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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.
Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological orders can
Intermediate-scale quantum technologies provide unprecedented opportunities for scientific discoveries while posing the challenge of identifying important problems that can take advantage of them through algorithmic innovations. A major open problem
Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations become comput
Generative adversarial networks are an emerging technique with wide applications in machine learning, which have achieved dramatic success in a number of challenging tasks including image and video generation. When equipped with quantum processors, t
We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of topological order with the spontaneous breaking of discrete time-translation symmetry. We show that many-body localiz