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

Milad Hasanzadeh, Amin Kargarian

TL;DR

The paper addresses online design of communication topologies for linear multi-agent systems achieving consensus. It formulates topology selection as a practical MIQP with flow-based connectivity and degree penalties, then proposes a three-block ADMM that isolates a convex $(z,f)$ subproblem, a binary proxy $r$, and a simple auxiliary update, delegating the binary core to a QUBO solved by QITE. This integration yields time-varying Laplacians $L_k$ that sustain first- and second-order consensus while keeping topologies connected and degree-bounded, with numerical results showing costs comparable to classical solvers. Overall, the work demonstrates a feasible pathway to embed near-term quantum optimization within closed-loop distributed control architectures, enabling quantum-assisted topology optimization for MASs.

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.

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

TL;DR

The paper addresses online design of communication topologies for linear multi-agent systems achieving consensus. It formulates topology selection as a practical MIQP with flow-based connectivity and degree penalties, then proposes a three-block ADMM that isolates a convex subproblem, a binary proxy , and a simple auxiliary update, delegating the binary core to a QUBO solved by QITE. This integration yields time-varying Laplacians that sustain first- and second-order consensus while keeping topologies connected and degree-bounded, with numerical results showing costs comparable to classical solvers. Overall, the work demonstrates a feasible pathway to embed near-term quantum optimization within closed-loop distributed control architectures, enabling quantum-assisted topology optimization for MASs.

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.
Paper Structure (20 sections, 3 theorems, 75 equations, 14 figures, 2 algorithms)

This paper contains 20 sections, 3 theorems, 75 equations, 14 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Motivation
  3. Contributions
  4. Preliminaries
  5. Problem Statement and Closed-Loop System
  6. Networked Consensus
  7. First-Order Consensus Dynamics
  8. Second-Order Consensus Dynamics
  9. Assumptions and Consensus Guarantee
  10. Communication Topology Optimization
  11. Three-Block ADMM Decomposition
  12. Three-Block Formulation
  13. Convergence and Stability of the Three-Block ADMM
  14. Quantum Optimization of the Binary Block
  15. Binary ADMM Block as QUBO Hamiltonian
  16. ...and 5 more sections

Key Result

Theorem 1

Consider the first-order system eq:csys1_tv or the second-order system eq:csys2_tv_x–eq:csys2_tv under Assumptions ass:ideal_comm–ass:connectivity. Then all agents achieve consensus. In particular, for all $i,j \in \{1,\dots,n\}$, and, in the second-order case,

Figures (14)

  • Figure 1: Visualization of a qubit in superposition and measurement outcomes.
  • Figure 2: Example of an ansatz circuit $U(\theta)$ for QITE
  • Figure 3: Schematic view of the QITE procedure
  • Figure 4: Example 1 (first-order consensus with $n=5$ agents): evolution of the agent positions
  • Figure 5: optimized communication graphs
  • ...and 9 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Remark 1
  • Lemma 1
  • Theorem 2