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.

具有非阿贝尔拓扑序的量子多体系统可以容纳任意子准粒子。有人提出，任意子可用于以拓扑保护的方式编码和操作信息，不受局部噪声的影响，量子门通过编织和融合任意子来实现。不幸的是，实现非阿贝尔拓扑有序态具有挑战性，直到最近才通过数字量子模拟方法观察到非阿贝尔统计的特征。然而，并非所有形式的拓扑序都可以用来实现通用量子计算。在这里，我们使用超导量子处理器来模拟斐波那契弦网模型的非阿贝尔拓扑有序状态，并演示具有通用计算能力的斐波那契任意子的编织。我们通过测量拓扑纠缠熵来证明量子态的非平凡拓扑性质。此外，我们创建了两对斐波那契任意子，并通过在底层物理量子位上应用酉门来演示它们的融合规则和非阿贝尔编织统计。我们的结果建立了一种数字方法来探索非阿贝尔拓扑状态及其与当前嘈杂的中级量子处理器相关的编织统计数据。