Quantinuum, Munich, Germany.
Walter Burke Institute for Theoretical Physics and Department of Physics, California Institute of Technology, Pasadena, CA, USA.
Nature. 2024 Feb;626(7999):505-511. doi: 10.1038/s41586-023-06934-4. Epub 2024 Feb 14.
Non-Abelian topological order is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of fault-tolerant quantum computers. However, despite extensive efforts, non-Abelian topological order and its excitations have remained elusive, unlike the simpler quasiparticles or defects in Abelian topological order. Here we present the realization of non-Abelian topological order in the wavefunction prepared in a quantum processor and demonstrate control of its anyons. Using an adaptive circuit on Quantinuum's H2 trapped-ion quantum processor, we create the ground-state wavefunction of D topological order on a kagome lattice of 27 qubits, with fidelity per site exceeding 98.4 per cent. By creating and moving anyons along Borromean rings in spacetime, anyon interferometry detects an intrinsically non-Abelian braiding process. Furthermore, tunnelling non-Abelions around a torus creates all 22 ground states, as well as an excited state with a single anyon-a peculiar feature of non-Abelian topological order. This work illustrates the counterintuitive nature of non-Abelions and enables their study in quantum devices.
非阿贝尔拓扑序是一种令人向往的物质状态，具有显著的性质，包括可以记住它们被交换顺序的准粒子。这些任意子激发是容错量子计算机有前途的构建块。然而，尽管付出了广泛的努力，非阿贝尔拓扑序及其激发仍然难以捉摸，不像阿贝尔拓扑序中的简单准粒子或缺陷。在这里，我们在量子处理器中制备的波函数中实现了非阿贝尔拓扑序，并演示了对其任意子的控制。我们使用 Quantinuum 的 H2 囚禁离子量子处理器上的自适应电路，在一个由 27 个量子比特组成的 kagome 晶格上创建了 D 拓扑序的基态波函数，每个位置的保真度超过 98.4%。通过在时空上创建和移动任意子沿着 Borromean 环，任意子干涉测量检测到一个内在的非阿贝尔编织过程。此外，隧穿非阿贝尔离子穿过环面可以创建所有 22 个基态以及一个具有单个任意子的激发态——这是非阿贝尔拓扑序的一个奇特特征。这项工作说明了非阿贝尔离子的反直觉性质，并使它们能够在量子设备中进行研究。
