Title: Superconducting Quantum Simulator for Topological Order and the Toric Code Show Chinese title

Title: 拓扑序和表面码的超导量子模拟器

Abstract: Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum spin liquids are receiving substantial interest because of their intriguing quantum correlations, their exotic excitations and prospects for protecting stored quantum information against errors. Here we show that the Hamiltonian of the central model of this class of systems, the Toric Code, can be directly implemented as an analog quantum simulator in lattices of superconducting circuits. The four-body interactions, which lie at its heart, are in our concept realized via Superconducting Quantum Interference Devices (SQUIDs) that are driven by a suitably oscillating flux bias. All physical qubits and coupling SQUIDs can be individually controlled with high precision. Topologically ordered states can be prepared via an adiabatic ramp of the stabilizer interactions. Strings of qubit operators, including the stabilizers and correlations along non-contractible loops, can be read out via a capacitive coupling to read-out resonators. Moreover, the available single qubit operations allow to create and propagate elementary excitations of the Toric Code and to verify their fractional statistics. The architecture we propose allows to implement a large variety of many-body interactions and thus provides a versatile analog quantum simulator for topological order and lattice gauge theories. Show Chinese abstract

Abstract: 拓扑序现在被确立为表征和分类凝聚态系统基态的中心标准，并补充了基于对称性的分类方法。 分数量子霍尔系统和量子自旋液体因其引人入胜的量子关联、奇特的激发以及保护存储的量子信息免受错误影响的前景而受到广泛关注。 在这里，我们表明，这类系统的核心模型——环码（Toric Code）的哈密顿量可以直接在超导电路晶格中实现为模拟量子模拟器。 其核心的四体相互作用在我们的概念中通过由适当振荡通量偏置驱动的超导量子干涉装置（SQUIDs）实现。 所有的物理量子比特和耦合SQUIDs都可以高精度单独控制。 可以通过稳定器相互作用的绝热斜坡制备拓扑有序态。 可以通过电容耦合到读出谐振器来读取包括稳定器和非可缩回环上的关联在内的量子比特算符字符串。 此外，可用的单量子比特操作允许创建和传播环码的基本激发，并验证它们的分数统计特性。 我们提出的架构可以实现多种多体相互作用，因此为拓扑序和格点规范理论提供了一个灵活的模拟量子模拟器。