We report on a fundamental disparity between stochastic noise models and algorithmic performance in NISQ-era classifiers. Utilizing the ibm_kingston processor, we characterize the "Kingston Constant" ($κ\approx 0.07$), representing a 93% signal magnitude collapse.
Despite this decay, we show via a hardware-calibrated stochastic digital twin that a Hadamard Test based Perceptron maintains a 93.9% accuracy for the MNIST dataset, validating our proposed Hadamard Resilience Effect under affine depolarization.
Through parametric simulation, we establish a critical gate-noise threshold at $λ_{\text{crit}} \approx 0.65$ (corresponding to a critical signal retention $α_{\text{crit}} \approx 0.35$) where topological rank preservation breaks down.
Furthermore, physical execution at high feature depths ($N = 256$) reveals a systemic divergence---the ``Coherence Gap'' ($Δρ\approx 0.91$)---where physical hardware classification accuracy collapses to 53.0\% due to a ``Coherence Wall'' at a circuit depth ($D \approx 10\text{k}$) exceeding the hardware's resilient depth limit ($D_{\text{max}} \approx 3.5\text{k}$). This gap is consistent with coherent phase errors and crosstalk being the dominant unmodeled contributors under the tested hardware configuration, establishing a predictive operational boundary for NISQ classification architectures.
We report on a fundamental disparity between stochastic noise models and algorithmic performance in NISQ-era classifiers. Utilizing the ibm_kingston processor, we characterize the "Kingston Constant" (κ≈0.07), representing a 93% signal magnitude collapse.
Despite this decay, we show via a hardware-calibrated stochastic digital twin that a Hadamard Test based Perceptron maintains a 93.9% accuracy for the MNIST dataset, validating our proposed Hadamard Resilience Effect under affine depolarization.
Through parametric simulation, we establish a critical gate-noise threshold at λcrit≈0.65 (corresponding to a critical signal retention αcrit≈0.35) where topological rank preservation breaks down.
Furthermore, physical execution at high feature depths (N=256) reveals a systemic divergence---the Coherence Gap'' ($Δρ\approx 0.91$)---where physical hardware classification accuracy collapses to 53.0\% due to a Coherence Wall'' at a circuit depth (D≈10k) exceeding the hardware's resilient depth limit (Dmax≈3.5k). This gap is consistent with coherent phase errors and crosstalk being the dominant unmodeled contributors under the tested hardware configuration, establishing a predictive operational boundary for NISQ classification architectures.
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.
As quantum processors move into the noisy intermediate-scale quantum (NISQ) era, the central question is no longer whether a quantum algorithm is asymptotically faster than its classical counterpart, but whether it can retain a meaningful speedup under realistic noise, compilation, and measurement constraints. This work develops a quantitative framework for characterizing the noise resilience of quantum advantage. We introduce the advantage robustness function RA(ε), which measures how the asymptotic and concrete performance of an algorithm A degrades with physical error rate ε, and we compute it analytically or numerically for twelve representative algorithm families, including Grover search, amplitude estimation, phase estimation, HHL, VQE/QAOA, Hamiltonian simulation, and sampling algorithms. For each class, we derive critical noise thresholds and depth limits beyond which classical algorithms regain supremacy, explicitly incorporating realistic connectivity and compilation overheads. We show that algorithms based on coherent amplitude amplification are more fragile to coherent errors than depolarizing noise, while variational algorithms display a tradeoff between expressivity and robustness. By combining these algorithm-specific robustness curves with current and projected hardware error rates for superconducting, trapped-ion, neutralatom, and photonic platforms, we map out a phase diagram of practical quantum advantage that links problem size, noise rate, and algorithm type. Our analysis identifies promising near-term application windows in risk analytics, small-molecule chemistry, and structured optimization, and also delineates regions where no advantage is realistic, providing valuable guidance for both algorithm designers and hardware architects.
Gate-level noise degrades the classification accuracy of Quantum Support Vector Machines (QSVMs) on Noisy Intermediate-Scale Quantum (NISQ) hardware, and the degree of degradation depends on how classical data is encoded into quantum states. We tested Z, ZZ, a Pauli, and an amplitude-inspired feature maps under depolarizing, bit-flip, and phase-flip noise channels in 52 controlled experiments with error probabilities p=0.01,0.05,0.10, and 0.50. The amplitude-inspired feature map had 100\% test accuracy up to p=0.10 across all three noise channels, while other feature maps fell to 65-90\% under the same noise level and type. The Z feature map was found to be immune to phase-flip noise to a significantly high error rate, a consequence of the commutation relation [RZ,Z]=0. Entangled circuit variants produced generalization gaps in train-test sets of up to 17.5\% under noise, whereas the amplitude variants maintained zero gap throughout. These results give practitioners data-driven criteria for a feature map on near-term quantum hardware.
