Quantum Algorithms

Robot Operating System 2 (ROS 2) standardizes application code against a middleware interface (RMW) whose reference implementations are built on the Data Distribution Service (DDS). We present AXON, an alternative ROS 2 RMW implementation that separates transport policy by deployment scope. A Rust core and C++ adapter use POSIX shared-memory rings for same-host communication, QUIC for remote communication, and a daemon for discovery and graph synchronization. We then describe two fail-closed TLS 1.3 key-establishment configurations for remote traffic. The classic configuration offers only the hybrid X25519MLKEM768 group, preventing negotiation of a classical-only group. The qkd configuration imports a 256-bit key obtained through the ETSI GS QKD 014 API as a pairwise external PSK and offers no Diffie-Hellman group. Its default messages10 strategy additionally protects remote application messages with AES-256-GCM, rotating KME material after ten outgoing messages and using a fresh nonce per envelope; session relies on QUIC protection alone. The external-PSK path requires a narrow extension to rustls, now bundled with AXON. We define the threat model, distinguish peer authentication in the two configurations, and delimit the implementation-level validation from ROS 2 conformance, comparative performance, and physical-QKD validation.

Classical simulation remains essential for developing and validating quantum algorithms, but its cost grows rapidly with circuit size. Tensor-network contraction can reduce this cost by exploiting circuit structure, although its efficiency depends strongly on the chosen contraction plan. On GPUs, plans with similar theoretical complexity may perform very differently because execution also depends on parallelism, reduction structure, memory traffic, and contraction geometry. We present a learning-to-rank framework for selecting efficient contraction plans before executing them. Each plan is represented by structural features derived directly from its sequence of pairwise contractions, and gradient-boosted rankers are trained from GPU measurements using listwise and pairwise objectives. We evaluate the resulting models on diverse circuit families, using separate in-distribution and circuit-family-shift test sets, and compare them with random and MinFill-based baselines. The learned rankers generally identify better plans, with the listwise model providing the strongest overall decision quality. We also study backend shift by comparing empirical plan orderings on two GPU architectures and evaluating the source-trained models on the second device without retraining. The rankings remain substantially, though not perfectly, stable across GPUs, and the models retain useful decision quality. These results support Learning to Rank as a practical way to reduce contraction-plan search, while showing that performance remains partly backend dependent.

Conventional BB84 Quantum Key Distribution (QKD) systems rely on a fixed 11% Quantum Bit Error Rate (QBER) threshold to detect eavesdropping. However, stealthy attacks can remain below this threshold while still compromising channel security. This paper proposes a temporal QBER based machine learning framework for detecting and classifying eavesdropping attacks in BB84 QKD systems. Rather than relying on average session level QBER, the framework extracts 63 physics-informed temporal features capturing burst behavior, temporal instability, basis dependent asymmetry, and QBER loss interactions. Random Forest, XGBoost, and Support Vector Machine with a Radial Basis Function kernel (SVM-RBF) classifiers are evaluated on seven eavesdropping attacks and a normal channel scenario under noisy and lossy conditions. Averaged over ten independent runs, XGBoost achieves the best performance with 88.01% (0.47%) accuracy and a macro F1 score of 0.8803, while SVM-RBF performs comparably, confirming the robustness of the proposed features. Evaluated as a binary attack-versus-normal detector for comparison with conventional monitoring, a fixed 11% QBER threshold achieves only 25.82% accuracy with a False Negative Rate (FNR) of 0.8477, whereas the proposed framework reduces the FNR to 0.0198, substantially improving detection of stealthy attacks that evade threshold-based monitoring. SHapley Additive exPlanations based (SHAP) explainability shows that physics-informed temporal and channel derived features are highly discriminative for identifying eavesdropping strategies. These results demonstrate that temporal QBER driven machine learning provides an accurate, explainable, and practical framework for multi attack security monitoring in BB84 QKD systems.

Reinforcement learning is a subfield of machine learning that studies how an agent interacts with an environment in order to extract as large a reward as possible. A standard approach to study such interaction is through Markov Decision Processes (MDPs) and the task of choosing an optimal policy --- a function that tells the agent which action to take. In this work, we study two types of MDPs --- finite-horizon and infinite-horizon discounted --- and propose new quantum algorithms for computing approximate optimal policies. Our quantum algorithms are based on a new combination of standard value iteration and quantum subroutines like quantum mean estimation and quantum maximum finding, overall enhanced with techniques from sample-optimal classical algorithms. Our resulting query complexities improve upon previous works, thus approaching already established quantum lower bounds.

