Theoretical treatise on transitioning the QITE formalism (Quantum-Inspired Thermal Equilibrium) from a classical quantum analogy to a quantum-native implementation on real quantum hardware. 21 pages, 12 chapters. Topics: qubit register architecture for the dual eigenvalue system, amplitude encoding of the lambda eigenvalues, entanglement-based BEC synchronization as a replacement for classical Bellman–Ford relaxation, physical quantum interference instead of numerical computation, quantum phase transition of the BEC collective, scaling analysis from 27 qubits (IBM Falcon) to 10,000+ logical qubits, gate counts and error budgets per hardware stage, hybrid classical-quantum architecture with VQE parameter optimization. Central result: the BEC collective on real qubits produces an emergent quantum field with nonlocality, vacuum fluctuations, Goldstone modes, diverging correlation length at the critical point, and topological properties (Berry phase). Reference implementation on IBM Falcon with 108 gates, depth 30, estimated fidelity 78% (92% with zero-noise extrapolation). German patent applications Az. 10 2025 003 906.9 and Az. 10 2025 004 891.2.
Theoretical treatise on transitioning the QITE formalism (Quantum-Inspired Thermal Equilibrium) from a classical quantum analogy to a quantum-native implementation on real quantum hardware. 21 pages, 12 chapters. Topics: qubit register architecture for the dual eigenvalue system, amplitude encoding of the lambda eigenvalues, entanglement-based BEC synchronization as a replacement for classical Bellman–Ford relaxation, physical quantum interference instead of numerical computation, quantum phase transition of the BEC collective, scaling analysis from 27 qubits (IBM Falcon) to 10,000+ logical qubits, gate counts and error budgets per hardware stage, hybrid classical-quantum architecture with VQE parameter optimization. Central result: the BEC collective on real qubits produces an emergent quantum field with nonlocality, vacuum fluctuations, Goldstone modes, diverging correlation length at the critical point, and topological properties (Berry phase). Reference implementation on IBM Falcon with 108 gates, depth 30, estimated fidelity 78% (92% with zero-noise extrapolation). German patent applications Az. 10 2025 003 906.9 and Az. 10 2025 004 891.2.
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)
On 4-5 July 2026, an identical shock protocol was executed on the same 156-qubit IBM Heron R2 architecture (ibm_fez) but with the QITE lambda feedback replaced by uniformly random rotation angles per cycle. This random-angle null control preserves every structural variable — RY+RZ+CZ layer, Heavy-Hex CZ coupling, 4096 shots/cycle, seed 20260602, the same 150 cycles, and the same six shocks at the same cycles (20/40/60/80/100/120), the same target qubits (q78, q69, q67, q47, q37, q16) with the same amplitudes (l1,l2) — while removing only the decentralized per-qubit lambda feedback dynamics. Backend selection was driven by queue availability; both are 156-qubit Heron R2 devices with identical architecture, and calibration differences cannot account for the qualitative burst-count contrast reported below. The result is a clean negative: zero collective bursts across all six shocks. The four non-parametric statistical tests (identical methodology to v1) all confirm the absence of shock-driven collective response: (1) permutation test yields p = 1.0 for shock alignment against the noise-saturated per-cycle transitions; (2) pairwise Pearson correlation between per-transition delta-p1 vectors drops from r_mean = +0.65 in the multi-shock run to r_mean = +0.017 in the null; (3) cross-session hypergeometric overlap between null "top-active" qubits and the v1 multi-shock top-active set is not significant (Jaccard = 0.11, p = 0.24); (4) Mann-Whitney U on shock-cycle max|delta p1| versus baseline shows ratio 0.989 with p = 0.89 — statistically indistinguishable from noise. Baseline global coherence exp(-8*Var(p1)) sits at 0.413 +/- 0.022 across all 150 cycles under random angles, versus 0.99 +/- 0.01 under QITE feedback in v1 — two distinct dynamical regimes. That the shock protocol itself executed