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arXiv:2602.14735

The Signal Horizon: Local Blindness and the Contraction of Pauli-Weight Spectra in Noisy Quantum Encodings

Ait Haddou Marwan

quant-phcs.LGSubmitted Feb 16, 2026• Announced Feb 17, 2026• 0 citations
v1 · Feb 16, 2026v2 · Aug 4, 2026
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Abstract

The performance of quantum classifiers is typically analyzed through global state distinguishability or the trainability of variational models. This study investigates how much class information remains accessible under locality-constrained measurements in the presence of noise. The authors formulate binary quantum classification as constrained quantum state discrimination and introduce a locality-restricted distinguishability measure quantifying the maximum bias achievable by observables acting on at most $k$ subsystems. For $n$-qubit systems subject to independent depolarizing noise, the locally accessible signal is governed by a Pauli-weight-dependent contraction mechanism. This motivates a computable predictor, the $k$-local Pauli-accessible amplitude $A_{k}(p)$, which lower bounds the optimal $k$-local classification advantage. Numerical experiments on four-qubit encodings demonstrate quantitative agreement between empirical accuracy and the prediction across noise levels. The research identifies an operational breakdown threshold where $k$-local classifiers become indistinguishable from random guessing despite persistent global distinguishability.

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The performance of quantum classifiers is typically analyzed through global state distinguishability or the trainability of variational models. This study investigates how much class information remains accessible under locality-constrained measurements in the presence of noise. The authors formulate binary quantum classification as constrained quantum state discrimination and introduce a locality-restricted distinguishability measure quantifying the maximum bias achievable by observables acting on at most kkk subsystems. For nnn-qubit systems subject to independent depolarizing noise, the locally accessible signal is governed by a Pauli-weight-dependent contraction mechanism. This motivates a computable predictor, the kkk-local Pauli-accessible amplitude Ak(p)A_{k}(p)Ak​(p), which lower bounds the optimal kkk-local classification advantage. Numerical experiments on four-qubit encodings demonstrate quantitative agreement between empirical accuracy and the prediction across noise levels. The research identifies an operational breakdown threshold where kkk-local classifiers become indistinguishable from random guessing despite persistent global distinguishability.
This study investigates classification performance and trainability of variational quantum classifiers on near-term noisy quantum hardware across circuit depth and qubit count regimes within the context of quantum computing and machine learning, an area of growing scientific importance given its implications for hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment. Using gradient-based parameter optimization of parameterized quantum circuits with hardware noise modeling via density matrix simulation and physical execution on IBM Eagle processors, we examine expressibility of parameterized circuits enabling nonlinear decision boundaries in feature Hilbert space, with trainability constrained by barren plateau gradients at large qubit counts in 96 circuit architectures (4 qubit counts x 4 depths x 6 ansatz families) evaluated across 5 classification datasets with 20 random initialization seeds each drawn from IBM Quantum Eagle (127-qubit) and Falcon (27-qubit) processors with noise mitigation via zero-noise extrapolation. Results indicate that 10-qubit, 4-layer VQC achieves 84.2% classification accuracy on the best benchmark, within 3.8 percentage points of classical SVM, but gradient variance decays exponentially with qubit count (variance halving per 2 added qubits), confirming barren plateau scaling (p < 0.001), with 84.2% accuracy, 3.8 pp gap to classical SVM baseline as the primary quantitative benchmark. Concordance between primary and confirmatory measurement approaches exceeded 93%, validating the analytical framework. These findings contribute empirically to quantum computing and machine learning and carry actionable implications for the design of programs and policies targeting hybrid quantum-classical algorithm design and practical NISQ hardware benchmarking for near-term quantum advantage assessment.
Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources for information processing tasks. A common feature of these models is the presence of inaccessible information, as captured by the concept of preparation contextuality: There are ensembles of quantum states described by the same density operator, and hence operationally indistinguishable, and yet in any probabilistic (ontological) model, they should be described by distinct probability distributions. In this work, we quantify the inaccessible information of a model in terms of the maximum distinguishability of probability distributions associated to any pair of ensembles with identical density operators, as quantified by the total variation distance of the distributions. We obtain a family of lower bounds on this maximum distinguishability in terms of experimentally measurable quantities. In the case of an ideal qubit this leads to a lower bound of, approximately, 0.07. These bounds can also be interpreted as a new class of robust preparation non-contextuality inequalities. Our non-contextuality inequalities are phrased in terms of generalizations of max-relative entropy and trace distance for general operational theories, which could be of independent interest. Under sufficiently strong noise any quantum system becomes preparation non-contextual, i.e., can be described by models with zero inaccessible information. Using our non-contextuality inequalities, we show that this can happen only if the noise channel has the average gate fidelity less than or equal to 1/D(1+1/2+...+1/D), where D is the dimension of the Hilbert space.
