Simulating topological order on quantum processors

It is an ongoing quest to realize topologically ordered quantum states on different platforms including condensed matter systems, quantum simulators and digital quantum processors. Unlike conventional states characterized by their local order, these exotic states are characterized by their non-local entanglement. The consequences of topological order can be as profound as they are surprising, ranging from the emergence of fractionalized anyonic excitations to potentially providing a scalable platform for quantum error correction. This deep connection to quantum computing naturally motivates the realization and study of topologically ordered quantum states on quantum processors. However, owing to the non-local nature of these states, their study presents a challenge for near-term quantum devices. This Perspective aims to review the recent progress towards the experimental realization of topologically ordered quantum states, their potential applications and promising directions of future research.