This preprint presents a finite-dimensional quantum-simulation framework for selected TEBAC 9D/9D+ topological phases, with emphasis on synthetic-dimensional encoding, spectral-gap diagnostics, portal-channel observables, and Qiskit-ready Hamiltonian construction. The manuscript formulates a finite-lattice simulation target for the internal TEBAC sector and encodes the model through Pauli-sum Hamiltonians suitable for NumPy exact diagonalization, Qiskit Aer simulation, and future IBM Runtime execution. The central simulation Hamiltonian is organized schematically as\[H_{\mathrm{sim}}=H_{\mathrm{Dirac}}^{(N)}+H_{\mathrm{gauge}}^{(N)}+H_{\mathrm{top}}^{(N)}+H_{\mathrm{channel}}^{(N)}.\] The paper develops a concrete two-qubit benchmark v0.1 and a four-qubit finite-lattice sector v0.2. For the four-qubit sector, the manuscript gives an explicit Pauli decomposition, exact spectrum, spectral-gap diagnostic, topological proxy, link-sector markers, fidelity diagnostic, and determinant diagnostic. A key contribution of this version is the transition from a hardware-ready protocol to an executed local emulator report. The v0.2 four-qubit sector is evaluated through NumPy exact computation and local Qiskit Aer execution, including ideal sampling, readout-noisy sampling, and readout-mitigation recovery. For the topological proxy\[Q_{4}=\langle ZZZZ\rangle,\]the reported values are:\[Q_{4}^{\mathrm{exact}}=0.986000,\]\[Q_{4}^{\mathrm{Aer,ideal}}=0.986572\pm 0.001805,\]\[Q_{4}^{\mathrm{Aer,noisy}}=0.775391\pm 0.006977,\]and\[Q_{4}^{\mathrm{mitigated}}=0.993137\pm 0.008936.\] The manuscript also includes a Qiskit Aer / IBM Runtime execution skeleton, an error-mitigation roadmap, and a validation ledger. The included code package provides the Python scripts used for the NumPy and local Qiskit Aer runs. This preprint should be read as a companion algorithmic module to the TEBAC portal-channel preprint. The portal-channel preprint formulates the geometric and quantum-informational target model; the present manuscript formulates and partially executes a finite-dimensional quantum-simulation protocol for selected spectral, topological, and channel-level diagnostics. The RH and BSD modules of the broader TEBAC 9D/9D+ programme are discussed only methodologically. They are not used as physical inputs for quantum simulation. Their role is to motivate the common operator--spectrum--trace/determinant--comparison architecture used across the TEBAC programme. This version does not claim a laboratory realization of a physical TEBAC portal, a physical 9D/13D geometry on quantum hardware, or a remote IBM/Google hardware backend result. It reports a local NumPy and Qiskit Aer execution and provides a hardware-ready path toward future cloud-backend experiments.
