A Multi-Level Integrity Evaluation Framework for Quantum Circuits under Controlled Anomaly Injection

Abstract: 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.

• The paper develops a multi-level integrity evaluation framework using Structural (SIS), Interaction (IGS), and Operational (OIS) metrics to detect circuit anomalies.
• It introduces graph-based semantic analysis and behavioral comparison via Jensen-Shannon distance to identify subtle deviations in quantum circuit operations.
• Empirical results demonstrate that relying solely on structural metrics is insufficient, as OIS detects 93.85% of anomalies compared to IGS at 72.58%.

Multi-Level Integrity Evaluation of Quantum Circuits under Controlled Anomaly Injection

Framework Overview

The paper "A Multi-Level Integrity Evaluation Framework for Quantum Circuits under Controlled Anomaly Injection" (2604.26430) presents a comprehensive approach to quantum circuit integrity validation by integrating structural, interaction-level, and behavioral metrics. The framework is motivated by the limitations of traditional methods that focus on a single perspective—typically structural analysis or behavioral evaluation—which are insufficient for detecting all forms of circuit deviation, especially in the context of the Noisy Intermediate-Scale Quantum (NISQ) era.

A three-metric scheme is devised:

• Structural Integrity Score (SIS): Quantifies similarity based on global structural descriptors (gate count, depth, two-qubit gate usage, topology).
• Interaction Graph Semantic-Logical Score (IGS): Models dependencies and gate-level semantics via graph-based representations pre-execution.
• Operational Integrity Score (OIS): Measures behavioral deviation through output distribution comparison using Jensen-Shannon distance.

Anomalies—including gate insertions/deletions, substitutions, reordering, Trojan operations, and qubit swaps—are systematically injected into benchmark circuits. The empirical analysis demonstrates distinct response characteristics for each metric.

Figure 1: Multi-layer quantum circuit integrity framework using SIS, IGS, and OIS. Black lines show the reference circuit; red lines indicate anomalies.

Metric Design and Theoretical Rationale

Structural Integrity Score (SIS)

SIS is computed as the complement of normalized deviation over four structural aspects—gate count, circuit depth, two-qubit gates, and interaction topology. Equal weighting is used for anomaly detection across circuit types. The metric is agnostic to execution, facilitating fast pre-deployment validation but suffers from insensitivity to semantic-preserving transformations.

Interaction Graph Semantic-Logical Score (IGS)

IGS represents the circuit as a labeled DAG, with nodes capturing gate characteristics (including unitary-based feature vectors) and edges encoding dependency structure and execution order. Several discrepancy terms (topology, node semantics, order, interaction, usage) are computed and weighted. This enables detection of perturbations affecting interaction patterns or causal relationships, particularly those invisible to global structural metrics.

Operational Integrity Score (OIS)

OIS utilizes the Jensen-Shannon distance between the output distributions of a reference and test circuit, mapping behavioral divergence to a normalized similarity score. It reliably uncovers functional deviations but is bottlenecked by simulation cost, especially for larger circuits.

Experimental Setup and Anomaly Injection Methodology

An exhaustive set of experiments is conducted on QASMBench circuits (≤40 qubits, ≤2000 gates), under both fixed and severity-scaled anomaly injection. Eight anomaly types are considered, each targeting distinct structural or interaction-level attributes. Evaluation is controlled for reproducibility: fixed random seeds, consistent circuit selection, and anomaly definitions.

The three metrics are analyzed for responsiveness and efficiency across anomaly types and severity levels. Pre-execution metrics (SIS, IGS) are compared to the simulation-dependent OIS. Implementation details include graph construction optimizations and caching strategies.

Results

Metric Responsiveness to Structural and Semantic Anomalies

SIS is highly sensitive to direct structural changes (gate insertion/deletion, depth modification) but is nearly invariant for structure-preserving modifications (substitution, reordering), confirming structural-blind spot scenarios. OIS, conversely, degrades with increasing severity across all anomaly types, reliably signaling behavioral divergence.

Figure 2: SIS response across defined anomalies.

Figure 3: IGS response across defined anomalies.

IGS exhibits sensitivity to interaction-level and ordering anomalies, capturing subtleties overlooked by SIS but not always matching OIS's behavioral response.

Complementarity and Blind-Spot Analysis

A pivotal set of experiments examines structural-blind spot cases (SIS ≥ 0.95). OIS detects anomalies in 93.85% of these, while IGS detects 72.58%, demonstrating the metrics' complementary strength. This underlines that structural similarity is not a reliable proxy for behavioral equivalence; interaction-level assessment partially bridges this gap.

Figure 4: SIS remains high for structure-preserving anomalies, while IGS and OIS degrade with increasing severity, capturing interaction level and behavioral deviations.

Cross-Metric Correlation and Efficiency

Analysis of IGS-OIS correlation reveals consistently weak alignment—Pearson $r$ declines from 0.293 (severity 0.1) to 0.158 (severity 0.6)—reinforcing the independence of interaction-level and behavioral attributes.

Figure 5: IGS and OIS exhibit weak correlation across severity levels, confirming that interaction-level similarity does not reliably reflect behavioral equivalence.

In terms of computational efficiency, IGS maintains low, stable runtime for all circuit sizes, unlike OIS, which exhibits exponential runtime growth and instability for circuits beyond 10 qubits.

Figure 6: IGS achieves stable and low runtime across qubit counts, while OIS incurs significantly higher and more variable computational cost.

Discussion and Implications

The framework reveals a clear need for multi-level integrity assessment in quantum circuit workflows, especially given the prevalence of structure-preserving optimizations and adversarial manipulations in NISQ settings. SIS is efficient for large-scale screening but unreliable for full validation. OIS offers precision but is computationally intractable for large circuits. IGS provides intermediate granularity, capturing interaction-level anomalies with a computational profile suitable for practical pre-execution analysis.

The results support a staged validation paradigm: structural screening (SIS), interaction-level diagnosis (IGS), and selective behavioral verification (OIS). Such an approach improves anomaly coverage, interpretability, and operational scalability.

Security implications are significant: adversaries or faulty compilers may modify circuit behavior without altering structural descriptors, necessitating multifaceted validation schemes. The integration of graph-based semantic analysis may inform future quantum hardware/software security mechanisms.

Threats to Validation

Controlled experimental conditions (single reference instance, idealized simulation, fixed transpilation settings) limit immediate generalizability to real-world quantum devices and heterogeneous workloads. OIS evaluation is constrained to small circuits due to exponential simulation cost. Metric component weights for IGS are not empirically optimized, and anomaly taxonomy covers only select perturbations.

Conclusion

The paper establishes the necessity of integrating structural, interaction-level, and behavioral metrics for robust quantum circuit integrity evaluation. Empirical results highlight structural-blind spot detection rates of 93.85% (OIS) and 72.58% (IGS), proving that structural similarity does not imply behavioral correctness. The weak correlation between IGS and OIS further demonstrates that no single metric suffices for comprehensive integrity assessment.

Theoretical and practical implications suggest multi-dimensional validation pipelines, possibly culminating in a unified integrity index. Future work includes refining the interaction-behavioral alignment and optimizing metric weighting for improved anomaly sensitivity and interpretability.

Conclusion

This study delivers a rigorous framework for quantum circuit integrity validation. By empirically demonstrating the limitations of single-perspective approaches and quantifying the complementarity of structural, interaction-level, and behavioral metrics, it advances both the theoretical understanding and practical methodology of quantum software verification. The framework is immediately applicable to quantum compilation, optimization, and cloud-deployed circuit validation workflows, with substantial implications for future research in quantum security and reliability.