entanglement quantification and measures

Efficiently identifying qubit entanglement in quantum programs is critical for circuit optimization and correctness verification, yet exact analysis suffers from exponential time complexity. This paper introduces the first static entanglement analysis framework based on abstract interpretation: it extends classical abstract interpretation by designing a quantum-state-specific abstract domain and corresponding transfer functions, and develops a linear-time approximate analysis algorithm. Implemented as a prototype in Standard ML, the system safely and efficiently determines potential entanglement between any pair of qubits—without incurring exponential overhead. The approach ensures both strong scalability and theoretical soundness, providing provably safe over-approximations. It constitutes the first systematic application of approximation-based program analysis techniques to quantum entanglement prediction, establishing a verifiable foundation for static analysis in quantum software engineering.

In the rapidly advancing field of quantum computing, measurement-based output verification faces fundamental limitations due to the probabilistic nature of quantum states, hindering rigorous validation of complex quantum program behavior. Method: We systematically classify existing measurement-based verification techniques and empirically analyze their shortcomings—particularly their inability to adequately characterize distribution-level and value-level correctness, especially for programs exhibiting nontrivial quantum phenomena. We then comparatively evaluate state-vector–based verification, conducting an empirical study across diverse quantum programs. Contribution/Results: Our results demonstrate that measurement-based verification is only suitable for rudimentary existential checks, whereas state-vector–based verification precisely captures superposition, entanglement, and other core quantum behaviors, significantly enhancing test depth and reliability. This work advances quantum program testing from a “result-oriented” paradigm toward a “process-traceable” one, providing both theoretical foundations and methodological guidance for building robust quantum software quality assurance frameworks.

Existing UML lacks native support for modeling qubits, quantum gates, and hybrid quantum-classical systems, hindering the engineering design of quantum software. This paper proposes QuanUML—the first quantum software modeling language deeply integrated into the UML standard framework—by extending the UML metamodel to natively support quantum circuits, dynamic quantum operations, and quantum-classical co-abstraction. Its key contribution is the first structural encoding of quantum computational primitives (e.g., superposition, entanglement, measurement) at the UML semantic level. Validation via modeling Shor’s algorithm and an efficient long-range entanglement protocol demonstrates that QuanUML significantly improves design traceability, team collaboration efficiency, and feasibility of formal verification. It thereby bridges a critical gap in model-driven development for quantum software engineering.

This paper addresses the natural quantization of continuous numerical data—automatically identifying statistically meaningful discrete “quantum” intervals whose boundaries align with human intuition. We propose a multi-criteria decision framework integrating the Silhouette coefficient (threshold > 0.65) for assessing inter-class separability, the Dip test (p < 0.5) to validate unimodality assumptions, and an information compression metric to evaluate representational conciseness. Experiments demonstrate that the Silhouette coefficient better captures human perceptual judgments than conventional compression-based approaches, and the synergistic use of all three criteria robustly determines quantization feasibility. We establish, for the first time, interpretable and reproducible quantitative thresholds for quantization validity. A user study confirms strong correlation (r > 0.82) between our metrics and human intuitive judgments. This work provides both theoretical foundations and practical tools for symbolic modeling and interpretable AI.

This study addresses the challenge of precise cancer subtyping from small-sample, high-dimensional multi-omics data. We conduct the first systematic evaluation of quantum kernel (QK) methods on real-world breast cancer (BC) multi-omics datasets to assess their clinical applicability. We propose a multi-level entanglement quantum encoding strategy and empirically validate its noise robustness on a real quantum processing unit (QPU); notably, low-expression encoding demonstrates both hardware feasibility and superior noise resilience on NISQ devices. Experiments show that QK-based clustering achieves performance comparable to classical kernel methods while resolving finer-grained subtype clusters with fewer samples. Our key contribution is uncovering the fundamental trade-off between quantum encoding expressivity and hardware-level robustness, and—critically—demonstrating the practical viability of QK methods in real biomedical applications.

This work addresses the lack of a standardized observability framework in quantum networks, which hinders effective fault diagnosis and adaptive control. It proposes the first multidimensional performance metric system tailored for quantum networks, encompassing key parameters such as entanglement fidelity, quantum bit error rate, dark count rate, and timing jitter, while integrating environmental sensor data. Building on this foundation, the authors design and implement a non-intrusive, integrable real-time monitoring prototype, which has been deployed and validated at Oak Ridge National Laboratory. The system enables real-time data acquisition, performance alerting, and dynamic feedback, thereby establishing a critical observability infrastructure for quantum software-defined networking and autonomous control.

This work proposes the first unified quantum embedding framework for counting subgraphs—such as triangles, cycles, and cliques—in graphs. The method encodes an N-vertex graph via its adjacency list into a quantum state and designs measurement operators tailored to the edge structure of the target subgraph. By performing measurements on the m-fold tensor product of this state, the algorithm estimates the number of occurrences of the subgraph. Requiring only 2⌈log₂N⌉ working qubits and two ancilla qubits, it achieves a worst-case gate complexity of O(N²) within quantum logspace, offering a significant advantage in space complexity over classical approaches. This result establishes a novel quantum paradigm for graph motif counting.

This work addresses the limitations of existing formalisms for hyperproperties in capturing quantitative aspects inherent in real-world systems, such as numerical relationships in information flow control. To overcome this, the paper introduces Quantitative Hyper-Logic (QHL), a novel framework that reformulates hyperproperty specifications using measure theory, replacing classical Boolean quantifiers with measures to support nested quantitative structures. Leveraging Hoeffding’s inequality and extreme value theory, the authors develop an efficient statistical verification algorithm and provide rigorous analyses of sample complexity and statistical guarantees. Experimental evaluation on quantitative information-flow benchmarks demonstrates that QHL substantially outperforms conventional qualitative approaches, offering superior expressiveness and verification capabilities that better align with the demands of practical systems.

This work addresses the lack of an efficient and concise flow structure for measurement-based quantum computation on high-dimensional qudits, which has hindered their application in fault tolerance and optimization. Focusing on qudit graph states, the paper proposes a streamlined definition of qudit flow, establishes the canonicity of focused flows, and introduces a flow-finding algorithm with O(n³) time complexity—significantly improving upon the previous O(n⁴) bound. Furthermore, it develops a suite of flow-preserving graph transformations, including pivoting and vertex addition/removal, to construct an algorithmic framework capable of generating large-scale flow-equipped qudit computations. This framework lays the groundwork for qudit circuit optimization and future applications in machine learning.

This study addresses the lack of systematic understanding regarding the challenges faced by quantum computing developers when using practical toolchains and algorithms. Through the first large-scale empirical analysis of 1,404 Stack Overflow posts, combining topic modeling, quantitative content analysis, and evaluation of answer acceptance rates and response times, the work reveals the topical landscape, tool adoption patterns, and algorithmic references within the developer community. Seven core themes are identified, with hybrid quantum-classical computing and quantum circuit implementation emerging as the most prominent. Qiskit and Q# dominate as the primary development frameworks, while Grover’s and Shor’s algorithms are the most frequently cited. The study further quantifies significant differences across topics in terms of problem-solving difficulty and levels of community support.