This preprint presents a finite-dimensional quantum-simulation framework for selected TEBAC 9D/9D+ topological phases, with emphasis on synthetic-dimensional encoding, spectral-gap diagnostics, portal-channel observables, and Qiskit-ready Hamiltonian construction. The manuscript formulates a finite-lattice simulation target for the internal TEBAC sector and encodes the model through Pauli-sum Hamiltonians suitable for NumPy exact diagonalization, Qiskit Aer simulation, and future IBM Runtime execution. The central simulation Hamiltonian is organized schematically as[H_{\mathrm{sim}}=H_{\mathrm{Dirac}}^{(N)}+H_{\mathrm{gauge}}^{(N)}+H_{\mathrm{top}}^{(N)}+H_{\mathrm{channel}}^{(N)}.] The paper develops a concrete two-qubit benchmark v0.1 and a four-qubit finite-lattice sector v0.2. For the four-qubit sector, the manuscript gives an explicit Pauli decomposition, exact spectrum, spectral-gap diagnostic, topological proxy, link-sector markers, fidelity diagnostic, and determinant diagnostic. A key contribution of this version is the transition from a hardware-ready protocol to an executed local emulator report. The v0.2 four-qubit sector is evaluated through NumPy exact computation and local Qiskit Aer execution, including ideal sampling, readout-noisy sampling, and readout-mitigation recovery. For the topological proxy[Q_{4}=\langle ZZZZ\rangle,]the reported values are:[Q_{4}^{\mathrm{exact}}=0.986000,][Q_{4}^{\mathrm{Aer,ideal}}=0.986572\pm 0.001805,][Q_{4}^{\mathrm{Aer,noisy}}=0.775391\pm 0.006977,]and[Q_{4}^{\mathrm{mitigated}}=0.993137\pm 0.008936.] The manuscript also includes a Qiskit Aer / IBM Runtime execution skeleton, an error-mitigation roadmap, and a validation ledger. The included code package provides the Python scripts used for the NumPy and local Qiskit Aer runs. This preprint should be read as a companion algorithmic module to the TEBAC portal-channel preprint. The portal-channel preprint formulates the geometric and quantum-informational target model; the present manuscript formulates and partially executes a finite-dimensional quantum-simulation protocol for selected spectral, topological, and channel-level diagnostics. The RH and BSD modules of the broader TEBAC 9D/9D+ programme are discussed only methodologically. They are not used as physical inputs for quantum simulation. Their role is to motivate the common operator--spectrum--trace/determinant--comparison architecture used across the TEBAC programme. This version does not claim a laboratory realization of a physical TEBAC portal, a physical 9D/13D geometry on quantum hardware, or a remote IBM/Google hardware backend result. It reports a local NumPy and Qiskit Aer execution and provides a hardware-ready path toward future cloud-backend experiments.
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=Φ0Φext, and the observable vector u⟼(Ic(u),Γϕ(u),νoscδνosc(u),Sϕϕ(ω;u)). Here Ic is the critical current, Γϕ is a phase-dephasing rate, δνosc/νosc is a fractional oscillator or clock-frequency shift, and Sϕϕ is a phase-noise spectral density. The Residual Clock–Energy input is represented by the residual phase-tension one-form α=dΦ−A, which is compared with the gauge-invariant superconducting phase difference ϕ=φ1−φ2−Φ02π∫12A⋅dℓ. The earlier v0.5r2 version introduced a positive-control toy residual drive, RJ(u)=r0sin2(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, where gi is the centered residual morphology, nk,i is a synthetic noise term, and hk,i is a nuisance contribution. The central sensitivity outputs are the detection probability, Pdet(A)=NMC1∑m=1NMC1[trial m passes], the minimum detectable amplitude, Amin=inf{A:Pdet(A)≥0.95}, and the false-positive rate, 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.
The construction of a large-scale fault-tolerant quantum computer is an outstanding scientific and technological goal. It holds the promise to allow us to solve a variety of complex problems such as factoring large numbers, quick database search, and the quantum simulation of many-body quantum systems in fields as diverse as condensed matter, quantum chemistry, and even high-energy physics. Sophisticated theoretical protocols for reliable quantum information processing under imperfect conditions have been de-veloped, when errors affect and corrupt the fragile quantum states during storage and computations. Arguably, the most realistic and promising ap-proach towards practical fault-tolerant quantum computation are topologi-cal quantum error-correcting codes, where quantum information is stored in interacting, topologically ordered 2D or 3D many-body quantum systems. This approach offers the highest known error thresholds, which are already today within reach of the experimental accuracy in state-of-the-art setups. A combination of theoretical and experimental research is needed to store, protect and process fragile quantum information in logical qubits effectively so that they can outperform their constituting physical qubits. Whereas small-scale quantum error correction codes have been implemented, one of the main theoretical challenges remains to develop new and improve existing efficient strategies (so-called decoders) to derive (near-)optimal error cor-rection operations in the presence of experimentally accessible measurement information and realistic noise sources. One main focus of this project is the development and numerical implementation of scalable, efficient decoders to operate topological color codes. Additionally, we study the feasibility of im-plementing quantum error-correcting codes fault-tolerantly in near-term ion traps. To this end, we use realistic modeling of the different noise sources, computer simulations, and most modern quantum information approaches to quantum circuitry and noise suppression techniques.
