Two paths, one flux: Trapped ions simulate Aharonov–Bohm interference in a lattice gauge theory

In a groundbreaking study published in Nature Physics, researchers have successfully simulated the Aharonov-Bohm effect using a hybrid trapped-ion quantum computer. This achievement represents a significant step forward in the field of quantum computing and our understanding of lattice gauge theories, which describe the interactions between matter and gauge fields.

Gauge theories, which form the foundation of the Standard Model of particle physics, govern how matter interacts through fields known as gauge fields. These fields carry the electromagnetic, weak, and strong forces. While lattice gauge theories model space as a grid with matter at its vertices and gauge fields on the connecting links, most previous simulations have been limited to one spatial dimension.

To overcome this limitation, researchers from the University of Oxford utilized trapped ions to simulate a Z₂ lattice gauge theory in a quasi-two-dimensional loop. Trapped ions serve a dual purpose in this experiment: their electronic states encode the gauge fields, while their vibrations encode the matter. The first author of the study, Sebastian Saner, highlighted the team's brainstorming process, which began in 2022 and led to the idea of using entangled qubits to encode the gauge-field flux.

The team constructed a closed loop using two trapped ions to study how a flux stored in entangled qubits would influence a moving particle. This setup allowed them to explore the effects of gauge fields on particle motion, a crucial aspect of quantum chromodynamics and other gauge theories.

Lattice gauge theories are particularly relevant to topological quantum error correction, a field that seeks to protect quantum information from errors due to environmental noise. In these theories, the gauge fields emerge from the collective behavior of electrons, and their interactions can give rise to exotic particles known as visons.

The researchers were able to simulate the two-dimensional geometry of the lattice by coupling qubits and vibrational modes, known as synthetic dimensions. By applying a laser to manipulate the vibrational modes, the physicists observed the particle tunneling between two sites, with the field line switching between present and absent. This observation is consistent with the Z₂ version of Gauss's law, which describes how electric fields behave in the presence of a magnetic flux.

This experimental breakthrough demonstrates the potential of trapped-ion quantum computers to tackle complex quantum simulations, opening up new avenues for research in quantum computing and theoretical physics.