We present an empirical study of observable noise behavior in quantum circuits under fixedworkload constraints. Using publicly available circuit archives and measurement data, we showthat observable dispersion metrics are monotonically ordered by pre-measurement interactionstructure derived solely from circuit topology, and not by gate count or circuit depth alone.Structure is quantified using topology-derived interaction matrices constructed prior to measurement, while noise is quantified using observable-level statistics such as measurement distribution entropy and fidelity proxies. The observed ordering persists across multiple system sizesand hardware-inspired datasets. These results indicate that circuit-level noise cannot be fullycharacterized by workload-local or gate-independent models, and suggest that pre-measurementstructural organization plays a decisive role in shaping observable noise.
We present an empirical study of observable noise behavior in quantum circuits under fixedworkload constraints. Using publicly available circuit archives and measurement data, we showthat observable dispersion metrics are monotonically ordered by pre-measurement interactionstructure derived solely from circuit topology, and not by gate count or circuit depth alone.Structure is quantified using topology-derived interaction matrices constructed prior to measurement, while noise is quantified using observable-level statistics such as measurement distribution entropy and fidelity proxies. The observed ordering persists across multiple system sizesand hardware-inspired datasets. These results indicate that circuit-level noise cannot be fullycharacterized by workload-local or gate-independent models, and suggest that pre-measurementstructural organization plays a decisive role in shaping observable noise.
Random circuit sampling (RCS) on noisy quantum hardware is widely modeled as exhibiting exponential decay of fidelity metrics (e.g., XEB, HOG) with circuit depth, converging toward Haar-random statistics beyond a characteristic noise-limited scale. This work introduces a minimal phenomenological recurrence for a coarse-grained local coherence observable defined on the qubit connectivity graph. The recurrence reproduces standard exponential decay in unstructured (fully scrambled) circuits but predicts delayed thermalization and a nonzero plateau when repeated local motifs are engineered into circuit compilation. The model introduces a single topology-dependent memory parameter α(µ), where µ denotes motif density. A transcritical bifurcation occurs when α(µ) exceeds the effective per-layer decoherence rate γ, producing a calculable plateau height and build-up depth scale. A matched-pair experimental protocol—holding qubit count, two-qubit gate count per layer, and reported hardware error rates fixed while varying only motif density—provides a direct falsification criterion. Absence of statistically significant topology dependence would rule out the model in its minimal form. The recurrence is an effective coarse-grained description at the metric level and does not modify underlying quantum channel structure or violate complete positivity.
Evaluating the reliability of noisy quantum circuits is essential for implementing quantum algorithms on noisy quantum devices. However, current quantum hardware exhibits diverse noise mechanisms whose compounded effects make accurate and efficient reliability evaluation challenging. While state fidelity is the most faithful indicator of circuit reliability, it is experimentally and computationally prohibitive to obtain. Alternative metrics, although easier to compute, often fail to accurately reflect circuit reliability, lack universality across circuit types, or offer limited interpretability. To address these challenges, we propose a fine-grained, scalable, and interpretable framework for efficient and accurate reliability evaluation of noisy quantum circuits. Our approach performs a state-independent analysis to model how circuit reliability progressively degrades during execution. We introduce the Noise Proxy Circuit (NPC), which removes all logical operations while preserving the complete sequence of noise channels, thereby providing an abstraction of cumulative noise effects. Based on the NPC, we define Proxy Fidelity, a reliability metric that quantifies both qubit-level and circuit-level reliability. We further develop an analytical algorithm to estimate Proxy Fidelity under depolarizing, thermal relaxation, and readout error channels. The proposed framework achieves fidelity-level reliability estimation while remaining execution-free, scalable, and interpretable. Experimental results show that our method accurately estimates circuit fidelity, with an average absolute difference (AAD) ranging from 0.031 to 0.069 across diverse circuits and devices.
Low-Dimensional Structure in Quantum Variability: Evidence from State-Space Reconstruction in Monitored Quantum Systems This study investigates whether quantum variability, typically interpreted as intrinsically stochastic, exhibits underlying dynamical structure. Using publicly available data from monitored quantum circuits, we analyze time-ordered observables across circuit depth and evaluate their predictability using state-space reconstruction techniques. By constructing trajectories from measurement outcomes and comparing first-order and second-order embeddings, we test whether future states can be inferred from prior states. Both linear and nonlinear models are employed, and results are evaluated using root mean squared error (RMSE). To ensure that observed structure is not a statistical artifact, all results are compared against shuffled controls that preserve marginal distributions while removing ordered dependence. We find that prediction error for real data is significantly lower than for shuffled controls, demonstrating the presence of genuine temporal structure. Incorporating prior state information improves predictive performance consistently, indicating measurable memory or path dependence. However, the improvement beyond first-order embedding is modest, and nonlinear models provide only limited additional gains. These results show that quantum variability in the monitored system is not fully characterized by featureless stochastic behavior. Instead, it exhibits low-dimensional, weakly nonlinear, and memory-dependent structure, with most predictive information contained in the immediately preceding state. This work provides empirical evidence that quantum variability can be described as a constrained dynamical process governed by a small number of effective degrees of freedom. While the probabilistic framework of quantum mechanics remains operationally valid, the findings suggest that observed randomness may reflect structured underlying dynamics rather than purely intrinsic indeterminacy.