We report genuine-un-compiled, textbook-faithful-quantum cryptanalysis of symmetric-cipher structures executed on real IBM quantum hardware (ibm_kingston, Heron generation). Using Simon's algorithm we recover the hidden period of the Even-Mansour cipher up to security parameter N = 10 on real hardware, beyond the largest previously reported real-hardware key recovery of N = 4, and we cleanly recover the periods of a 3-round Feistel (DES-family) construction at block sizes 6 and 8; a 21-qubit block-10 instance is verified in simulation and submitted to hardware. We further provide a breadth-first benchmark of five genuine quantum attacks spanning four symmetric-cipher design paradigms -- Bernstein-Vazirani (linear structure, single query), Grover (SPN key search, quadratic), and Simon (Even-Mansour, CBC-MAC forgery, and Feistel; exponential-to-polynomial in query complexity) -- validated to the classical-simulation ceiling of 25 qubits. We are deliberately explicit about scope: these attacks target reduced or structured constructions in the Q2 (quantum-query) model, asymptotically follow the birthday bound and therefore do not constitute quantum advantage over classical collision-finding, do not break full AES/RSA or 16-round DES, and rely on error mitigation rather than fault-tolerant error correction. Our contribution is the real-hardware demonstration at record structure sizes, the breadth of genuine algorithmic coverage across four paradigms, and an honest, reproducible benchmark with public artifacts.

AI coding agents produce code faster than humans can review it. In our approach, the prover is the judge of whether the code is correct. Under a verifier-driven loop, AI agents wrote and verified bare-metal security software in Ada/SPARK spanning classical and post-quantum cryptography, TLS 1.3, IKEv2, X.509, and a Matrix client. GNATprove discharged 49,280 proof obligations, established functional correctness for selected primitives, and proved the absence of run-time errors for the rest, at roughly 20-40 times lower supervision cost than comparable hand verification. GNATprove alone was insufficient: some defects could not be detected and were resolved using known-answer tests, interoperability, or human review of specifications. Given weak checks, the agent tried to bypass them and reported success. We report where each layer caught faults and draw the central lesson: what an agent can be trusted to establish is bounded by the strength of its feedback.

The potential capabilities of quantum computers motivated the development of cryptographic protocols suitable for securing communication against adversaries with access to large fault-tolerant quantum computers. However, even though current quantum computers are limited in terms of size and precision, they can still be useful for finding loopholes and weaknesses in the post-quantum cryptographic protocols. In this work, we present an attempt to utilize the capabilities of Quantum Generative Adversarial Networks (QGANs), one of the promising architectures used in quantum machine learning, for this purpose. We describe an example application of QGAN architecture for the purpose of loading the probability distribution of the hash-based digital signatures into the memory of a quantum computer. Our results confirm that near-term hybrid quantum-classical methods possess capabilities required for this purpose. The presented approach can be used as a first step in the workflow, enabling the utilization of quantum computing for attacking post-quantum cryptographic primitives.

Machine learning models have scaled to unprecedented sizes, making training across distributed devices the de facto standard in the field. In this work, we explore how quantum communications can make distributed training both more communication-efficient and information-theoretically private, for both classical and quantum learning models. Ring all-reduce is the foundational communication primitive for large-scale distributed training. We present a quantum version that reduces per-link online communication by a provably optimal factor of two using pre-shared entanglement and superdense coding, without requiring the learning model or gradient computation to change. Beyond bandwidth, the primitive enables privacy guarantees that are information-theoretically impossible for any classical protocol, achieving composable ε-secure aggregation, via verified entanglement, at a 2x overhead in GHZ copies. Our hybrid quantum-classical communication architecture yields simultaneous communication and security advantages for large scale distributed training, regardless of whether the learning itself is quantum or classical. Finally, we characterise quantum advantages in gradient conflict detection for server-to-client communication under bandwidth constraints, a setting that arises after ring all-reduce is completed, when full gradient broadcast to external clients is infeasible. Two variants of the problem admit different separations. For margin-based alignment testing (\textsc{GapIP}_τ), the quantum advantage is quadratic in the margin parameter: \widetilde{O}(τ^{-1}\log P) qubits versus \widetilde{O}(\min(\τ^{-2},P)) bits. For sign-consistency auditing against a private parameter matching (\textsc{TieAudit}_ε), the advantage represents an exponential separation in communication complexity: Ω(\sqrt{P}) bits whereas O(ε^{-2}\log P) qubits suffice.

