Combinatorics

Quantum entanglement

Physics

Topology (electrical circuits)

Quantum technology

Mathematics

Topological order

Quantum error correction

Symmetry protected topological order

Mathematical optimization

Quantum algorithm

Hamiltonian (control theory)

Quantum network

Open quantum system

Topological degeneracy

Topological quantum computer

Anyon

Theoretical physics

Quantum computer

Quantum mechanics

Quantum

Toric code

Science

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.

Realizing topologically ordered states on a quantum processor