Quantum Networks and Percolation Theory
How do we scale up the quantum internet? Our group tackles this challenge by bringing statistical physics and complex network science into the quantum realm. We study the fundamental topological properties of quantum networks, using tools like percolation theory—the mathematical study of how networks connect, scale, and break apart—to understand how entanglement distributes across large systems. For example, we explore entanglement percolation in both discrete- and continuous-variable quantum networks and have shown why non-shortest paths are actually crucial for robust quantum communication. Essentially, we are drawing the theoretical blueprints to understand how complex networks behave when their connections are governed by quantum mechanics.
Quantum Finance and Market Dynamics
Modern financial markets, particularly high-frequency trading, are incredibly complex, noisy environments. We are developing quantum algorithms to model these dynamics, using concepts like quantum Brownian motion—originally a framework for describing quantum particles in a noisy environment—to simulate market microstructures. By bridging statistical physics and finance, we aim to uncover more efficient, quantum-native ways to analyze market volatility and liquidity.
