Realizing topologically ordered states on a quantum processor
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Abstract
Description Synthesizing topological order Topologically ordered matter exhibits long-range quantum entanglement. However, measuring this entanglement in real materials is extremely tricky. Now, two groups take a different approach and turn to synthetic systems to engineer the topological order of the so-called toric code type (see the Perspective by Bartlett). Satzinger et al. used a quantum processor to study the ground state and excitations of the toric code. Semeghini et al. detected signatures of a toric code–type quantum spin liquid in a two-dimensional array of Rydberg atoms held in optical tweezers. —JS Topological order of the toric code type is realized in two synthetic quantum systems. The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error–correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of –ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.