Non-Abelian braiding of Fibonacci anyons with a superconducting processor

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Abstract
Quantum many-body systems with a non-Abelian topological order can host anyonic quasiparticles. It has been proposed that anyons could be used to encode and manipulate information in a topologically protected manner that is immune to local noise, with quantum gates performed by braiding and fusing anyons. Unfortunately, realizing non-Abelian topologically ordered states is challenging, and it was not until recently that the signatures of non-Abelian statistics were observed through digital quantum simulation approaches. However, not all forms of topological order can be used to realize universal quantum computation. Here we use a superconducting quantum processor to simulate non-Abelian topologically ordered states of the Fibonacci string-net model and demonstrate braidings of Fibonacci anyons featuring universal computational power. We demonstrate the non-trivial topological nature of the quantum states by measuring the topological entanglement entropy. In addition, we create two pairs of Fibonacci anyons and demonstrate their fusion rule and non-Abelian braiding statistics by applying unitary gates on the underlying physical qubits. Our results establish a digital approach to explore non-Abelian topological states and their associated braiding statistics with current noisy intermediate-scale quantum processors.
Funding Information
  • National Natural Science Foundation of China (T2225008, 92065204, T2225008, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, T2225008, T2225008, T2225008, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204, 92065204)
  • The funding information is given in the Acknowlegements.

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