The transition to Post Quantum Cryptography (PQC) introduces considerable implementation complexity, requiring strict adherence to constant-time execution, side channel resistance, and precise parametrisation. Simultaneously, large language models (LLMs) are heavily embedded in software development workflows, including cryptographic engineering. While LLMs improve productivity, evidence shows that they frequently generate insecure or suboptimal code, particularly in security critical domains. This paper introduces Secure Coding Drift in PQC, a novel socio technical vulnerability model capturing the gradual degradation of secure coding practices due to sustained reliance on LLM-generated code. Unlike prior work that focuses on static vulnerabilities, we conceptualise security risk as a longitudinal behavioural phenomenon rising from human AI interaction. To mitigate this, we propose a gamified, LLM augmented secure coding framework that embeds adversarial evaluation, behavioural feedback, and security scoring into development workflows. Our approach reframes LLMs from passive assistants into active security co-pilots, contributing toward safer PQC implementation in AI mediated environments.

Internet of Medical Things (IoMT) devices operate under strict resource constraints while handling highly sensitive health data, making security and privacy critical concerns. Federated learning (FL) further complicates this landscape, as model updates exchanged during training may unintentionally expose private medical information. Emerging quantum computing capabilities threaten the long-term viability of conventional lightweight cryptographic mechanisms, motivating the integration of Post-Quantum Cryptography (PQC) into IoMT systems. This article discusses key enabling technologies for quantum-resilient IoMT, including post-quantum key establishment, lightweight encryption, and edge-native orchestration. We propose a scalable Kubernetes-based framework that integrates PQC into FL-enabled IoMT environments and validate it on a Raspberry Pi testbed. Results demonstrate that distributed cryptographic processing significantly reduces latency compared to sequential designs while maintaining feasible resource overhead. The primary contribution of this work lies in the design and validation of a secure orchestration and communication framework for FL-enabled IoMT systems. We conclude by outlining future directions toward energy-aware architectures, intelligent security optimization, and resilient next-generation Intelligent Internet of Medical Things (IIoMT) ecosystems.

AI-assisted mathematics is often evaluated on solving predefined problems. In practice, however, many important advances begin earlier, when a vague research intuition is transformed into a concrete problem, a promising route, and a theorem family worth proving. This report studies that stage through a case study that led to sign-embedding quantum algorithms for matrix equations and matrix functions, foundational primitives in quantum linear algebra and operator-output quantum algorithms. The project began with a human-originated intuition that rational approximation is especially effective for jump-type functions such as the sign function, and might therefore serve as a design principle for quantum algorithms. Rather than merely assisting after the problem was fixed, AI-assisted exploration, including workflows later integrated into the agentic AI-mathematician system AIM, played a key role in expanding this intuition into a route map, comparing candidate formulations, and converging toward sign embedding as the central framework. AIM then helped connect a known matrix-sign identity to wider classes of matrix equations and matrix functions, and drafted proof and complexity calculations. The decisive scientific judgments remained human: selecting which human-AI-expanded routes were worth pursuing, rejecting a Cayley-trapezoidal approximation when its validity required a hidden condition, and refining the Sylvester implementation from a coarse quadratic-gap query route to the final factorized and scaled analysis. The report argues that human-AI co-discovery workflows, with systems such as AIM as important components, are most valuable not as standalone theorem provers, but as research partners for problem formation, connection discovery, derivation, and skeptical review inside a human-gated research loop.

