=0.1 to R=8.0 (factor 80) with complete self-correction The null test proves: recovery is an active process, not a hardware artefact No drift, no collapse across 209 consecutive measurements Optimized circuit: depth 13, 120 CZ gates, at the hardware noise floor (ZNE-confirmed)
Quantum Spectrodynamics (QSD) is a framework for deriving physical dynamics from eigenvalue spectra of quantum error correction codes. Its starting point is an observation: The universe is suspiciously stable. An isolated qubit in the best laboratory on Earth decoheres in microseconds. A warm, dense, radiation-bathed universe has maintained coherent, lawful, persistent structure for 13.8 billion years — the same particles, the same couplings, the same interference phenomena, everywhere we look. Quantum states are fragile; the quantum universe is not. Physics knows exactly one class of systems that preserve quantum information against continuous noise: error-corrected ones. QSD takes that observation as its single structural axiom: (L0) The universe is a quantum error-correcting code [[n,k,d]]q — with all four parameters initially unknown. Everything else is derivation. The code parameters are selected, not chosen: a seven-step exclusion chain plus Landauer's thermodynamic principle single out the perfect five-qubit code [[5,1,3]]2 as the unique minimal, thermodynamically ground-state solution. The selected code's geometry then fixes three constants, and those constants fix the dynamics. QSD is a framework for deriving physical dynamics — not, specifically, a model of the Standard Model. The Standard Model sector (gauge couplings, masses) is its first worked application (v1.0, this repository's original release); the same machinery derives the code-selection theorem itself and gravitational dynamics (Phase 2, releasing incrementally as v2.x). - Holographic bit density Hb4=1/(4ln2) — from K4 (the n−k=4 stabiliser/face count; the Bekenstein–Hawking factor 4 is a consequence) - Spectral bond ϖ=πφ2 — from C5 (spectral class ratio φ2) - Geometric strain ς=3/(80φ2) — from K4∪C5 (the frustration of the two geometries; the framework's small parameter) Symbol Observable QSD Prediction Experimental Value Agreement α−1 Fine structure constant 137.033137.036−21.7 ppm αs(MZ) Strong coupling at MZ3π/80=0.117810.1180±0.00090.16%sin2θW Weak mixing angle 0.231220.23122±0.00003<0.01%mH Higgs boson mass 126.7 GeV 125.25 GeV 1.3%Esyn Snap energy 28.24 GeV ∼28 GeV* 0.2% * falsifiable 28.24 GeV snap energy coinciding with the CMS dimuon excess at ~28.3 GeV (CMS-PAS-HIG-20-009) A modular record This record grows by parts. Each version adds a self-contained paper with its supplements as a new section; published sources are never rewritten. Part 0 — Phase 1: the Standard Model sector (v1.0, March 2026) Main preprint (quantum_spectrodynamics) + supplements S1–S7 + technical note TN-1, with the computational validation suite and interactive visualizations. S1 formal proofs · S2 energy scale · S3 Lagrangian · S4 topological renormalization (α⁻¹) · S5 the 28 GeV prediction & proton stability · S6 string correspondence · S7 cosmological constant · TN-1 Hb notation. Part 1 — Phase 2, Paper 1: code selection (v2.0, July 2026) P1 — The QECC Selection Theorem (qsd2_p1_code_selection): why [[5,1,3]]2 and nothing else — the seven-step exclusion chain from L0 plus Landauer's principle as the thermodynamic selector. With supplements: S8 — Crossing errors and Deutsch CTCs (qsd2_s8_crossing_ctc): the crossing-error channel is a Deutsch closed timelike curve; fixed-point consistency and its forensic record. S9 — The observer (qsd2_s9_observer): the observer as a code-internal structure; measurement as syndrome extraction. Supplement numbering is programme-wide (S1–S7 phase 1, S8+ phase 2). *(Future parts: P2 node & triad → v2.1 · P3 lattice → v2.2 · P4 transition → v2.3 · P5 Einstein equations → v2.4, each with its supplements. The derivation-walkthrough series and the QSD wiki knowledge base are slated for v3.)* Files on this record - quantum_spectrodynamics.pdf — main preprint (start here) - qsd2_p1_code_selection.pdf — Phase 2 Paper 1 (v2.0 entry document) - qsd2_s8_crossing_ctc.pdf — S8 crossing errors and Deutsch CTCs - qsd2_s9_observer.pdf — S9 the observer within QSD - qsd_pdfs.zip — v1 +v2 + the v1 errata, as PDFs - qsd_v2.0_full.zip — complete repository snapshot (sources, code, visualization) Epistemic transparency Phase 2 documents tag every major claim: [R] rigorous (derived from L0 + established mathematics) [C+] well-supported conjecture (named external premise) [T] thermodynamic principle (empirical) [EXP] exploratory/speculative [O] open problem Phase 1 used the coarser Derived/Constructed/Open scheme; the mapping is one-to-one. Known corrections to published sources are collected in the v1 errata (ships with v2.0); published files themselves stay frozen. Version history Version Date Adds v1.0.0 2026-03 Phase 1: main preprint, S1–S7, TN-1, code, visualizations v2.0.0 2026-09 Phase 2 Part 1: P1 code selection, S8, S9; unified preamble & bibliography; v1 errata; repository restructure (manuscripts/supplements/derivations)
