Anyon statistics with qubits

Quantum simulators are specially designed systems that allow physicists to study exotic quantum phenomena. One particularly intriguing example is anyon statistics—a type of particle behavior that lies between the familiar categories of bosons and fermions. Anyons can only exist in low-dimensional systems, and recent experiments with ultracold atoms in one-dimensional optical lattices have shown that this behavior can be engineered using hopping processes whose phase depends on how many particles occupy a site. However, many modern quantum simulation platforms—such as quantum computers built from qubits—naturally restrict each lattice site to hold at most one particle. This raises an important question: can anyonic physics still arise through number-dependent tunneling despite this limitation?

In this theoretical project, we will explore new ways to simulate anyon statistics in qubit-based lattice models. Using numerical methods such as exact diagonalization and matrix product state (MPS) techniques, we will study how anyonic behavior can emerge when particles are allowed to tunnel over longer distances with occupation-dependent phases. The project will focus on understanding the resulting quantum states, correlations, and observable signatures of anyon statistics. The ultimate goal is to develop a concrete proposal—a blueprint—for implementing and testing these ideas on a real quantum computing platform, such as an IBM quantum device. This project is well suited for students interested in quantum mechanics, condensed matter physics, and quantum information science, and provides hands-on experience with modern computational tools used in quantum research.