Near-term quantum machine learning (QML) models operate in environments wherein noise is unavoidable, arising from both imperfect classical data acquisition and the limitations of noisy intermediate-scale quantum (NISQ) hardware. Although most existing studies have focused primarily on quantum circuit noise in isolation, the combined influence of corrupted classical inputs and quantum hardware noise has received comparatively little attention.
In this work, we present a systematic experimental study of the robustness of a variational quantum classifier under realistic multi-level noise conditions. Using the Titanic dataset as a benchmark, a range of dataset-level noise models-including speckle noise, impulse noise, quantization noise, and feature dropout are applied to classical features prior to quantum encoding using a ZZ feature map. In parallel, hardware-inspired quantum noise channels such as depolarizing noise, amplitude damping, phase damping, Pauli errors, and readout errors are incorporated at the circuit level using the Qiskit Aer simulator.
The experimental results indicate that noise in classical input data can significantly intensify the effects of quantum decoherence, resulting in less stable training and noticeably lower classification accuracy. Together, these observations emphasize the importance of designing and evaluating quantum machine learning pipelines with noise in mind, and highlight the need to consider classical and quantum noise simultaneously when assessing QML performance in the NISQ era
Abstract The arrival of noisy intermediate-scale quantum (NISQ) devices defines an era in which quantum utility is fundamentally constrained by finite coherence times, limited qubit counts, gate infidelities, restricted connectivity, and measurement noise. Within this regime, hybrid quantum-classical frameworks have emerged as the dominant operational paradigm, particularly for quantum machine learning (QML). This review identifies a fundamental trade-off between expressivity, trainability, and noise resilience that governs the performance and scalability of NISQ-era QML systems. To contextualize these challenges, we introduce the resource-constrained iterative routing framework, a hardware-aware conceptual architecture that integrates topology-aware classical compression and distributed quantum orchestration to maintain circuit depths within device-dependent limits while routing representations toward symmetry-constrained Hilbert subspaces to mitigate noise-induced barren plateaus. Furthermore, we shift the discussion of quantum advantage away from asymptotic fault-tolerant complexity toward the notion of operational NISQ advantage based on finite-resource scaling, trainability preservation, and sampling complexity. We evaluate the practical resource efficiency of variational quantum algorithms, quantum kernel methods, and quantum neural networks across superconducting, trapped-ion, neutral-atom, and photonic platforms. The review also examines reproducibility challenges, emphasizing benchmarking against optimized classical baselines, and discusses strategies for managing the sampling overhead of error mitigation alongside distributed execution and quantum circuit compilation. Ultimately, NISQ in Practice positions hybrid QML as a physically constrained computational paradigm while outlining a pathway from contemporary noisy workflows toward early fault-tolerant quantum architectures.
Abstract As the volume of global data approaches the yottabyte scale, classical computational architectures are encountering insurmountable bottlenecks in processing efficiency. Quantum Computing (QC) presents a theoretical solution by offering exponential speedups for processing high-dimensional, complex datasets. However, a significant disparity remains between these algorithmic potentials and the current state of physical hardware. This paper investigates the "scalability tension" by evaluating primary Quantum Machine Learning (QML) algorithms—specifically Quantum Principal Component Analysis (QPCA), Quantum Support Vector Machines (QSVM), and Variational Quantum Eigensolvers (VQE)—against the constraints of Noisy Intermediate-Scale Quantum (NISQ) devices. Utilizing the Resource-Utility Framework (RUF), we analyze error rates and qubit decoherence through simulations. Our findings reveal a "fidelity collapse" in QSVM for datasets exceeding 50 dimensions, where output becomes indistinguishable from white noise due to gate-depth requirements exceeding coherence times. We conclude that while theoretical speedups are robust, practical deployment is currently hindered by the overhead of Quantum Error Correction (QEC) and the "data loading problem." We propose hybrid quantum-classical frameworks as a necessary intermediary step toward achieving practical quantum advantage.