Union Dipole Theory postulates two distinct channels of transfer: the particle moves through the permeable medium at a bounded speed, while a disturbance within that medium is stated to propagate at an unbounded one (Al-Mayahi, 2014). This paper asks what that structure implies for correlated pairs, and obtains the singlet joint distribution and the Tsirelson value from a single principle. The principle is single-valuedness of the internal phase — the same condition that produced the phase-closure result of the companion paper. Applied to a pair, it does two things at once. It indexes admissible transitions by integers, so that a shared pair quantum resolves into one channel and not partly into both. And, applied to the two pair channels as degrees of freedom of the medium, it fixes their action integrals, which for a linear medium are proportional to the stored energy. The channel weights are therefore not an added rule about rates: they are what closure gives. One condition supplies both the counting and the quadratic weighting. The consequences follow without further assumption. Writing the pair on its shared internal phase, the two channel amplitudes are 2cos(θ/2)cos φ and −2sin(θ/2)sin φ. Their closed action integrals stand in the ratio cos²(θ/2) to sin²(θ/2); a single shared quantum normalises them; and the correlation is E = −a·b with a CHSH maximum of exactly 2√2. An inversion symmetry then fixes the four joint outcome probabilities uniquely and makes the single-station marginals exactly one half at every angle, so no-signalling holds for the construction and not only for the architecture. Three negative controls are computed rather than asserted, and each is derived in closed form. Extracting outcomes by any local rule gives −(1 − 2θ/π) and |S| = 2 exactly. Sending the indivisible transition to the channel of larger instantaneous drive gives the same linear correlation and the same value 2, and no threshold weight repairs it. Weighting the channels by amplitude rather than by action gives S = 1.657 at the standard settings and, on optimisation over the four settings, exactly 2. All three controls therefore terminate at the Bell bound, and the distance between 2 and 2√2 is attributable to the closure measure and to nothing else in the construction. Two structural results complete the account. The correlation is independent of distance because it is a ratio: any common factor multiplying both channel weights — the inverse-square attenuation of the medium included — cancels identically between numerator and denominator, so the disturbance law is obeyed in full while the correlation does not register it. And a residual anisotropy of the medium leaves every prediction unchanged: perfect anticorrelation at zero angle survives at every order, and the CHSH maximum remains exactly 2√2 on the circular sections of the response ellipsoid. Finally, generalising the channel weighting to an arbitrary exponent shows that the correlation is an ordinary cosine for exactly one value, n = 2, and that the maximal CHSH value is strictly increasing in the exponent and passes through 2√2 at exactly that value. The position of the quantum ceiling is thereby tied to a constitutive property — the quadratic, that is linearly elastic, response of the medium — which is itself what the closure condition selects. The framework is not a local hidden-variable theory, does not evade Bell’s theorem, and lies outside the class the theorem constrains; this is stated as a classification and not as an achievement. What is read rather than derived is named, and what remains open is named: in particular, no dynamical account is given of how the shared medium delivers the single transition to one channel across two separated stations. Two appendices follow. The first compares the predicted angular form with Bell correlations reported on three physically unrelated platforms, spanning CHSH values from 2.07 to 2.71, all of which report the same angular form: strength varies, shape does not. The second sets out a two-coordinate hardware diagnostic which follows from the result and which is the subject of United Kingdom patent application GB 2619873.9, filed 26 August 2026. Companion papers: Al-Mayahi, A. (2026a). Internal Time as a Counted Quantity. https://doi.org/10.5281/zenodo.22110704 — Al-Mayahi, A. (2026b). Union-Dipole Continuum Electrodynamics. https://doi.org/10.5281/zenodo.22110528
The ability to perform measurements on a quantum system, combined with the ability to feed back the measurement results via coherent control, allows one to control the system to follow any desired coherent or incoherent quantum dynamics. Such universal dynamical control can be achieved, in principle, through the repeated application of only two coherent control operations and a simple ``Yes-No'' measurement. As a consequence, a quantum computer can simulate an arbitrary open-system dynamics using just one qubit more than required to simulate closed-system dynamics.
