Realizing topologically ordered states on a quantum processor

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 $\ln 2$, 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.

6 pages 4 figures, plus supplementary materials

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Cited by in corpus (12)

• Demonstration of fault-tolerant universal quantum gate operations
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Logical-qubit operations in an error-detecting surface code
• Simulating Chern insulators on a superconducting quantum processor
• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer
• Interplay between disorder and topology in Thouless pumping on a superconducting quantum processor
• A quantum processor based on coherent transport of entangled atom arrays
• Quantum simulation and ground state preparation for the honeycomb Kitaev model
• Sequential Adiabatic Generation of Chiral Topological States
• Generalized Gibbs ensembles in weakly interacting dissipative systems and digital quantum computers
• Error Crafting in Mixed Quantum Gate Synthesis
• Experimental protocol for observing single quantum many-body scars with transmon qubits