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Artifact of Live Noise Fingerprints as an Empirical Semantics for Noisy Quantum Channels

Anonymous for Peer Review

Published Jul 5, 2026• 0 citations
Publisher

Abstract

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

DOI
10.5281/zenodo.21206822

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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. 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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
Contemporary quantum computers are inherently noisy, posing significant challenges for the development and testing of quantum software. Simplified or outdated noise assumptions can lead to incorrect assessments of program correctness, obscure debugging, and hinder cross-platform portability, creating a critical quantum software development gap. Providing accurate, practical noise characterisation is challenging as traditional reconstruction methods scale exponentially and rapidly become outdated. In this vision paper, we address this gap via a novel classical shadow tomography-based pipeline, SIMSHADOW, enabling efficient, continuously updatable noise fingerprinting from empirical observations, suitable for integration into quantum software development workflows, including testing and validation. We prototyped the pipeline to investigate fingerprints' ability to capture structured, interpretable noise and cross-platform discrepancies affecting quantum programs' behaviour to support realistic testing and debugging in future tools. Our evaluation with Qiskit and Cirq under widely used hardware-informed profiles, IBM Boston and Quantinuum H2, shows fingerprints exhibit channel-specific structure and yield interpretable heatmaps. We observed systematic cross-platform discrepancies under matched noise configurations, quantified by large Frobenius distances at a fraction of full tomography cost. On 69 MQTBENCH programs, larger fingerprint differences correlate with output distributions divergences, highlighting threats for testing and cross-platform debugging tasks.
Contemporary quantum computers are inherently noisy, posing significant challenges for the development and testing of quantum software. Simplified or outdated noise assumptions can lead to incorrect assessments of program correctness, obscure debugging, and hinder cross-platform portability, creating a critical quantum software development gap. Providing accurate, practical noise characterisation is challenging as traditional reconstruction methods scale exponentially and rapidly become outdated. In this vision paper, we address this gap via a novel classical shadow tomography-based pipeline, SIMSHADOW, enabling efficient, continuously updatable noise fingerprinting from empirical observations, suitable for integration into quantum software development workflows, including testing and validation. We prototyped the pipeline to investigate fingerprints' ability to capture structured, interpretable noise and cross-platform discrepancies affecting quantum programs' behaviour to support realistic testing and debugging in future tools. Our evaluation with Qiskit and Cirq under widely used hardware-informed profiles, IBM Boston and Quantinuum H2, shows fingerprints exhibit channel-specific structure and yield interpretable heatmaps. We observed systematic cross-platform discrepancies under matched noise configurations, quantified by large Frobenius distances at a fraction of full tomography cost. On 69 MQTBENCH programs, larger fingerprint differences correlate with output distributions divergences, highlighting threats for testing and cross-platform debugging tasks.
Accurate noise classification is essential for operating near-term quantum processors, yet existing approaches, such as quantum process tomography, scale exponentially with system size, limiting their practicality for routine calibration. We propose a measurement-efficient noise fingerprinting pipeline that combines structured classical shadow tomography with physics-informed feature engineering to identify noise channels from a fixed set of 3-qubit probe circuits. Each sample is represented by a feature vector constructed from randomized Pauli measurements and derived observables designed to resolve physically similar noise channels that produce overlapping signatures under generic measurement sets. We evaluate random forest, extra trees, and a multilayer perceptron on 10,000 labeled samples spanning ten noise models. The three classifiers achieve comparable performance. In the reported runs, random forest and extra trees perform similarly, achieving approximately 0.736 test accuracy and 0.729-0.730 macro F1, compared with 0.715 accuracy and 0.699 macro F1 for the multilayer perceptron. We further analyze the effect of the noise-strength sampling range and conduct a limited sensitivity check using analogous 2- and 4-qubit probes. Confusion analysis shows that readout error, phase flip, thermal relaxation, and bit flip are classified with high reliability, while most remaining errors occur among channels with similar physical effects.