Abstract Quantum computations execute on noisy hardware whose effective noise is opaque and varies across platforms and over time. Complete descriptions of the underlying noise channel are often too detailed for reasoning, comparison, or analysis. We therefore study the semantic problem of constructing tractable abstractions of noisy quantum channels: given a finite set of observations, how can we summarise channel behaviour while preserving properties of interest? We characterise the effective noise of a quantum channel as an abstract domain of noise fingerprints. A noise fingerprint is an observational abstraction of a quantum channel over a finite experiment interface. We formalise the relation between concrete channels and fingerprints through an approximate Galois connection and derive four abstraction properties: soundness, conciseness, efficiency, and adaptiveness. We provide an executable instantiation of the abstraction function using the classical-shadow estimator, together with a partial concretisation function that reconstructs channels from fingerprints via semidefinite programming. We evaluate this abstraction against the formal properties: the soundness bound is shown to be tight, compression over the concrete domain is exponential with near-lossless retention, sample complexity is (poly)logarithmic, and incremental updates track channel drift at the optimal rate. Additional experiments show that fingerprints preserve physically meaningful noise signatures and distinguish cross-platform behaviours. Together, this work brings abstract interpretation to the empirical semantics of noisy quantum channels, providing a lightweight, formally grounded abstraction for characterising, comparing, and monitoring noisy quantum executions. Context Characterising noisy quantum channels remains challenging: full process tomography scales exponentially with system size, while commonly used noise metrics provide limited semantic guarantees. This artifact accompanies a paper that introduces live noise fingerprints as a reusable semantic abstraction for noisy quantum channels. A noise fingerprint is defined as the matrix of deviations between observed and ideal Pauli expectation values over a fixed experimental interface. We show that these fingerprints form an abstract domain for completely positive trace-preserving (CPTP) maps through an approximate Galois connection to the concrete channel space. The framework is evaluated against four formal requirements: Soundness — a Lipschitz bound relating abstract distance to diamond-norm distance. Conciseness — substantial compression relative to the underlying channel representation. Estimation efficiency — practical estimation from finite measurements. Adaptiveness — support for incremental updates under channel drift. The concrete instantiation uses the Huang–Kueng–Preskill classical-shadow estimator with median-of-means aggregation. Every theoretical claim is machine-verified. The artifact includes exact SDP-based diamond norms for small systems, two independently validated large-system ground truths (completely bounded norm multiplicativity for single-site channel pairs and the exact Pauli-channel ℓ₁ formula), and a product-factorised classical-shadow sampler proven distribution-identical to the full sampler. All four research questions are evaluated for n = 1–8 qubits across 12 experimental configurations, combining three channel families with hardware-informed profiles derived from IBM Boston and Quantinuum H2 calibrations under both Qiskit and Cirq simulation variants. All stochastic measurements are reported as mean ± standard deviation, and every figure includes error bars. New in this version. The artifact now includes a self-contained worked example, worked_example.ipynb, which runs the abstraction end to end on small quantum programs: from OpenQASM source, through the gates and the noise a backend inserts around them, to the observation interface a program's test defines, the resulting fingerprints, and the decision they support. It is written for readers approaching the work from programming languages and software engineering rather than quantum information, and it is the shortest path into the artifact: it requires only NumPy, runs in seconds, and needs no SDP solver, quantum SDK, or hardware. The artifact also characterises the operational limits of the approach, including detectability thresholds at realistic hardware noise rates, readout-error-induced bias floors, explicit interface-blindness constructions and their informationally complete remedies, and drift regimes where warm-started updates remain beneficial. Artifact Evaluation file This artifact accompanies the paper "Live Noise Fingerprints as an Empirical Semantics for Noisy Quantum Channels" and provides the complete implementation, experiments, and evaluation pipeline used to validate the proposed