Noise in contemporary quantum hardware is highly non-uniform across qubits and couplers, giving rise to localized low-noise "islands" within otherwise noisy device topologies. As quantum workloads scale, executions are increasingly forced to traverse high-noise regions, degrading algorithmic fidelity. Circuit cutting provides a route to circumvent such regions by decomposing large circuits into smaller subcircuits, but its practicality is limited by exponential sampling overhead and the lack of systematic guidance on how cut strategies should align with heterogeneous hardware noise. In this work, we present a hardware-noise-aware circuit cutting framework that explicitly exploits the spatial non-uniformity of noise in quantum devices. Rather than proposing a new cut-finding algorithm, we formalize the problem of device-constraint selection under realistic hardware noise and show that this choice critically determines both execution overhead and effective noise. Using a unified gate- and wire-cutting formulation, we demonstrate that small, hardware-informed relaxations in the device constraint yield exponential reductions in execution overhead while preserving alignment with low-noise hardware regions. Across representative workloads, our method achieves an average reduction in the number of circuit executions ranging from 5-54x for 20-qubit circuits, and enables tractable circuit cutting for 50-qubit circuits and application-level benchmarks where conventional strategies incur prohibitive overhead. These results establish noise-aware device-constraint selection as a necessary ingredient for making circuit cutting resource-efficient and practically deployable on contemporary quantum hardware.
Quantum computers in the Noisy Intermediate-Scale Quantum (NISQ) era face significant challenges due to inherent noise and limited qubit coherence. Accurate fidelity evaluation of quantum states necessitates multiple repeated measurements to obtain statistical results. But determining the optimal number of measurements remains an open problem due to the dynamic, device-dependent nature of quantum noise. Existing methods either assume prior knowledge of the noise model or inherently employ a fixed measurement strategy, which limits their applicability in practical deployment scenarios. This paper presents AutoFid, an adaptive and noise-aware fidelity measurement framework that automatically determines the number of required tests based on circuit structure and hardware feedback. AutoFid models quantum circuits as Directed Acyclic Graphs and estimates structural complexity via random walks, enabling estimation of measurement effort. It further incorporates transpilation-aware features such as gate fidelity, depth inflation, and crosstalk to refine iteration budgets. During runtime, AutoFid dynamically samples fidelity results and employs an early stopping strategy based on confidence intervals to reduce redundant measurements while preserving accuracy guarantees. We evaluate AutoFid on 18 quantum benchmarks executed on real IBMQ hardware platforms. Experimental results show that AutoFid reduces measurement costs by more than 50% compared to both fixed-shot and learning-based baselines, while consistently maintaining fidelity bias below 0.01. Additional analysis using classical software testing metrics and ablation studies demonstrate its effectiveness, robustness, and adaptability across a wide range of quantum workloads.
Ensuring the integrity of quantum circuits is a significant challenge in the Noisy Intermediate-Scale Quantum (NISQ) era, where circuits are subject to compilation transformations, hardware constraints, and potential adversarial modifications. Existing validation approaches typically rely on either structural analysis or behavioral evaluation, leading to incomplete assessment of circuit correctness.
In this work, we investigate the relationship between structural, interaction-level, and behavioral perspectives of circuit integrity, demonstrating that a single aspect of integrity is insufficient to guarantee circuit integrity; structural similarity alone does not ensure behavioral equivalence. To address this problem, we use a three-layer metric framework that combines the Structural Integrity Score (SIS), the Operational Integrity Score (OIS), and the Interaction Graph Semantic-Logical Score (IGS). SIS captures global structural properties, OIS quantifies behavioral divergence using Jensen-Shannon distance, and IGS models interaction patterns and dependencies in a pre-execution setting.
Through controlled anomaly injection on benchmark quantum circuits, we demonstrate that each metric captures a different aspect of circuit deviation. In particular, structural blind-spot cases (SIS >= 0.95) reveal a clear limitation of structural analysis, where OIS detects anomalies in 93.85% of instances, while IGS detects 72.58%. These results highlight that the metrics provide complementary insights and that a single metric is insufficient for reliable circuit validation.