This repository accompanies the preprint “Mapping the Limits of Architecture-Sensitive Noise Fingerprints in Quantum States.” The work investigates when and why simple classical measurement statistics obtained from noisy quantum systems retain information about the underlying quantum state architecture, and when such information collapses entirely. Building on earlier results demonstrating the existence of architecture-dependent classical fingerprints for stabilizer states under local noise, this study systematically maps the boundaries and failure modes of that phenomenon. Using exact probability distributions for small-to-moderate system sizes, we introduce controlled departures from stabilizer structure and track the degradation of classical features under dephasing and depolarizing noise. The analysis reveals sharply conditional survival of architecture sensitivity, a consistent feature-dependent collapse ordering, and a strong dependence on measurement basis and perturbation geometry. In particular, regimes of genuine diagnostic blindness are identified, where classical statistics become architecture-indistinguishable even though the underlying quantum states remain highly structured. The archive includes the full manuscript (PDF and LaTeX source), all figures appearing in the paper, the scripts required to reproduce the numerical experiments and figures, and the corresponding data outputs. All results are based on exact numerical evaluation (no sampling, optimisation, tomography, or machine learning). The work is intended as a lightweight, diagnostic limits study, providing practical guidance on when simple classical measurements are informative and when their use is fundamentally unreliable. Together with the companion papers in this series, the repository contributes to a coherent empirical and theoretical programme on the classical observability of quantum structure under noise.Version 1.1 notes.This revision clarifies the collapse criterion used to define architecture indistinguishability, explicitly specifies numerical precision and robustness checks, and adds a qualitative reliability chart summarising when different classical features remain informative. The presentation of noise-model dependence, system-size stability, and perturbation geometry has been sharpened, and the relationship to companion papers in the series has been made explicit. No new phenomena are introduced; the update improves transparency, interpretability, and practical usability of the results.
The primary aim of the thesis is to introduce and investigate an original protocol for the design and the optimization of parameterized noisy quantum channels, with the goal of mitigating hardware-induced noise. Significant attention is also devoted to the design of noise models, which are essential for emulation purposes. The protocol begins with the derivation of a noise model for a hardware gate, represented as a quantum channel, that can be simulated classically. This task is achieved through process tomography, a procedure that enables the characterization of the channel. It should be noted that such simulation is feasible on classical computers, since the optimization task concerns low-dimensional gates typically acting on 2–3 qubits. The noisy channel is then engineered by embedding it into a probabilistic ensemble of circuits, in which additional single-qubit parameterized gates — assumed to be noiseless — are introduced. Through this procedure, the noisy channel becomes parameterized and can be optimized according to an appropriate metric. Following a worst-case, agnostic perspective, we choose the diamond distance between the noisy channel and the target unitary channel as the cost function. This metric is generally considered the most suitable for distinguishing quantum channels. The resulting optimal ensemble of circuits can be implemented on real hardware under fixed calibration conditions, yielding a channel that approximates the target more closely than the original noisy channel. This approach can be interpreted as a noise mitigation strategy based on pre-processing design and optimization: rather than correcting errors after the computation, less noisy channels are employed during the computation itself. In this context, the protocol — within the noise-aware variational quantum compiling framework — shares with the randomized compiling the principle of circuit dressing to tailor noise during execution. The methodology is validated on two toy models of the single-qubit identity with amplitude damping noise, combining both analytical and numerical approaches. The analysis highlights the role of convexity in the space of quantum channels, with explicit demonstrations of optimal convex combinations and connections to encoding-decoding and dynamical decoupling strategies. The analysis of these simple models is intended as a proof-of-principle of the protocol in a controlled and well-characterized environment. In addition, this thesis introduces the design of random noise models that are constrained to maintain a fixed diamond distance from a target quantum channel. The controlled addition of random noise to a unitary channel represents a significant and — to our knowledge — previously unexplored approach within noise modeling. Indeed, in principle, the currently available built-in noise models may limit the expressivity of the emulation. The task was achieved by enriching the noise spectrum through the addition of random Kraus operators and small systematic rotations. To assess the effects of hardware-induced noise, we proposed an experimental design aimed at simulating the time evolution of a triangular Ising model in a transverse field. Our approach employs Trotterization, adapted to the topology and connectivity of a certain quantum processing unit (QPU) profile. Building on the noisy native gates of the QPU profile, we propose the emulation, engineering and optimization of a noisy CZ gate, subsequently employed within sequences of non-native gates. Using the designed noise models, we perform several emulations aimed at evaluating the effectiveness of the protocol in the presence of progressively dominant systematic rotations, and at comparing it with Pauli twirling, a technique of randomized compiling.
Abstract Noise sources unavoidably affect any quantum technological device. Noise’s main features are expected to strictly depend on the physical platform on which the quantum device is realized, in the form of a distinguishable fingerprint. Noise sources are also expected to evolve and change over time. Here, we first identify and then characterize experimentally the noise fingerprint of IBM cloud-available quantum computers, by resorting to machine learning techniques designed to classify noise distributions using time-ordered sequences of measured outcome probabilities.