Recent advances in error-corrected qubits have accelerated the timeline for practical quantum computing. It poses a threat to cryptographic primitives used to secure financial systems, government infrastructure, communication networks, and DeFi (Decentralized Finance) ecosystems. This paper introduces a post-quantum secure federated DeFi framework that enables inter-bank collaboration to improve the inclusivity of individuals underserved by local lenders due to limited financial histories. Multiple banks contribute encrypted information batches to a virtual server, where lattice-based Fully Homomorphic Encryption (FHE) enables end-to-end homomorphic computation. The server fuses local data-driven probabilistic assessments, expert beliefs, and verifiable evidence generated by the NASA-IBM Prithvi Geospatial Foundation Model (GFM), in encrypted format. Decentralized technologies are employed to ensure tamper-proof evidence and auditable accountability for all encrypted data exchanges between institutions and the server. The framework is tested on agricultural lending decisions for rural borrowers in Virginia.

The deployment of embodied artificial intelligence via world-model-based robotics presents a transformative opportunity for blockchain infrastructure, establishing urgent demand for trustworthy data provenance, cross-organizational governance, and incentive-compatible sharing across decentralized ecosystems. Simultaneously, quantum computing advances recognized by the 2025 Nobel Prize in Physics and the Turing Award threaten the cryptographic primitives securing these data economies, creating an interdependent imperative: long-lived verification for embodied AI depends on crypto-agile architectures capable of withstanding quantum adversaries. This tutorial examines blockchain as the coordination layer bridging this dual transition, from financial substrate to foundational Cyber-Physical-Social Systems infrastructure that simultaneously secures against quantum cryptanalysis and enables scalable, trustworthy data economies. The session opens with an immersive AWS Braket demonstration engaging participants with superconducting, trapped-ion, and neutral-atom hardware to assess cryptographic threat timelines and witness ECDSA-to-post-quantum signature transitions. Five integrated modules progress from embodied AI and world-model requirements through quantum hardware reality and evidence-based security migration, to scalable cross-shard architectures via BrokerChain protocols, trustworthy data economies implementing Croissant metadata standards and robotic learning provenance, and industry ecosystem integration for multi-modal cloud deployment. By bridging quantum hardware realities with embodied AI data requirements, this tutorial charts blockchain as unified infrastructure for next-generation decentralized intelligent environments, providing open-source frameworks and roadmaps for architecting quantum-resistant, interoperable, and data-trustworthy systems.

Financial crashes, cascading failures in infrastructure, and critical errors in AI systems are frequently triggered by events that occur with extremely small probability. Efficiently discovering and sampling events with probability below a threshold is therefore of critical interest. Yet this task is highly non-trivial using existing classical or quantum methods. Being rare, such events require an immense sampling overhead to collect sufficient data samples. Moreover, because the rare events are not known in advance, they cannot be flagged for amplification using standard techniques. Here, we introduce a quantum algorithm for rare-event discovery and sampling without first learning which events are rare. The algorithm achieves the optimal quantum scaling with the rarity threshold. We further demonstrate that this can achieve a quadratic speedup for heavy-tailed systems whose tail has nonvanishing total mass, and translates into a robust polynomial speedup for stationary stochastic processes, with the exponent determined by its entropy-rate structure.

Quantum key distribution (QKD) is increasingly considered for deployment in realistic communication networks, where long distances, heterogeneous fiber infrastructure, and coexistence with classical traffic present substantial challenges. Here, we demonstrate trusted-node QKD between Linköping University and the Stockholm hub of the Swedish national quantum communication infrastructure over 270 km of deployed single-mode fiber, extended by a 33 km multi-core fiber (MCF) segment emulating a metropolitan access link, for a total distance of 303 km. The two sub-links use commercial QKD systems whose receivers are interfaced with external superconducting nanowire single-photon detectors, enabling operation at losses beyond those supported by standard internal gated-mode detectors. We operate the link while actively switching the QKD channel between two MCF cores, with co-propagating Ethernet traffic and injected broadband optical noise in the other cores. The results demonstrate the integration of commercial QKD into demanding, dynamically reconfigurable fiber infrastructure relevant to future hybrid quantum-classical networks. Finally, using the generated secret keys, we illustrate how limited and time-varying QKD throughput affects one-time-pad-protected image transmission: image fidelity depends strongly on the available QKD-generated key budget and the choice of compression algorithm, highlighting application-level challenges for QKD-based encryption in realistic scenarios.

