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.
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.
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 convergence of quantum computing and robotics represents a paradigm shift in autonomous systems design, promising to overcome fundamental computational limitations that have constrained classical robotic capabilities. This comprehensive review surveys the rapidly evolving field of quantum machine learning (QML) for robotics, systematically analyzing 107 peer-reviewed contributions spanning quantum algorithms, machine learning techniques, and their robotic applications. We provide a detailed historical perspective on the field's development, from the early theoretical foundations established by Grover's search algorithm and quantum reinforcement learning proposals to current experimental implementations on noisy intermediate-scale quantum (NISQ) devices. The review systematically examines five major application domains: (1) quantum reinforcement learning for navigation and control, (2) quantum search and path planning algorithms, (3) quantum-enhanced localization and mapping, (4) quantum optimization for inverse kinematics and task allocation, and (5) multi-robot coordination and swarm intelligence. For each domain, we present detailed algorithmic formulations, computational complexity analyses, and critical assessments of experimental results. Our analysis reveals that while provable quantum advantage in robotics remains largely prospective, recent demonstrations show promising results: quantum deep reinforcement learning achieving 40\% parameter reduction in navigation tasks, Grover-based kinematic optimization demonstrating up to 93x speedups, and quantum annealing providing practical solutions for multi-robot routing. We identify key technical challenges, including barren plateaus in variational circuits, noise-induced performance degradation, and the quantum-classical integration bottleneck. Finally, we outline a strategic roadmap for quantum robotics research, distinguishing near-term opportunities in hybrid algorithms from long-term goals requiring fault-tolerant quantum computation. This paper serves as both an authoritative technical reference and a comprehensive guide for researchers working at the intersection of quantum computing and autonomous systems.
The convergence of quantum computing and robotics represents a paradigm shift in autonomous systems design, promising to overcome fundamental computational limitations that have constrained classical robotic capabilities. This comprehensive review surveys the rapidly evolving field of quantum machine learning (QML) for robotics, systematically analyzing 107 peer-reviewed contributions spanning quantum algorithms, machine learning techniques, and their robotic applications. We provide a detailed historical perspective on the field's development, from the early theoretical foundations established by Grover's search algorithm and quantum reinforcement learning proposals to current experimental implementations on noisy intermediate-scale quantum (NISQ) devices. The review systematically examines five major application domains: (1) quantum reinforcement learning for navigation and control, (2) quantum search and path planning algorithms, (3) quantum-enhanced localization and mapping, (4) quantum optimization for inverse kinematics and task allocation, and (5) multi-robot coordination and swarm intelligence. For each domain, we present detailed algorithmic formulations, computational complexity analyses, and critical assessments of experimental results. Our analysis reveals that while provable quantum advantage in robotics remains largely prospective, recent demonstrations show promising results: quantum deep reinforcement learning achieving 40\% parameter reduction in navigation tasks, Grover-based kinematic optimization demonstrating up to 93x speedups, and quantum annealing providing practical solutions for multi-robot routing. We identify key technical challenges including barren plateaus in variational circuits, noise-induced performance degradation, and the quantum-classical integration bottleneck. Finally, we outline a strategic roadmap for quantum robotics research, distinguishing near-term opportunities in hybrid algorithms from long-term goals requiring fault-tolerant quantum computation. This paper serves as both an authoritative technical reference and a comprehensive guide for researchers working at the intersection of quantum computing and autonomous systems.
A new paradigm of an entangled swarm intelligence is proposed. It is an abstract quantumcomputational model for a super-fast, high-dimensional, parallel and fault tolerant swarm intelligence. In other words, it is a deep convolutional neural network that is fully entangled (i.e., all processing units, or ‘multineurons’, or robots are inseparably interconnected as a single intelligent entity). It isformally defined as a tensor product of a large number of Hilbert spaces, all forming a very large matrix with elements representing individual n-qubit multineurons. This abstract quantum brain model is targeting quantum silicon chips with many millions of qubits, which will certainly be available in the near future.