In a robotic swarm, parameters such as position and proximity to the target can be described in terms of probability amplitudes. This idea led to recent studies on a quantum approach to the definition of the swarm, including a block-matrix representation. However, the size of such matrix-based representation increases drastically with the swarm size, making them impractical for large swarms. Hence, in this work, we propose a new approach for modeling robotic swarms and robotic networks by considering them as mixed quantum states that can be represented mathematically via density matrices. The size of such an approach only depends on the available degrees of freedom of the robot, and not its swarm size and thus scales well to large swarms. Moreover, it also enables the extraction of local information of the robots from the global swarm information contained in the density matrices, facilitating decentralized behavior that aligns with the collective swarm behavior. Our approach is validated on several simulations including large-scale swarms of up to 1000 robots. Finally, we provide some directions for future research that could potentially widen the impact of our approach.
In a robotic swarm, parameters such as position and proximity to the target can be described in terms of probability amplitudes. This idea led to recent studies on a quantum approach to the definition of the swarm, including a block-matrix representation. However, the size of such matrix-based representation increases drastically with the swarm size, making them impractical for large swarms. Hence, in this work, we propose a new approach for modeling robotic swarms and robotic networks by considering them as mixed quantum states that can be represented mathematically via density matrices. The size of such an approach only depends on the available degrees of freedom of the robot, and not its swarm size and thus scales well to large swarms. Moreover, it also enables the extraction of local information of the robots from the global swarm information contained in the density matrices, facilitating decentralized behavior that aligns with the collective swarm behavior. Our approach is validated on several simulations including large-scale swarms of up to 1000 robots. Finally, we provide some directions for future research that could potentially widen the impact of our approach.
The swarms of robots are examples of artificial collective intelligence, with simple individual autonomous behavior and emerging swarm effect to accomplish even complex tasks. Modeling approaches for robotic swarm development is one of the main challenges in this field of research. Here, we present a robot-instantiated theoretical framework and a quantitative worked-out example. Aiming to build up a general model, we first sketch a diagrammatic classification of swarms relating ideal swarms to existing implementations, inspired by category theory. Then, we propose a matrix representation to relate local and global behaviors in a swarm, with diagonal sub-matrices describing individual features and off-diagonal sub-matrices as pairwise interaction terms. Thus, we attempt to shape the structure of such an interaction term, using language and tools of quantum computing for a quantitative simulation of a toy model. We choose quantum computing because of its computational efficiency. This case study can shed light on potentialities of quantum computing in the realm of swarm robotics, leaving room for progressive enrichment and refinement.
Quantum computing is a branch of computer science derived from the fundamental laws of quantum mechanics, such as state superposition, multi-value logic and destructive measure. An open challenge in itself is to re-think in quantum terms classic problems and solving techniques. Another nature-inspired field is the development of swarm-based robotic applications, where the challenge is catching the fundamental laws governing swarm dynamics, such as pattern formation and target reaching. Here, we review some recent approaches on swarm dynamics, the organizational rules of which are formalized according to quantum computing. In this way, the shades of probability in decision-making for multiple-robot systems can be expressed according to the multi-value logic underlying quantum computing. In our review, specific quantum circuits are sketched to give an idea of how these problems have been faced in computational terms. The article is enriched by references to sonification, a strategy adding one more sensory dimension to data representation, a human-friendly tool to navigate the complexity of swarm-robotic movements in a given arena.This article is part of the theme issue 'The road forward with swarm systems'.
Computational resources of quantum computing can enhance robotic motion, decision making, and path planning. While the quantum paradigm is being applied to individual robots, its approach to swarms of simple and interacting robots remains largely unexplored. In this paper, we attempt to bridge the gap between swarm robotics and quantum computing, in the framework of a search and rescue mission. We focus on a decision-making and path-planning collective task. Thus, we present a quantum-based path-planning algorithm for a swarm of robots. Quantization enters position and reward information (measured as a robot’s proximity to the target) and path-planning decisions. Pairwise information-exchange is modeled through a logic gate, implemented with a quantum circuit. Path planning draws upon Grover’s search algorithm, implemented with another quantum circuit. Our case study involves a search and rescue scenario, inspired by ant-foraging behavior in nature, as an example of swarm intelligence. We show that our method outperforms two ant-behavior simulations, in NetLogo and Java, respectively, presenting a faster convergence to the target, represented here by the source of food. This study can shed light on future applications of quantum computing to swarm robotics.
