quantum-classical integration

The growing complexity of software engineering (SE) optimization problems necessitates rigorous investigation into emerging paradigms such as quantum computing. Method: We conducted the first systematic literature review (SLR) specifically focused on quantum optimization in SE, screening 2,083 publications from six major academic databases and selecting 77 empirical studies through structured searching, multi-stage filtering, and thematic coding. Contribution/Results: Our analysis constructs the first comprehensive research landscape of quantum optimization in SE, revealing strong concentration in test case generation and deployment optimization, while critical areas—including requirements engineering, maintenance, and software evolution—remain severely underexplored. Furthermore, many influential contributions appear outside mainstream SE venues, highlighting pronounced interdisciplinary fragmentation. The study identifies key research gaps and proposes concrete collaborative pathways, thereby establishing both a theoretical foundation and practical guidance for advancing SE–quantum computing convergence.

Addressing the challenges of heterogeneous resource scheduling, cross-paradigm data movement, and unified access to both NISQ and fault-tolerant quantum devices in deep quantum–HPC integration, this paper proposes the first hardware-agnostic quantum–supercomputing fusion software stack. Methodologically, it introduces (1) a quantum–classical unified resource management framework; (2) a hardware-abstracted programming interface and a cross-platform Quantum Platform Manager API; and (3) a quantum gateway supporting REST/gRPC, a hybrid scheduler, and a quantum-circuit co-optimization toolchain. The stack seamlessly integrates with mainstream HPC job schedulers (e.g., Slurm, PBS). Empirical evaluation on hybrid algorithms—including the variational quantum linear solver—on real supercomputing systems demonstrates significant improvements in quantum–classical resource utilization and task throughput. The design is both practically deployable and inherently scalable, establishing a foundational infrastructure for large-scale quantum–HPC convergence.

This work proposes the first cloud-native scheduling framework systematically designed for hybrid quantum-classical computing to address the challenge of efficiently orchestrating heterogeneous computational resources at scale. Built upon Kubernetes, Argo Workflows, and Kueue, the framework enables unified, resource-aware dynamic scheduling across CPUs, GPUs, and quantum processing units (QPUs), supporting multi-stage, reproducible, and observable hybrid workflows. The effectiveness of the framework is demonstrated through end-to-end collaborative experiments on distributed quantum circuit cutting tasks, which highlight its significant advantages in scalability, flexibility, and reproducibility.

Current quantum software development overly emphasizes algorithms while neglecting architectural design, thereby limiting the scalability and engineering maturity of hybrid quantum-classical systems. To address this gap, this work proposes the Quantum Software Architecture Framework (QSAF), which for the first time categorizes 34 quantum circuit primitives by functionality and abstracts them into reusable architectural components with explicit interfaces and design constraints. QSAF establishes a multi-level abstraction hierarchy spanning from quantum gates to system-level constructs. By incorporating non-functional properties—such as circuit depth, error sensitivity, and information flow—to characterize component behavior, QSAF enables structured decomposition and optimization of hybrid workflows like variational quantum algorithms, significantly enhancing the rigor, modularity, and development efficiency of quantum system design.

This work addresses the lack of interoperability among current quantum compilation tools, which hinders the development of a unified software stack. It presents the first systematic integration of PennyLane and the Munich Quantum Toolkit (MQT) through the MLIR framework, leveraging MLIR’s intermediate representation and LLVM infrastructure to establish reusable integration pathways and best practices. By lowering the barrier to entry for quantum software engineers adopting MLIR, this approach enables seamless interoperability between distinct quantum toolchains. The study provides both a practical roadmap and actionable strategies for constructing a modular, interoperable quantum software ecosystem, thereby advancing the standardization and composability of quantum programming tools.

This work addresses the challenge of meeting user quality-of-service (QoS) requirements under the constraints of noisy intermediate-scale quantum (NISQ) devices by proposing a service-oriented architecture for hybrid quantum-classical systems. It pioneers the integration of service-oriented architecture (SOA) with quantum computing, employing formal architectural style modeling and QoS-driven design space exploration to delineate architectural decision boundaries. The approach dynamically selects optimal execution strategies at both structural and behavioral levels in response to varying QoS demands. Experimental results demonstrate that the proposed method can dynamically configure the system under realistic NISQ constraints to deliver quantifiable performance guarantees aligned with user-specified QoS requirements.

This work addresses the inefficiency in developing hybrid quantum-classical algorithms caused by the current isolation of quantum processing units (QPUs) from classical high-performance computing (HPC) systems. To bridge this gap, the paper proposes a Quantum-Centric Supercomputing (QCSC) reference architecture that deeply integrates QPUs, GPUs, and CPUs through co-design across hardware, middleware, and application layers, enabling end-to-end workflows for domains such as quantum chemistry and materials science. The study further establishes, for the first time, a systematic three-stage evolutionary roadmap for QCSC: beginning with QPUs as specialized accelerators, progressing to heterogeneous cooperative scheduling, and ultimately achieving full-stack co-design. This architecture provides a standardized technical pathway for quantum-HPC convergence, substantially enhancing algorithmic exploration efficiency and system scalability.

Existing approaches struggle to automate formal verification of hybrid quantum-classical programs due to the absence of a unified model capturing mixed control flow, measurement operations, and classical data structures. This work proposes the first framework enabling automated verification of such programs, centered on a novel symbolic representation called “Hybrid Path-Sums.” We develop a corresponding rewrite system and an assertion language to precisely characterize and reason about hybrid program states. Leveraging symbolic execution and probabilistic semantic extraction, we implement a dedicated verification engine and demonstrate its correctness and substantially improved efficiency over existing methods across several representative hybrid quantum-classical programs.

Existing hybrid quantum programs lack end-to-end, workflow-level evaluation methodologies. Method: This paper proposes a workflow-aware systematic assessment framework: (i) it formally defines workflow-oriented quantum readiness levels and quantum utility metrics; (ii) it introduces a quality-constrained normalized speedup ratio, a workflow-aware quantum readiness score, and a time–drift joint auditing mechanism for hybrid pipelines; and (iii) it establishes an evaluation system balancing budget alignment and experimental reproducibility. A Python-based open-source reference tool is implemented, integrating Qiskit, PennyLane, and other frameworks to support metric instantiation and automated auditing of classical–quantum co-solvers. Contribution/Results: The work delivers a reusable metrics library and standardized auditing patterns, significantly improving the accuracy of performance evaluation and enabling precise bottleneck identification in hybrid quantum workflows.

This study addresses industrial job shop scheduling by developing a customized model that incorporates hardware constraints and systematically evaluates the performance of quantum annealing (D-Wave), digital annealing (Fujitsu), quantum-inspired algorithms, and classical approaches—including mixed-integer linear programming (MILP) and exact solvers—on platforms such as IBM Quantum. Through a hardware-software co-design methodology, the work demonstrates the practical utility of quantum and quantum-inspired techniques in enhancing the quality of approximate solutions, guiding solver selection, and integrating into classical computational workflows. The research establishes a scalable hybrid solving paradigm for industrial scheduling and validates its feasibility and potential during early-stage proof-of-concept demonstrations.