Quantum Simulations of Opinion Dynamics

TL;DR

The paper presents a quantum framework for opinion dynamics where agents are encoded as qubits with initial-belief and interaction Hamiltonians, enabling both imaginary-time and real-time evolution. It introduces observables such as magnetization and entanglement entropy to quantify consensus, metastable states, and inter-agent correlations across different network topologies, including open chains, round-table, and leader–follower structures. The approach is validated through a proof-of-principle IBM Quantum hardware demonstration using variational quantum imaginary time evolution, showing compatibility with exact diagonalization within realistic noise. A key finding is that network connectivity and leader strength jointly shape the emergence and speed of consensus, with potential connections to Kuramoto-type synchronization and Schrödinger–Lohe models, highlighting the practical potential of quantum simulators for exploring complex social dynamics.

Abstract

Consensus formation is a central problem in collective behavior. In this work, we develop quantum models of opinion dynamics that can be exactly solved and implemented on current quantum hardware. By exploiting quantum superposition, measurement-induced state collapse, and entanglement, our framework captures key features of opinion evolution and allows a systematic investigation of how network connectivity shapes consensus formation. We demonstrate our approach using practical quantum circuits and validate representative cases on IBM Quantum devices for the open-chain. Further results demonstrate that quantum platforms can serve as a viable framework for simulating opinion dynamics and for probing the interplay between leadership, network structure, and collective behavior.

Figures (12)

• Figure 1: Schematic illustration of the quantum opinion dynamics framework. a. Representation of individual opinions as qubit states on the Bloch sphere. b. Quantum circuit implementation, where initial states evolve under interaction gates and measurements yield observable opinion distributions. c. Dynamics governed by a Hamiltonian $H=H_0+H_I$, with imaginary-time evolution described by $\exp{-\tau H}$. d. Distinct quantum properties relevant to opinion dynamics, including superposition, collapse, and entanglement.
• Figure 2: Different connection schemes and observables. a. One dimensional opinion chain with fixed boundary condition; b. Round table connection with periodic boundary condition; c. Leader-follower connection; d Imaginary-time evolution of opinions in agent-time space.
• Figure 3: Evolution of magnetization $M(\tau)$, and entanglement entropy $S(\tau)$ between two agent groups. The orange, blue, and green curves correspond to the open chain, round table, and leader-follower connections, respectively.
• Figure 4: Time evolution of the opinion expectations $p_i$ on a one dimensional opinion chain with 8 agents, measured using hardware , noiseless circuit simulator, and QITE by the exact diagonalization (ED). The error bar denotes the statistical error from 8192 repeated measurements.
• Figure 5: Magnetization dynamics $M(\tau)$ under varying leader influence strengths $d$. Different colored curves correspond to different values of $d$, increasing from weak (cool colors) to strong (warm colors).