Dynamic Quantum Optimal Communication Topology Design for Consensus Control in Linear Multi-Agent Systems

TL;DR

This paper introduces a quantum-enhanced method for designing dynamic communication topologies in multi-agent systems to optimize consensus control, leveraging quantum algorithms to solve complex combinatorial problems efficiently.

Contribution

It develops a novel quantum framework and an ADMM-based approach to optimize communication graphs in multi-agent systems, integrating quantum algorithms for topology design.

Findings

Quantum algorithms effectively solve topology optimization problems.

The method achieves consensus with cost comparable to classical solutions.

Generated topologies satisfy connectivity and degree constraints.

Abstract

This paper proposes a quantum framework for the design of communication topologies in consensus-based multi-agent systems. The communication graph is selected online by solving a mixed-integer quadratic program (MIQP) that minimizes a cost combining communication and distance penalties with degree-regularization terms, while enforcing exact connectivity through a flow-based formulation. To cope with the combinatorial complexity of this NP-hard problem, we develop a three-block ADMM scheme that decomposes the MIQP into a convex quadratic program in relaxed edge and flow variables, a pure binary unconstrained subproblem, and a closed-form auxiliary update. The binary subproblem is mapped to a quadratic unconstrained binary optimization (QUBO) Hamiltonian and approximately solved via quantum imaginary time evolution (QITE). The resulting time-varying, optimizer-generated Laplacians are applied to linear first- and second-order consensus dynamics. Numerical simulations on networks demonstrate that the proposed method produces connected topologies that satisfy degree constraints, achieve consensus, and incur costs comparable to those of classical mixed-integer solvers, thereby illustrating how quantum algorithms can be embedded as topology optimizers within closed-loop distributed control architectures.