quantum algorithm analysis

This study addresses the synergistic threat posed by quantum computing and artificial intelligence to current cryptographic systems: Shor’s algorithm can break public-key schemes such as RSA and ECC, while AI-driven side-channel attacks can circumvent physical countermeasures. The paper presents the first systematic evaluation of cryptographic vulnerability under combined quantum–AI attacks and proposes a defense-in-depth framework integrating post-quantum cryptography (ML-KEM/ML-DSA and SLH-DSA), implementation hardening, and cryptographic agility. Findings indicate that lattice-based and hash-based signatures resist known quantum attacks but remain susceptible to side-channel leakage at the implementation layer; symmetric encryption retains security in the quantum setting only if key lengths are doubled to compensate for halved effective strength. This work underscores that cryptographic security must be treated as a continuously evolving process and offers a practical roadmap for mitigating coordinated quantum–AI threats.

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.

Quantum algorithm design is hindered by quantum mechanical complexity and stringent control requirements, compounded by the absence of a dedicated benchmark for large language models (LLMs). Method: We introduce the first LLM-oriented benchmark for quantum algorithm design, comprising 25 canonical algorithms and 120,290 formally verified QASM circuits, underpinned by a novel formal framework integrating program synthesis, hierarchical task modeling (categorized into three algorithmic suites), fully automated verification, and interactive reasoning. Contribution/Results: Empirical analysis uncovers systematic error patterns in LLMs—particularly counterintuitive degradation under fine-tuning versus few-shot learning. End-to-end evaluation confirms baseline generation capability but reveals severe generalization bottlenecks. This work establishes a reproducible, verifiable infrastructure and delivers foundational insights for AI-driven quantum programming.

This work addresses the low efficiency of detecting critical security vulnerabilities—such as use-after-free, null-pointer dereference, and division-by-zero—in classical formal program verification. We propose the first systematic approach that models defect detection as a structured optimization problem amenable to quantum computation. Methodologically, we encode program semantics into SAT instances and map them onto a quantum optimization framework, integrating the Quantum Approximate Optimization Algorithm (QAOA), Grover’s search, and Quantum Singular Value Transformation (QSVT) to establish an end-to-end solution pathway from logical constraints to quantum state evolution. Empirical evaluation on synthetic benchmarks and real-world vulnerability cases demonstrates that our method efficiently recovers satisfying assignments on both quantum simulators and actual quantum hardware, exhibiting asymptotic polynomial speedup potential. This work establishes a novel paradigm for leveraging quantum computing to enhance software trustworthiness and reliability assurance.

This study addresses the urgent challenge posed by quantum computing to classical cryptographic systems and advocates for a systematic transition to post-quantum cryptography (PQC). It comprehensively reviews the principal PQC approaches—including lattice-based, code-based, hash-based, multivariate, and isogeny-based schemes—and provides an in-depth analysis of the threats from Shor’s algorithm, the current status of NIST standardization, and practical deployment challenges. The work introduces an innovative incremental migration architecture that integrates mathematical foundations with security engineering, bridging the gap from foundational understanding to strategic migration decisions. Notably, it delivers the first authoritative technical guide tailored for the Portuguese-speaking academic community, thereby supporting the development of a secure and coherent PQC governance framework.

Whether quantum computing can deliver substantial acceleration for deep learning remains an open and critical question. Method: This work conducts the first systematic assessment of quantum algorithms’ applicability to deep learning, integrating quantum algorithmic analysis, hardware trend modeling, QRAM feasibility evaluation, and an extended version of Choi et al.’s quantitative prediction methodology. Contribution/Results: We identify three promising acceleration pathways—quantum-enhanced matrix operations, optimization solving, and kernel methods—but rigorously expose their fundamental limitations: inefficient quantum matrix multiplication, severe physical constraints on QRAM implementation, and insufficient problem–algorithm alignment, respectively. Crucially, we propose a unified algorithm–hardware co-evaluation framework that delineates both theoretical limits and engineering constraints of current quantum deep learning. Our analysis establishes concrete quantitative benchmarks and clarifies viable research directions for future breakthroughs.

This study addresses the limited systematic understanding of real-world quantum software development practices. It presents the first empirical investigation into programming patterns in quantum software by analyzing 80 open-source projects comprising 985 Jupyter Notebooks built with Qiskit, PennyLane, and Classiq. The authors construct a knowledge base of these patterns and develop an automated approach combining semantic search, static analysis, and natural language processing to detect their usage. The work identifies nine previously undocumented patterns and reveals a three-tiered paradigm of quantum programming—from basic circuit construction to domain-specific applications—demonstrating that higher-level abstractions are already widely adopted in fields such as finance and optimization. These findings indicate that quantum software engineering is transitioning toward maturity through the increasing use of structured, high-level development practices.

This study addresses the current lack of systematic empirical comparisons between quantum machine learning (QML) and classical machine learning in terms of performance, training efficiency, and stability. The authors establish a unified experimental framework to evaluate seven pairs of quantum and corresponding classical models across multitask supervised and reinforcement learning settings, using real-world datasets and diverse hardware environments. Their results demonstrate that existing QML models do not yet surpass classical baselines in overall performance, training speed, or stability. However, they reveal that QML exhibits distinctive potential in noise suppression and controlling false positives. This work provides the first systematic characterization of the practical advantages and fundamental challenges facing QML, delineating its current boundaries relative to classical approaches.

This study systematically evaluates the practical applicability of quantum computing in industrial optimization and machine learning. Building upon the QCHALLENGE initiative, we establish a unified benchmarking framework encompassing both superconducting and trapped-ion architectures. We introduce three standardized metric categories and a traffic-light–style decision mechanism to quantitatively compare the performance boundaries of quantum, hybrid, and classical approaches across dimensions including model formulation, scalability, solution quality, runtime, and portability. Our analysis identifies the most promising near-term quantum application scenarios, delineates domains where hybrid strategies offer the greatest feasibility, and clarifies areas where classical methods remain superior, thereby providing a clear roadmap for industrial deployment.