Realizing topologically ordered states on a quantum processor

TL;DR

This paper demonstrates the preparation and analysis of topologically ordered states on a superconducting quantum processor, providing insights into topological quantum matter and error correction.

Contribution

It presents the first experimental realization of the toric code ground state and measures topological entanglement entropy on a quantum processor.

Findings

Measured topological entanglement entropy near ln(2)

Simulated anyon braiding statistics successfully

Investigated surface code aspects like logical state injection

Abstract

The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy near the expected value of $\ln2$, and simulate anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigate key aspects of the surface code, including logical state injection and the decay of the non-local order parameter. Our results demonstrate the potential for quantum processors to provide key insights into topological quantum matter and quantum error correction.