correctly on the null run is verified locally at the target qubit: for each of the six shocks, the measured p1[q_target] at the shock cycle agrees with the theoretical prediction from theta_shock = 2*atan2(l2, l1) to within <5% (q78 shock: predicted 0.016, measured 0.018; q69 shock: predicted 0.985, measured 0.939; and so on for all six). One cycle after each shock, the target qubit returns to the random baseline distribution — with no feedback dynamics, there is no restoring trajectory. The shocks are physically executed; what is absent is the collective response. Causal conclusion: the QITE per-qubit lambda feedback dynamics are necessary for the observed collective burst phenomenology. The circuit structure (RY+RZ+CZ on Heron R2 Heavy-Hex topology) and shock protocol alone do not produce bursts. Six identical shocks on QITE-stabilized baseline produce 10 collective bursts with 6/10 shock-aligned (p = 0.008); the same six shocks on random baseline produce zero. This 10-vs-0 hardware contrast, verified by four independent non-parametric tests, establishes feedback necessity as a falsifiable causal claim rather than a phenomenological observation. The v2 bundle contains the complete null-control primary data (150-cycle JSONL, consolidated JSON, p1 numpy matrix), all IBM Runtime job IDs with per-cycle timestamps, Tee'd console logs of both the initial run and the resume run (a mid-run job-poll stall on 4 July required a resume from cycle 7 with deterministic per-cycle RNG seeds), five analysis figures including direct null-vs-multi comparison plots, the full side-by-side statistical comparison JSON, the v1 multi-shock p1 matrix and statistical test outputs for reanalysis, an 8-page supplement PDF (Section 5) integrating with the v1 paper, and SHA-256 checksums of every file in MANIFEST_v2.json. Backend (v2 null control): IBM Heron R2 (ibm_fez), 156 qubits, 4096 shots/cycle.Companion patents: DPMA Az. 10 2025 003 906.9 (QITE), 10 2025 004 891.2 (QISE).Predecessor (v1): Westrick, Reproducible Collective Burst Modes on 156 Qubits: Decentralized Per-Qubit QITE Lambda Field on IBM Heron R2, 1 June 2026. On 1 June 2026, a decentralized per-qubit lambda field was implemented on the IBM Heron R2 processor (ibm_kingston, 156 qubits) and probed with a multi-shock excitation protocol. Unlike the predecessor work (Westrick, Controllable Quantum Collective States on 156 Qubits: Experimental Results of the QITE Formalism on IBM Heron R2, 12 April 2026), which tested a globally controlled QITE quantum collective, each qubit here carries its own lambda state and receives, in the feedback loop, only its own measurement statistic p1_i. The only inter-qubit coupling propagates physically through the CZ gates of the Heavy-Hex topology. Six shocks were applied at six different positions on the chip: central (q*=78), nearest neighbor (d=1), intermediate (d=3, d=5), deep (d=8), and edge (d=12). Each individual shock triggered a chip-wide burst within 1-8 cycles (peak |delta p1| between 0.308 and 0.366; 10 to 22 simultaneously active qubits). Four additional spontaneous bursts were detected between shocks, for a total of 10 bursts in 150 cycles. The 6/6 reproducibility was verified by four independent non-parametric statistical tests, all positive: (1) permutation test p = 0.008 against chance alignment; (2) pairwise burst-vector Pearson correlation r_mean = +0.65 with all 15 pairs above noise; (3) cross-session reproducibility 9/10 qubit overlap between two independent IBM Quantum sessions, hypergeometric p = 0.008; (4) Mann-Whitney U test of burst amplitude versus Phase-A baseline, ratio 2.7, p < 0.0001. This bundle contains the complete primary data (raw JSON logs, NumPy matrices), all 27 visualizations, IBM job IDs of every submitted job, console logs of all runs, the pre-registration documents with locked detection thresholds, and SHA-256 checksums of every file (MANIFEST.json) for independent verification. Backend: IBM Heron R2 (ibm_kingston), 156 qubits, 4096 shots/cycle.Patent filings: DPMA Az. 10 2025 003 906.9 (QITE), 10 2025 004 891.2 (QISE).Predecessor: Westrick, Controllable Quantum Collective States on 156 Qubits, 12 April 2026.