Quantum classification faces two key challenges. First, the difficulty of distinguishing between different classes varies: some class pairs are easy to separate, while others are more challenging. Second, practical execution is affected by noise, finite sampling, and measurement overhead. To address these issues, we propose the Pauli-Space Discriminative-Representation based Quantum Classifier (PdrQC), a framework for task-adaptive multiclass quantum classification. The method evaluates candidate upload circuits using low-weight Pauli features and formulates upload design as a structured model selection problem based on discriminative representations. By progressively selecting upload structures and compact Pauli readout features for the target multiclass task, the framework achieves a better balance between classification accuracy and resource efficiency. Numerical simulations were conducted on the MNIST and Fashion-MNIST datasets with K∈{2,3,5,7,10}K\in\{2,3,5,7,10\}K∈{2,3,5,7,10}. The results demonstrate that PdrQC, through its task-adaptive Pauli representation, achieves an effective balance among multiclass classification accuracy, quantum-circuit complexity, and measurement overhead, making it suitable for multiclass quantum classification under limited hardware resources.
With the rapid development of quantum technology, understanding the properties of entanglement states has become an urgent task.Various classifications of entanglement states have been proposed to cater to distinct quantum applications, highlighting the significance of entanglement classification. This paper presents a variational quantum classifier for entanglement classification discrimination which can effectively reduce the measurement resources, specifically for four-qubit entanglement equivalence classifications under SLOCC (Stochastic Local Operations and Classical Communication). Through training one-to-one and one-to-many models, our proposed method achieves excellent performance in the entanglement classification. We further investigate the impact of parameterized quantum circuit layers and various measurement settings on the classifier’s performance. Considering the inherent noise present in near-term quantum computers, we also analyze how noise affects the model’s performance. Moreover, we explore the classifier’s capabilities in the context of multi-qubit entanglement systems. Numerical simulations demonstrate that high-precision entanglement classification tasks can be accomplished with shallow circuit depths, and the model exhibits resilience to noise. Additionally, the results reveal the versatility and potential application of our proposed model in larger-scale quantum systems by effectively handling entanglement classification tasks involving an increased number of qubits.
We demonstrate that a two-qubit encode-after quantum circuit implementing temporal XOR parity classification achieves asymptotic immunity to the Dynamical Horizon Principle (DHP) through a sign-preservation mechanism. The DHP, an empirically observed characterization related to the classical vanishing gradient problem, predicts training failure when the convergence time T_conv exceeds 0.72 times the Lyapunov coherence time τ_L. We show that for even convergence steps, the Bloch sphere contraction factor (1−4p/3)^T_conv remains strictly positive for all Pauli depolarizing rates p ∈ [0, 0.75), ensuring gradient direction is preserved regardless of noise magnitude. We term this the quantum parity trap: a regime where the optimizer receives consistent directional signal even as coherence approaches zero. Threshold sweeps confirm convergence at T_conv/τ_L ratios exceeding 15×, compared to the classical DHP limit of 0.72×—a quantum advantage that diverges as p → 0.75. Supplementary experiments establish that (1) Rigetti QPU hardware yields >50σ margin above chance with 4096 shots and readout error mitigation; (2) gradient direction alone is sufficient for convergence—signSGD matches Adam while vanilla SGD fails; and (3) T1 amplitude damping does not replicate the landscape regularization effect of Pauli depolarizing noise, revealing that isotropic Bloch sphere contraction is the mechanistic source of partial-attractor erasure. These results demonstrate that task structure, channel geometry, and optimizer design jointly determine whether quantum noise enables or impedes machine learning convergence.
Quantum amplifiers are intrinsically nonlinear systems whose performance limits are set by quantum mechanics. In quantum measurement, amplifier operation is conventionally optimized in the linear regime by maximizing signal-to-noise ratio, an objective that is well-suited to parameter estimation but is typically insufficient for more general tasks such as arbitrary quantum state discrimination. Here we show that single-shot quantum state classification can benefit from operating a quantum amplifier outside the linear regime, when the measurement chain is optimized end-to-end for a task-specific cost function. We analyze a realistic superconducting readout architecture that includes state preparation, cryogenic nonlinear amplification, and room-temperature detection with finite noise. By introducing performance metrics tailored to state discrimination, we identify operating regimes in which nonlinear amplification provides a measurable advantage and clarify the trade-offs that ultimately limit classification fidelity. Building on these results, we propose a qubit readout architecture without cavity displacement that exploits nonlinear amplification to enhance single-shot state discrimination performance. Our results establish the practical value of nonlinear quantum amplifiers for quantum state discrimination and lay the foundation for a broader program to develop a general, end-to-end framework for resource-constrained optimization of nonlinear amplification in quantum information processing tasks.