As swarm robotics evolves into a paradigm-shifting approach for distributed autonomous systems, communication vulnerabilities pose risks in hostile environments. Conventional cryptography is limited by decentralized nature, energy constraints, and node density, while quantum computing threatens public-key encryption via Shor's algorithm. This chapter explores Quantum Key Distribution (QKD) and entanglement-based networking for information-theoretic security. We examine mobile quantum networks, highlighting drone-based relays and satellite links. Beyond security, quantum principles like superposition and entanglement can enhance swarm intelligence, task allocation, and coordination. Despite promising validations, hurdles remain: SWaP constraints, atmospheric interference, and mobility-induced decoherence. Through case studies in aerial, maritime, space, and disaster domains, we propose a quantum-native architecture integrating post-quantum cryptography, adaptive PAT systems, and hybrid trust models for mission-critical resilience.
The increasing convergence of quantum computing (QC) and advanced robotic control is giving rise to a new class of intelligent automation systems. Utilizing quantum-inspired computational principles, contemporary robotic platforms demonstrate greater optimization efficiency, superior perceptual processing, and improved decision-making performance. This survey outlines the principal quantum-oriented control methodologies utilized in robotics, with particular emphasis on approaches that incorporate Quantum Neural Networks (QNN), Quantum Machine Learning (QML), and Quantum-behaved Particle Swarm Optimization (QPSO). The investigation systematically reviews recent advances in quantum-assisted adaptive control, trajectory planning, and optimization frameworks, spotlighting their contributions to improved robustness, precision, and energy efficiency. By analyzing research in quantum reinforcement learning, distributed Noisy Intermediate-Scale Quantum (NISQ) computing, and hybrid quantum-classical approaches, this review clarifies how quantum principles are transforming both theoretical and practical aspects of robotic control. Likewise, several real-world implementations ranging from industrial manipulators to autonomous and cognitive robotic systems demonstrate the growing feasibility of quantum-enhanced decision-making. The review concludes that while remarkable progress has been made in quantum-inspired control for robotics, most existing studies remain constrained to simulations with restricted experimental validation on physical platforms. Addressing this gap will be essential in future research to transition from theoretical and simulated models toward hardware-level implementations, enabling the realization of scalable, fault-tolerant quantum control architectures.
Since a few years, swarms of drones are used in both the civil and military domains. They might be composed of tens, hundreds if not thousands of drones (e.g. to achieve saturation effect). It thus becomes hard to deal with each of the individual drones that make it. Therefore, making a swarm a single object, that could then be controlled as a single entity, whatever its size and its surface, is the grail.Many projects have been working on this issue. Still, as far as we know, none has been convincingly successful. There are a number of reasons for that.From a conceptual point of view, the controls that make sense at the level of a swarm are not simply an upscale of the operations that make sense for the drones that compose it. Some controls are easy to upscale (take off, land) and to map back from the swarm to its individual components. Some are more difficult. For instance, what does it mean and does it even make sense to move a swarm to a given location? There is an underlying notion of synchronization that remains hidden if stating things so simply: when should the move begin, should the members go together, when is the move terminated, etc.? Whatever the answers to these questions, this requires stable communication and strong synchronization between the members of the swarm, which cannot be guaranteed in most theaters of operations, especially for large swarms. Additionally, there are operations that only make sense at the level of a swarm, not of an individual drone. For instance, it might be useful to split a swarm into two smaller sub swarms, and later reconnect them as a single object.From a technical point of view, two major configurations are to be considered. First, it the swarm is controlled by some central system on the ground (C2, Command and Control) it makes things partly tractable. The C2 has a global view of all the members of the swarm and the above issues can be dealt with, knowing the required information about each unitary system. Still this does not solve the problems of congestion, latences and disruptions. Second, if the swarm is composed of autonomous systems, i.e. when the swarm is composed of drones that decide on their own on their behavior, it becomes much more difficult. Still, this is the most interesting configuration in real world operation because autonomy makes it possible to address BLOS (Beyond Line of Sight) missions and avoids swarm to ground communication.The question to solve is what do we precisely expect when willing to make a swarm a single object? We claim that the perfect result would be to break the locality of each individual drone making the swarm a non-local object as if the drones were some sort of entangled (by analogy with quantum physics and the EPR principle). Therefore, our provocative claim that future swarms generation will be quantum swarms.