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QI: Fachverband Quanteninformation

QI 21: Quantum Information: Concepts and Methods III

QI 21.2: Talk

Friday, March 13, 2026, 10:00–10:15, BEY/0245

Graph-State Gates as Scrambling Primitives: Entanglement Growth and Complexity in Quantum Circuits — •Zahra Raissi¹, Himanshu Sahu², Mario Flory³, and Aranya Bhattacharya⁴ — ¹Paderborn University, Germany — ²Perimeter Institute, Canada — ³Jagiellonian University, Poland — ⁴University of Bristol, UK

Understanding how quantum information spreads in many-body systems is central to quantum simulation, error correction, and quantum network design. In this work, we investigate structured random circuits built from graph-state gates, where small multi-qubit graph states are repeatedly embedded into a one-dimensional Clifford circuit at random locations. Each gate acts on a fixed number of qubits but carries an internal graph structure, allowing us to disentangle the role of local graph geometry from that of global circuit architecture.

Within this model, we use stabilizer methods to compute bipartite entanglement entropies, height functions, and light-cone diagnostics based on both Pauli spreading and out-of-time-order correlators (OTOCs). We find that the entanglement growth rate and saturation time are strongly correlated with two graph-theoretic features: a local light-cone capacity (degree and connectivity) and a cross-entanglement capacity (edge cuts/height). This reveals a hierarchy of graph-state gates according to their entangling and scrambling power. Our results provide a graph-theoretic design principle and a concrete ranking for selecting small graph blocks that optimize entanglement generation and operator spreading in Clifford quantum circuits.

Keywords: Graph States; Clifford Circuits; Entanglement Growth; Quantum Scrambling; Quantum Complexity