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Observation of topological phenomena in a programmable lattice of 1,800 qubits

机译：在1,800量子比特的可编程晶格中观察拓扑现象

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The work of Berezinskii, Kosterlitz and Thouless in the 1970s(1,2) revealed exotic phases of matter governed by the topological properties of low-dimensional materials such as thin films of superfluids and superconductors. A hallmark of this phenomenon is the appearance and interaction of vortices and antivortices in an angular degree of freedom-typified by the classical XY model-owing to thermal fluctuations. In the two-dimensional Ising model this angular degree of freedom is absent in the classical case, but with the addition of a transverse field it can emerge from the interplay between frustration and quantum fluctuations. Consequently, a Kosterlitz-Thouless phase transition has been predicted in the quantum system-the two-dimensional transverse-field Ising model-by theory and simulation(3-5). Here we demonstrate a largescale quantum simulation of this phenomenon in a network of 1,800 in situ programmable superconducting niobium flux qubits whose pairwise couplings are arranged in a fully frustrated squareoctagonal lattice. Essential to the critical behaviour, we observe the emergence of a complex order parameter with continuous rotational symmetry, and the onset of quasi-long-range order as the system approaches a critical temperature. We describe and use a simple approach to statistical estimation with an annealing-based quantum processor that performs Monte Carlo sampling in a chain of reverse quantum annealing protocols. Observations are consistent with classical simulations across a range of Hamiltonian parameters. We anticipate that our approach of using a quantum processor as a programmable magnetic lattice will find widespread use in the simulation and development of exotic materials.
机译：Berezinskii，Kosterlitz和Thouless在1970年代的研究（1,2）揭示了异物相物质受低维材料（如超流体和超导体薄膜）的拓扑特性支配。这种现象的标志是，由于热波动，涡旋和反涡旋的出现和相互作用在自由度角上（由经典XY模型代表）。在二维Ising模型中，经典情况下不存在该角度自由度，但是通过添加横向场，它可以从无奈和量子涨落之间的相互作用中出现。因此，通过理论和仿真（3-5），在量子系统二维横电场伊辛模型中预测了Kosterlitz-Thouless相变。在这里，我们在1800个原位可编程超导铌磁通量子位的网络中演示了此现象的大规模量子模拟，其成对耦合布置在完全受挫的八角形晶格中。对于临界行为至关重要，我们观察到具有连续旋转对称性的复杂阶次参数的出现，以及随着系统接近临界温度而出现准远距离阶次。我们描述并使用一种简单的方法，通过基于退火的量子处理器进行统计估计，该量子处理器在反向量子退火协议链中执行蒙特卡洛采样。观测结果与一系列汉密尔顿参数的经典模拟结果一致。我们预计，将量子处理器用作可编程磁点阵的方法将在异质材料的仿真和开发中得到广泛应用。

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