The χ-spectral framework developed in this work proposes a unified operator-geometric foundation for physical law, integrating quantum measurement, modular state reduction, spectral geometry, and gravitational curvature into a single postulated structure. Physical measurement is formulated as an intrinsic operator-spectral transition generated by the bounded observable M_χ(k) = Φ_χ(k) + B_χ(k) + R_χ(k), which combines phase geometry, boundary tension, and χ-spectral curvature into a non-singular measurement mechanism. Probability amplitudes P_n(k) = |<e_n(k), Ψ_χ>_χ|^2 follow from the postulated χ-inner product structure, reproducing the Born rule within the framework — not as an independent axiom, but as a consequence of the postulated positive-definite inner product geometry. A central claim of the χ-spectral framework is the postulated compatibility between ZEBTS-SUPER gravitational dynamics and quantum mechanics. Gravitational curvature R_χ(k) enters the measurement operator M_χ(k) as a bounded geometric observable, postulated to ensure ultraviolet stability, finite expectation values, and unitarity across all scale layers. Collapse dynamics are formulated as bounded modular projections, postulated to guarantee non-perturbative, divergence-free state reduction. Decoherence is modeled as a structural spectral gradient D_χ(k) = M_χ(k+1) - M_χ(k), providing a proposed geometric mechanism for coherence loss without environmental reservoirs. The scale-layer commutator C_χ(k) = [M_χ(k+1), M_χ(k)] encodes contextuality and order-dependence as structural consequences of χ-operator geometry. Together, these results demonstrate that quantum dynamics, gravitational curvature, measurement theory, and modular collapse are postulated to be compatible and mutually reinforcing within the χ-spectral operator framework. The theory is designed to achieve mathematical closure: all physical observables are postulated to remain bounded, all transitions are postulated to remain unitary, and quantum-gravitational consistency is proposed as a consequence of χ-spectral geometry. The framework is a system of postulates whose scientific value lies in its falsifiable predictions (§7), not in proven closure.
Quantum engineering has seen rapid growth in the past two decades. Physicists, mathematicians and engineers have been working in unison to control a number of diverse systems in the quantum regime. Quantum control involving feedback has become particularly topical, as using information gained from a system can lead to more stable operation of a control protocol. Quantum feedback can be split into two paradigms: measurement based feedback and coherent feedback. Although it is increasingly evident that retaining the coherence of the feedback signal provides an intrinsic advantage over measurement-based feedback, coherent feedback is still a new paradigm. In particular, there are a limited number of options for coherently estimating a state within a feedback loop. As a step towards better understanding and implementation of quantum feedback, this thesis reports on modelling, estimation and control of quantum systems. The first topic is physical realisability of a variety of quantum systems, especially finite level systems and their outgrowths. Bilinear quantum stochastic differential equations (QSDEs) have to be employed to characterise these systems, which is a significant complement to the previous work on linear QSDEs. In light of the fact that direct and indirect couplings play a vital role in quantum network and control, we also provide state-space models for different classes of coupled open quantum systems incorporating both bidirectional and directional interactions. The second topic is coherent observers and optimal filtering. It is well established that classically estimation using the Kalman filter can provide improved performance over direct feedback schemes, and similar demonstrations have been performed for measurement-based quantum feedback. In this thesis I present coherent observers, including least mean squares estimators, which are driven by the coherent output of a specified quantum plant and designed such that some subset of the observer and plant's expectation values converge in the asymptotic limit. Not only can estimators "observe" mean quantities of quantum plant, but also they can "estimate" quantum correlations such as entanglement. This is of much importance to coherent feedback design in the absence of measurement steps without loss of fidelity. Last but not least, several topics regarding stabilisation and control design of quantum systems are discussed in my thesis. To be specific, tools for quantum stability analysis (e.g. Lyapunov conditions) are provided. Both measurement-based feedback and coherent feedback control design are taken into account. A measurement-based optimal controller for opto-mechanical systems aimed at synchronising different mechanical modes is presented, which is application-oriented. Moreover, A general observer-based coherent feedback control framework is studied, and I demonstrate a pole-placement approach via coherent observers that can be applied to various scenarios.