noise-fingerprint abstraction. The package includes a pure Python/NumPy implementation of noisy quantum channels, classical-shadow fingerprint estimation, semidefinite-programming-based concretisation, machine-checked tests, a worked-example notebook, and scripts to reproduce every figure and quantitative claim reported in the paper. Evaluators can start from the notebook for a program-level walkthrough of the abstraction, verify correctness using an automated verification target, and regenerate all experimental results, including scalability, convergence, variance, detectability, and warm-start analyses. Precomputed datasets and figures are included to enable immediate inspection, while the full experimental pipeline can be rerun from scratch without requiring GPUs, quantum hardware, or network access after dependency installation. The artifact is released under the MIT License and is designed for reuse by allowing new quantum programs, hardware noise profiles, qubit counts, and abstraction properties to be incorporated with minimal modification. Package Contents worked_example.ipynb — a self-contained, executed walkthrough of the abstraction on small programs. It covers: an OpenQASM front end and the ideal denotation of a program; the realisation of that program on a backend, with the backend's noise inserted after every gate and rendered in the printed circuit; the observation interface, derived from what a program's test asserts rather than chosen freely; fingerprints and the equivalence decision, over five benchmark programs and five backend configurations, with a diagnostic per program naming the observation that carries the difference; interface blindness and its repair by refinement; prefix sweeping to localise which gate two realisations first disagree on; a control panel for running the whole chain on the reader's own .qasm file; measurement-reuse accounting, and numerical checks of three properties from the paper. Outputs are stored in the notebook, so it can be read without execution. src/ Pure NumPy implementation of: Quantum states and channels Noise fingerprints Literal classical-shadow estimators (full and product-factorised) Optional readout-error models Exact diamond-norm computation via Watrous SDPs Validated large-system diamond-norm ground truths General SDP-based concretisation procedures Configurable noise models Registry of all 12 experimental configurations (profiles.py) experiments/ Experiment drivers for all research questions: rq1_sweep.py — Soundness rq2_sweep.py — Conciseness rq3_sweep.py — Estimation Efficiency rq4_sweep.py — Adaptiveness Additional components include audited single-size reproductions, a stress-test suite (realistic_limits.py), a seed-sweep audit framework, and a figure-generation pipeline with shared publication styling. results/ — JSON outputs containing every measured data point for each research question. figures/ — Results figures, one file per figure. tests/ — Forty-one machine-checked tests, including validation of exact diamond-norm ground truths, verification of the product-factorised sampler, and consistency checks required before experimental execution. Additional files — README.md (overview, results summary, and reproduction guide), Dockerfile (containerised environment), requirements.txt (pinned dependencies). Installation The artifact requires Python 3.10 or later. Install dependencies: pip install -r requirements.txt Required packages: NumPy, SciPy, CVXPY, scikit-learn, matplotlib. Opening the worked-example notebook additionally requires jupyter; the notebook itself imports only NumPy and can also be read as-is, since its outputs are stored. No quantum SDK is required; all simulations use a pure NumPy density-matrix implementation. A containerised environment is also provided: docker build . Getting started: the worked example jupyter notebook notebooks/worked_example.ipynb Approximate runtime: under one minute; NumPy only. This is the recommended entry point. It takes a program in OpenQASM, shows what a backend does to it, derives the observation interface from the program's test, computes the fingerprints, and decides whether the two backends are interchangeable for that test — the abstraction of the paper, on objects small enough to check by hand. Expected results Two backends implementing the same physical noise by different means are judged interchangeable on all five programs, with deviations at machine precision (≈ 10⁻¹⁶). A leftover coherent phase rotation, of the kind an optimisation pass can introduce, is flagged on four of the five programs and correctly cleared on the fifth, whose test reads only populations and therefore cannot be affected by it. Judged on a population-only interface, the same phase rotation is invisible; refining the interface to the observables the program's test actually reads restores it. The prefix sweep localises a fault confined to the two-qubit gate at exactly that gate, and reports the earliest divergence when the