Die Verknüpfung von Qubits gehört zu den aktuellen Herausforderungen der Quantentechnologie. Dies betrifft einerseits Systeme, die weit voneinander entfernt sind, als auch hybride Systeme, in denen unterschiedliche Realisierungen der Qubits ihre individuellen Stärken ausspielen und anschließend den Quantenzustand auf einen anderen Typ übertragen sollen. In dieser Arbeit wird ein Mischcryostat vorgestellt, der Supraleiter auf Temperaturen unterhalb hundert Millikelvin abkühlen kann und zugleich eine Apparatur zur Präparation von ultrakalten Atomen enthält. Es konnte gezeigt werden, dass es möglich ist, ultrakalte Atomwolken in dieser Umgebung zu präparieren und zu manipulieren. Im nächsten Schritt müssen die Atomwolken in die Millikelvin-Umgebung transportiert und an einen Chip mit funktionalen supraleitenden Elementen herangeführt werden. Zwar steht die Demonstration des Austausches von Quanteninformation noch aus, dennoch stellt dies einen bedeutenden Schritt in Richtung eines hybriden Quantensystems dar. Es ist von zentraler Bedeutung, den Wärmeeintrag in die Millikelvinumgebung zu minimieren. Gleichzeitig erfordern die typischen magnetischen Fallenpotentiale Ströme im Bereich einiger Ampere. Konventionelle Spulen aus supraleitenden Drähten erzeugen zwar keine Heizleistung, allerdings verbleibt ein Wärmeeintrag durch Wärmeleitung. Einen Ausweg bieten geschlossene supraleitende Schleifen, die von einem permanenten Strom durchflossen werden. In dieser Arbeit wurde die Idee der Baseball-Falle aufgegriffen, die mit einem einzelnen Strompfad eine vollständige Falle realisiert. Dies wurde in einem zweiten System mit einer supraleitenden Schleife umgesetzt. Eine zusätzlich angebrachte konventionelle Spule koppelt magnetischen Fluss in die Schleife ein, wodurch der permanente Strom moduliert werden kann. Diese Spule kann sich an einer anderen Temperaturstufe des Cryostaten befinden, so dass auch die Wärmeleitung unterbunden wird. Als Vermittler zwischen unterschiedlichen Qubits können Rydberg-Atome eine Schlüsselrolle einnehmen, da ihr Anregungsspektrum einen weiten Frequenzbereich überdeckt. Ihre Sensitivität gegenüber elektrischen Feldern erfordert allerdings eine sorgfältige Betrachtung der Umgebung und ggf. eine Abschirmung oder Kompensation der Störfelder. In der vorliegenden Arbeit wurde ein Referenzsystem aufgebaut, an dem die absoluten Übergangsfrequenzen mit verbesserter Genauigkeit ermittelt und der Einfluss externer Felder untersucht wurden. Auf dieser Basis können nun die Korrekturen vorgenommen werden. Als Referenz für die Frequenzmessungen dient bislang ein Mikrowellenübergang. Verwendet man stattdessen einen optischen Übergang, so wird die Zeit in kleinere Abschnitte unterteilt und somit die Unsicherheit reduziert. Diese optischen Uhren aus neutralen Atomen haben bislang den Nachteil, dass die Messung destruktiv erfolgt. Durch die erneute Präparation steht die Uhr nur einen Bruchteil der Zeit zur Verfügung. Hier wurde ein Konzept erarbeitet, das den Betrieb einer kontinuierlichen optischen Uhr ermöglichen soll. Die erste Stufe der Präparation eines Ensembles ultrakalter Atome konnte bereits demonstriert werden. Im weiteren Verlauf ist eine zweite Präparationsstufe, sowie eine Spektroskopie erforderlich. Letztendlich ist die Anbindung des bestehenden Frequenzkamms geplant, um die erhöhte Genauigkeit auch auf andere Frequenzbereiche zu übertragen. Die erzielten Erkenntnisse tragen zur Weiterentwicklung der Quantentechnologien bei. Einerseits bieten sie die Perspektive Quanteninformationsverarbeitung mit hybriden Systemen aus Supraleitern und ultrakalten Atomen durchzuführen. Dabei kann die optische Schnittstelle mehrere derartige Systeme auch über große Entfernungen miteinander verknüpfen und so die Vision eines Quanten-Internets wahr werden lassen. Optische Uhren werden in absehbarer Zeit die Cäsium-Uhren zur Definition der Sekunde ablösen. Ihre hohe Sensitivität lässt neue Anwendungen in der Metrologie, Geodäsie oder auch Astronomie erwarten.