Training Variational Quantum Circuits (VQCs) under Noisy Intermediate-Scale Quantum (NISQ) constraints introduces severe computational limitations: classical statevector simulation memory scales exponentially ($\mathcal{O}(2^n)$), and global cost functions suffer from barren plateaus where gradient variance decays exponentially ($\mathcal{O}(1/2^n)$). This paper introduces and evaluates the Quantum Algorithm for Distributed Reduction of Entanglements (QADR), a hybrid quantum-classical machine learning framework that decomposes a global $n$-qubit VQC into localized sub-circuits operating approximately within the causal light cones of individual target qubits. QADR reduces classical simulation memory scaling from $\mathcal{O}(2^n)$ to $\mathcal{O}(n \cdot 2^{2d+1})$ for a light cone radius $d$, while naturally mitigating global barren plateaus. We benchmark QADR against standard global VQCs, Support Vector Machines (SVM), and two customized classical parameter-matched neural networks (CANN and PMNN) on the MNIST dataset and the high-dimensional NASA IMS wind turbine drivetrain diagnostic task. QADR demonstrates excellent scalability, operating successfully at $n_{\text{features}}=2000$ where standard global VQCs crash due to memory exhaustion, while matching or exceeding the performance of optimized classical architectures.

Traditional cryptography, rooted in problems, e.g., integer factorisation or discrete log, is inevitably vulnerable to a fully operational quantum computer. Although it remains an engineering frontier, the looming threat extends to encrypted data stored today, which could be decrypted in the future with quantum capabilities. To safeguard against this eventuality, the backbone of the modern quantum-safe cryptography is the Shortest Vector Problem (SVP). We enhance Laarhoven's treatment of Ajtai et al.'s sieving as a genetic algorithm (GA) for the SVP by incorporating domain-informed SVP representation and crossover while naturally extending application to the module lattices.

Distributed quantum learning (DQL) has emerged as a promising paradigm to scale quantum-enhanced machine learning by interconnecting multiple quantum devices. However, for efficient real-world deployment, it is essential to characterize how DQL converges under practical scenarios while simultaneously safeguarding multi-device quantum infrastructures from evolving security threats. Addressing these aspects in an integrated manner is key to ensuring both performance and resilience in large-scale DQL systems. Therefore, this paper presents a new DQL study where our innovation lies in: (i) conducting a holistic convergence analysis for DQL under practical settings, i.e., partial device participation, non-convex loss functions, and heterogeneous data distributions, (ii) developing a novel multi-layered post-quantum cryptographic architecture with a quantum neural network-powered adaptive mechanism that monitors conditions, evaluates threats, and adjusts parameters across three National Institute of Standards and Technology (NIST)-compliant levels. Our theoretical framework and empirical validation reveal two key insights: (i) the derived convergence bound uncovers a fundamental trade-off between convergence rate, measurement shots, and the size of the participating device subset; and (ii) findings from our evaluations on a physical testbed modeling quantum control architectures expose the performance limitations of static post-quantum security, while confirming that our adaptive framework effectively mitigates these overheads to preserve overall system efficiency. Specifically, the hardware experiments demonstrate that our dynamic security mechanism reduces total security execution time by approximately 49% relative to static high-security baselines, while maintaining a threat detection accuracy of over 91%. Furthermore, extensive simulations validate our theoretical analysis.....

Our computing ecosystem is being transformed by two emerging paradigms: the increased deployment of agentic AI systems and advancements in quantum computing. With respect to agentic AI systems, one of the most critical problems is creating secure governing architectures that ensure agents follow their owners' communication and interaction policies and can be held accountable for the messages they exchange with other agents. With respect to quantum computing, existing systems must be retrofitted and new cryptographic mechanisms must be designed to ensure long-term security and quantum resistance. In fact, NIST recommends that standard public-key cryptographic algorithms, including RSA, Diffie-Hellman (DH), and elliptic-curve constructions (ECC), be deprecated starting in 2030 and disallowed after 2035. In this paper, we present MAGIQ, a framework for policy definition and enforcement in multi-agent AI systems using novel, highly efficient, quantum-resistant cryptographic protocols with proven security guarantees. MAGIQ (i) allows users to define rich communication and access-control policy budgets for agent-to-agent sessions and tasks, including global budgets for one-to-many agent sessions; (ii) enforces such policies using post-quantum cryptographic primitives; (iii) supports session-based enforcement of policies for agent-to-agent and one-to-many agent sessions; and (iv) provides accountability of agents to their users through message attribution. We formally model and prove the correctness and security of the system using the Universal Composability (UC) framework. We evaluate the computation and communication overhead of our framework and compare it with the state-of-the-art agentic AI framework SAGA. MAGIQ is a first step toward post-quantum-secure solutions for agentic AI systems.

