Quantum Algorithms Now Optimise Swarm Behaviour for Complex Tasks Efficiently

Researchers are increasingly focused on optimising communication networks within multi-agent systems to achieve robust consensus control. Milad Hasanzadeh and Amin Kargarian, both from the Department of Electrical Engineering at Louisiana State University, alongside M. Hasanzadeh et al., present a novel framework for dynamically designing these communication topologies. Their work addresses the significant challenge of selecting optimal network connections in real-time, utilising a mixed-integer quadratic program solved with an innovative alternating direction method of multipliers scheme and quantum-inspired optimisation. This approach allows for the creation of connected, cost-effective topologies that demonstrably improve consensus performance in linear multi-agent systems, offering a pathway towards more efficient and adaptable distributed control architectures. This work addresses a critical challenge in coordinating multiple interacting devices, such as robots or drones, by improving the efficiency of their real-time communication. The study centres on designing optimal communication topologies, where connections between agents are strategically chosen to enhance system performance and minimise costs. A key innovation lies in formulating the complex problem of multi-agent system communication topology design as a mixed-integer quadratic program. To overcome the computational difficulties inherent in this NP-hard problem, the researchers implemented a three-block alternating direction method of multipliers (ADMM) scheme. This decomposition breaks down the complex program into more manageable parts: a convex quadratic program, a binary unconstrained subproblem, and an auxiliary update. The binary subproblem was then mapped onto a quadratic unconstrained binary optimization (QUBO) Hamiltonian and solved approximately using a quantum imaginary time evolution (QITE) algorithm. This approach allows for the exploration of quantum solutions to a classically challenging optimisation task. Numerical simulations demonstrate that the proposed method generates connected topologies that adhere to degree constraints and achieve consensus. Importantly, the costs incurred by this quantum-enhanced method are comparable to those obtained using classical mixed-integer solvers. This finding is particularly significant as it suggests a promising level of performance even within the constraints of the noisy intermediate-scale quantum (NISQ) era. The research illustrates how quantum algorithms can be integrated as topology optimisers within closed-loop distributed control architectures, paving the way for more efficient and responsive multi-agent systems. This advancement has implications for a range of applications requiring coordinated action between multiple devices. Decomposition of MIQP and QUBO solution via Imaginary Time Evolution A three-block Alternating Direction Method of Multipliers (ADMM) scheme decomposes a mixed-integer quadratic program (MIQP) into manageable subproblems for solving complex multi-agent system communication topology design problems. This MIQP minimizes a cost function combining distance penalties and degree-regularization terms, while ensuring exact network connectivity through a flow-based formulation. The decomposition yields a convex quadratic program involving relaxed edge and flow variables, a binary unconstrained subproblem, and a closed-form auxiliary update, streamlining the optimisation process. Crucially, the binary subproblem is mapped onto a quadratic unconstrained binary optimization (QUBO) Hamiltonian, preparing it for quantum computation. This QUBO Hamiltonian is then approximately solved using imaginary time evolution (QITE), a quantum algorithm designed to find low-energy states representing optimal or near-optimal solutions. The implementation of QITE leverages the principles of quantum mechanics to explore the solution space more efficiently than some classical approaches. Following the quantum computation, the resulting time-varying, optimizer-generated Laplacians are applied to both linear first-order and second-order consensus dynamics, simulating the behaviour of the multi-agent system with the newly designed communication topology. Numerical simulations were conducted on networks to assess the performance of the proposed method. These simulations demonstrate that the method produces connected topologies satisfying predefined degree constraints and achieving consensus among the agents. Importantly, the costs incurred by this method are comparable to those achieved by classical mixed-integer solvers, indicating a promising level of performance despite utilising a quantum approach within the noisy intermediate-scale quantum (NISQ) era. This comparability, with costs at approximately 0.2 relative to classical solvers, highlights the potential for quantum algorithms to enhance the efficiency of coordinating multiple interacting devices. Quantum optimisation of multi-agent communication topologies for consensus dynamics Researchers successfully mapped a complex multi-agent system communication topology design problem, formulated as a mixed-integer quadratic program, onto a quantum algorithm utilising imaginary time evolution (QITE). This work demonstrates that the resulting time-varying, optimizer-generated Laplacians can be applied to linear first- and second-order consensus dynamics. Numerical simulations were conducted on networks to evaluate the performance of the proposed method, revealing connected topologies that satisfy degree constraints and achieve consensus. Critically, the method achieves costs comparable to those of classical mixed-integer solvers, indicating a promising level of performance despite utilising a quantum approach in the noisy intermediate-scale quantum (NISQ) era. Experiments involved networks of five and six agents, employing first- and second-order consensus dynamics to assess the algorithm’s efficacy. The simulations were executed on a classical computer utilising a Qiskit simulator for the quantum routines, specifically version 0.46.3 and qiskit-algorithms version 0.3.1. The QITE solver implemented VarQITE from qiskit-algorithms, combined with the ImaginaryMcLachlanPrinciple and an EfficientSU2 ansatz with linear entanglement, discretised with 30 steps and an imaginary-time horizon of 1.5. In the five-agent, first-order consensus example, agent positions converged to a common value close to the initial average, aligning with theoretical expectations. The resulting topology was sparse and path-like, adhering to the degree constraint of γ = 2 and the quadratic degree penalty. Further analysis with six agents and second-order dynamics confirmed convergence of both agent positions and velocities to common values. The auxiliary penalty parameter β was tuned based on network size, ranging from 200 for five agents to 600 for seven agents, achieving stable residual histories and reasonable convergence speed. The ADMM hyperparameters were fixed at ρ = 20 and μcard = 0.1, with a maximum of 500 iterations and a tolerance of 10−3. The closed-loop simulation terminated when the position disagreement fell below a tolerance of 10−3 or after a maximum simulation time of 10 seconds. Quantum optimisation of multi-agent communication topologies via classical-quantum decomposition Researchers have developed a dynamic quantum framework for designing communication topologies in multi-agent systems, achieving results comparable to classical optimisation methods. The core of this work lies in formulating the problem of optimising communication networks as a mixed-integer quadratic program, incorporating costs related to communication distance, degree constraints, and ensuring reliable connectivity between agents. A novel three-block alternating direction method of multipliers (ADMM) scheme was implemented to decompose this complex problem, isolating a binary optimisation core suitable for quantum computation. This approach leverages imaginary time evolution (QITE) to approximate solutions to the binary subproblem, embedding a quantum routine within a broader classical decomposition. Numerical simulations, conducted with networks of up to seven agents, demonstrate the method’s ability to generate sparse, degree-bounded, and connected topologies that successfully achieve consensus. Importantly, the resulting communication costs are comparable to those obtained using conventional mixed-integer solvers, suggesting a viable pathway for integrating near-term quantum optimisers into real-time distributed control systems. The authors acknowledge that this work operates within the noisy intermediate-scale quantum (NISQ) era, implying limitations in the scale and fidelity of current quantum hardware. Future research could focus on exploring the performance of this framework with larger agent populations and more complex network dynamics. Further investigation into the robustness of the QITE algorithm under increased noise conditions would also be beneficial, potentially paving the way for more reliable and efficient multi-agent coordination in practical applications. 👉 More information 🗞 Dynamic Quantum Optimal Communication Topology Design for Consensus Control in Linear Multi-Agent Systems 🧠 ArXiv: https://arxiv.org/abs/2602.