We present a simple, malleable and low-overhead approach for improving generic biased quantum error mitigation (QEM) methods, achieving up to 15% fidelity improvements over standard QEM on 100-qubit circuits with up to 2000 entangling gates. We do so by constructing verifiable benchmark circuits which mirror the application circuit's native-gate structure and thus noise profile. These circuits can be used to benchmark and mitigate the bias of the underlying error mitigation method, requiring only the application circuit and hardware native gate set. We present two methods for generating benchmark circuits; one is agnostic to the target hardware at the expense of a small overhead of single-qubit gates, while the other is specific to the IBM superconducting hardware and has no gate overhead. As a corollary, we introduce benchmarked-noise zero-noise extrapolation (bnZNE) as a simple adaptation of zero-noise extrapolation (ZNE), one of the most popular error mitigation methods. We consider as an example the bias-mitigated ZNE and bnZNE of Trotterized Hamiltonian simulations, observing that our approaches outperform standard ZNE using both small-scale classical simulations and 100-qubit utility-scale experiments on the IBM superconducting hardware. We consider the measurement of both single-site observables as well as two-site correlations along a one-dimensional qubit chain. We also provide a software package for implementing the error mitigation techniques used in this research.
On 1 June 2026, a decentralized per-qubit lambda field was implemented on the IBM Heron R2 processor (ibm_kingston, 156 qubits) and probed with a multi-shock excitation protocol. Unlike the predecessor work (Westrick, QITE Hardware Results 156Q, 8-12 April 2026), which tested a globally controlled QITE quantum collective, each qubit here carries its own lambda state and receives, in the feedback loop, only its own measurement statistic p1_i. The only inter-qubit coupling propagates physically through the CZ gates of the Heavy-Hex topology. Six shocks were applied at six different positions on the chip: central (q*=78), nearest neighbor (d=1), intermediate (d=3, d=5), deep (d=8), and edge (d=12). Each individual shock triggered a chip-wide burst within 1-8 cycles (peak |delta p1| between 0.308 and 0.366; 10 to 22 simultaneously active qubits). Four additional spontaneous bursts were detected between shocks, for a total of 10 bursts in 150 cycles. The 6/6 reproducibility was verified by four independent non-parametric statistical tests, all positive: (1) permutation test p = 0.008 against chance alignment; (2) pairwise burst-vector Pearson correlation r_mean = +0.65 with all 15 pairs above noise; (3) cross-session reproducibility 9/10 qubit overlap between two independent IBM Quantum sessions, hypergeometric p = 0.008; (4) Mann-Whitney U test of burst amplitude versus Phase-A baseline, ratio 2.7, p < 0.0001. This bundle contains the complete primary data (raw JSON logs, NumPy matrices), all 27 visualizations, IBM job IDs of every submitted job, console logs of all runs, the pre-registration documents with locked detection thresholds, and SHA-256 checksums of every file (MANIFEST.json) for independent verification. Backend: IBM Heron R2 (ibm_kingston), 156 qubits, 4096 shots/cycle. Patent filings: DPMA Az. 10 2025 003 906.9 (QITE), 10 2025 004 891.2 (QISE). Predecessor: Westrick, QITE Hardware Results 156Q (8-12 April 2026).