Simulating quantum-mechanical systems is a very challenging issue due to the high computational costs. The main reason for this is related to the dimension of the Hilbert space that grows exponentially with the number of degrees of freedom, making an exact implementation impossible even for the most powerful today’s supercomputers. \nOn this ground it appears clear the need of a new simulation method, i.e. quantum simulation. The general idea is very simple: using a controllable quantum system, called quantum simulator, to emulate and to analyze another quantum system that usually results less controllable or accessible. Quantum simulation is currently a growing and multidisciplinary physical area that involves theoretical and experimental research. From the theoretical side, the main focus is on the study of simulation-models that create a mapping between the target physics and the simulator. \nIn the first two parts of this thesis, we explore these ideas by studying the ground-state properties and the real-time dynamics of a class of Zn lattice gauge theories in 1+1 dimensions, in which the gauge fields are coupled to fermionic matter. These models can be considered as quantum simulation-models of lattice 1+1 Quantum Electrodynamics (QED), which is the simplest gauge theory that shows non-trivial phenomena, like confinement, that are also observed in more complicated gauge theories, such as 3+1 Quantum Chromodynamics (QCD). \nIn the third part of this thesis, we unveil an interesting interplay of symmetry and topology by demonstrating the existence of symmetry-protected topological (SPT) phases in the presence of gauge interactions. More specifically, we introduce an alternative discretization of the Schwinger model leading to a new type of topological-QED. We use bosonization and Density-Matrix Renormalization Group (DMRG) techniques to analyze the phase diagram of the model, opening an interesting route to study topological phases of matter in the context of gauge theories.
In the previous chapters we introduced anyons and their properties, we presented how to perform topological quantum computation and studied several examples of topological models. There is a wide variety of research topics concerned with topological quantum computation. Among the many open questions, two have a singular importance. The first natural question is: which physical systems can support non-Abelian anyons? Realising non-Abelian anyons in the laboratory is of fundamental and practical interest. Such exotic statistical behaviour has not yet been encountered in nature. The physical realisation of non-Abelian anyons would be the first step towards the identification of a technological platform for the realisation of topological quantum computation. The second question concerns the efficiency of topological systems in combating errors. It has been proven that the effect of coherent environmental errors in the form of local Hamiltonian perturbations can be suppressed efficiently without degrading the topologically encoded information (Bravyi et al. , 2010). Nevertheless, there is no mechanism that can protect topological order from incoherent probabilistic errors. Topological systems nevertheless constitute a rich and versatile medium that allows imaginative proposals to be developed (Chesi et al. , 2010; Hamma et al. , 2009). Regarding the first question, we can identify two main categories of physical proposals for the realisation of two-dimensional topological systems: systems that are defined on the continuum and discrete systems defined on a lattice. It is natural to ask, which are the most promising architectures to realise in the laboratory?
This is a non-peer-reviewed theoretical preprint intended for community discussion and public dissemination. This preprint develops a TEBAC 9D/9D+ boundary-kernel framework for structured-light quantum metrology, using entangled orbital-angular-momentum optical rotatory dispersion as the motivating setting. The framework interprets chirality as an oriented E1M1 phase defect, the OAM index as a transverse winding channel, Gouy phase as propagation holonomy, detector pixelation as finite-rank boundary projection, and Fisher information as the induced phase metric on the observed boundary data. The preprint proposes experimentally testable signatures, including OAM-dependent winding, Gouy-shifted Fisher maxima, detector-resolution scaling, enantiomeric sign reversal, Bell-sector symmetry splitting, and a non-factorizable coincidence residual distinguishing product coincidence data from genuinely two-boundary correlations. The manuscript does not claim journal peer review or acceptance. It is released as a public theoretical preprint to make the TEBAC 9D/9D+ phase-kernel interpretation visible and citable.