This paper presents Quantum Gatekeeper, a context-bound image steganography framework where successful payload recovery depends on both cryptographic decryption and the reconstruction of a precise extraction path. The system integrates lossless least significant bit (LSB) embedding with a deterministic variational quantum circuit (VQC)-derived gate key, multi-factor contextual binding, and authenticated encryption. Payload extraction is contingent upon four requisite factors: a password, a shared secret, a user-supplied context string, and a reference image signature. Any deviation in these factors causes the system to read from an incorrect pixel sequence or fail authentication, resulting in silent rejection rather than partial disclosure. The proposed method derives a gatecontrolled extraction key from a seed-conditioned variational circuit, with parameters generated via cryptographic hash expansion and context-dependent image features. To ensure encode/decode consistency, the cryptographic key path is generated via exact statevector simulation; concurrently, IBM superconducting quantum hardware is utilized to evaluate the statistical behavior of the circuit family under physical noise. We introduce a dual-region image layout to resolve the nonce bootstrapping dependency, separating header recovery from payload recovery through independently derived keys. Experimental results confirm successful end-to-end message embedding and recovery on PNG images, demonstrating deterministic success under correct conditions and failure otherwise. The framework supports both text and image payloads; in the image-in-image configuration, a secret image is resized to a fixed resolution prior to embedding, enabling exact pixel-level recovery under correct contextual reconstruction.

In the context of quantum secure scenarios, existing research on mobile edge devices and intelligent computing and edge (ICE) systems based on the Non-Orthogonal Multiple Access (NOMA) communication model have overlooked the energy consumption overhead of Post-Quantum Cryptography (PQC) modules, and the high complexity of traditional resource allocation algorithms fails to meet the demands of real-time decision-making. To address these challenges, this paper proposes a lightweight agentic AI framework designed for online joint optimization within ICE-enabled mobile devices. The scheme constructs a multi-stage stochastic Mixed Integer Nonlinear Programming (MINLP) model that incorporates static power-consumption constraints for PQC modules. Based on Lyapunov optimization theory, the long-term optimization problem is decoupled, and a linear complexity algorithm is proposed to solve the nonconvex challenges of NOMA power allocation . Simulation results verify that the proposed scheme significantly improves computational throughput while ensuring system queue stability and energy consumption constraints. Compared with traditional Successive Convex Approximation (SCA) algorithms, the complexity is reduced to $\mathcal{O}(N)$, achieving a speedup of approximately 46 times when the number of devices $N=35$, thereby meeting the real-time decision-making requirements in dynamic wireless environments.

The impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors, cloning an arbitrary unknown pure state requires as many initial copies as needed to fully learn the state. Rather than arbitrary unknown states, modern quantum learning theory often considers structured classes of states and exploits such structure to develop learning algorithms that outperform general-state tomography. This raises the question: How do the sample complexities of learning and cloning relate for such structured classes? We answer this question for an important class of states. Namely, for $n$-qubit stabilizer states, we show that the optimal sample complexity of cloning is $Θ(n)$. Thus, also for this structured class of states, cloning is as hard as learning. To prove these results, we use representation-theoretic tools in the recently proposed Abelian State Hidden Subgroup framework and a new structured version of the recently introduced random purification channel to relate stabilizer state cloning to a variant of the sample amplification problem for probability distributions that was recently introduced in classical learning theory. This allows us to obtain our cloning lower bounds by proving new sample amplification lower bounds for classes of distributions with an underlying linear structure. Our results provide a more fine-grained perspective on No-Cloning theorems, opening up connections from foundations to quantum learning theory and quantum cryptography.

This manuscript provides a comprehensive review of the Maximum Clique Problem, a computational problem that involves finding subsets of vertices in a graph that are all pairwise adjacent to each other. As such, this review is a continuation of the series of previous reviews from 1994, 1999 and 2014. The manuscript covers in a simple way classical algorithms and includes a review of recent developments in graph neural networks and quantum algorithms.