Die Komplexitat vieler interessanter physikalischen Systeme macht es nahezu unmoglich diese auf herkommlichen Computern zu simulieren. Feynmans Idee eines Quantensimulators fur komplexe Systeme von 1982 bietet die Moglichkeit komplexe Phanomene ausserhalb der Reichweite eines normalen Computers mithilfe von massgeschneiderten Hamiltonians zu studieren. Die Welt der ultrakalten Atome bietet dafur mit unerreicht sauberen Quantengassystemen und flexiblen aber hoch prazise kontrollierbaren Parametern hervorragende Eigenschaften. Ultrakalte Quantengase sind daher ein perfektes Werkzeug fur die Realisierung von Quantensimulatoren und der Untersuchung von Phasenraumdiagrammen von Modellsystemen. Diese Arbeit stellt ein neues Experiment fur Bose-Fermi-Mischungen im Hinblick auf Quantensimulationen in optischen Gittern und willkurlichen Lichtpotentialen mit hoher optischer Auflosung fur Detektion und Manipulation vor. Der Aufbau einschliesslich neuer Technologieentwicklungen wurde auf hohe Wartungsfreiheit und Robustheit optimimiert. Beide Quantenstatistiken und verschiedene Wechselwirkungsregime werden mit Hilfe von Feshbachresonanzen untersucht werden konnen. Alle Entscheidungen bezuglich des Designs und des Aufbaus wurden hinsichtlich der Umsetzung von optischen Gittern und eines hochauflosenden Abbildungssystems getroffen. Das magneto-optische Fangen von Bose-Fermi-Mischungen mit 87Rb und 40K und die Bose-Einstein Kondensation (BEC) von 87Rb wurde erstmals in dieser Arbeitsgruppe verwirklicht. Das Laserkuhlen mit divergenten Strahlen wurde dabei erfolgreich demonstriert. Im Rahmen neuer Technologieentwicklungen wurde ein robustes, flexibles, miniaturisiertes Lasersystem fur zwei unterschiedliche Spezies zur Laserkuhlung designt, aufgebaut und getestet. Ein neues kompaktes Spulendesign mit hohem optischen Zugang und geringer Verlustleistung wurde entwickelt und fur die Realisierung des BECs verwendet. Dabei ist einer der Magnetspulensatze fur homogene Magnetfelder fur die Anwendung von Feshbachresonanzen optimiert worden. Desweiteren wurde eine vielseitige Vakuumversiegelungstechnik mit Indium realisiert. All diese Technologieentwicklungen zielen auf einen kompakten und robusten Aufbau mit hoher Flexibilitat ab. Die Atome werden zunachst in einem 2D-3D MOT Komplex eingefangen und lasergekuhlt. Danach werden die Atome magnetisch gefangen und mithilfe beweglicher Spulen zur Science chamber transportiert. RF Evaporation in der magnetischen Quadrupolfalle kuhlt das Ensemble soweit herunter, dass die Atomwolke in eine optische Dipolfalle geladen werden kann in welcher weitere Evaporation zur Bose-Einstein Kondensation von 87Rb fuhrt. Der Aufbau hat somit das Regime der Quantengase erreicht, eine notwendige Vorraussetzung fur Quantensimulationen mit ultrakalten Atomen.
Many interesting physical systems have one thing in common. Their complexity makes it impossible to simulate them on conventional computers. Feynman's idea of a quantum simulator for complex systems from 1982 gives the possibility to study complex phenomena out of the reach of normal computers with tailored Hamiltonians. The world of ultra cold atoms offers a wide range of tunable parameters combined with a degree of control in unprecedented clean systems. Ultra cold quantum gases are the ideal tool for the realisation of quantum simulators and the study of phase diagrams of model systems. This thesis presents a new setup for Bose-Fermi mixtures experiments with regard to quantum simulations in optical lattices and arbitrary light potentials with a high resolution for detection and atom manipulation. The setup was designed to be a low maintenance, robust tool box for quantum simulations incorporating new technology developments. Both fundamental quantum statistics can be observed and different interaction regimes can be investigated with the help of Feshbach resonances. From the beginning all decisions concerning the setup design take the implementation of optical lattices and a high resolution imaging system into account.
The magneto-optical trapping of Bose-Fermi mixtures with 87Rb and 40K and the Bose-Einstein condensation (BEC) of 87Rb had been achieved. Another aim in the context of this thesis was the development and testing of new versatile technologies. A robust, flexible, miniaturised dual species laser system for laser cooling had been setup and tested. A new narrow coil design allowing for high magnetic fields with great optical access at a low power dissipation had been developed and used for the realisation of the BEC. One of the magnetic coil sets had been optimised for homogeneous magnetic fields for the application of Feshbach resonances. Furthermore an indium sealing technique for vacuum chambers had been realised. All these technology developments aimed for a compact and robust setup with high flexibility. For the procedure the atomic sample was first laser cooled and trapped in a combined 2D-3D MOT complex before the atoms are magnetically trapped and transported with a linear rail over a macroscopic distance to the science chamber. In the science chamber the atoms were transferred to a different magnetic trap where forced RF evaporation cooled the atomic cloud further down. Loading the atomic cloud into an optical dipole trap and further evaporation lead to the Bose-Einstein condensate of 87Rb. Hence, the setup reached the quantum regime necessary for quantum simulation for further studies.