Surface Codes with Superconducting Quantum Circuits: From a Topological Quantum Memory to the Quantum Emulation of the Fermi-Hubbard Model

1982年，理查德·费曼（Richard Feynman）提出，量子计算机可以编程来模拟某些量子系统，比经典计算机更有效。这种令人着迷的可能性激发了目前的研究计划，在那里我们将建立一个基于超导设备的多用途量子处理器。超导材料可以很容易地在硅晶片上生长成薄膜，并形成复杂的微电路。当冷却到绝对零度以上千分之几十度的温度时，适当设计的超导微电路可以表现为量子比特（或量子比特）。量子位的行为与经典位不同，经典位只能假定值为0或1，量子位可以以0和1的任何叠加来制备。此外，可以在所谓的纠缠态中制备量子比特对，从而实现量子机器上的连接。我们将实现一个量子机器，其中一组四个量子位，每个量子位与一个公共辅助量子位相互作用，形成二维（2D）晶格或表面代码的一个单位单元。表面代码将使实现量子存储器成为可能，在这种存储器中，量子信息可以在2D晶格中的单位单元簇中存储几乎无限的时间。此外，每个表面编码单元上的四体相互作用将自然导致拓扑序和非平凡多粒子量子系统的仿真。因此，我们的研究将从基础物理学的角度和技术应用的相关。我们相信，在未来五年内，在小尺寸表面代码上进行长寿命量子存储器的实验测试是可以实现的。在类似的时间窗口中，将有可能达到几个表面代码单元的基态冷却，并执行单元对之间的相关测量。这些将代表对量子计算和凝聚态物理学领域的开创性贡献。此外，加拿大作为一个国家将从地面代码的发展中受益，既支持关键的科学和技术探索，又帮助教育下一代顶尖研究人员。

In 1982 Richard Feynman conjectured that a quantum computer can be programmed to simulate certain quantum systems much more efficiently than a classical computer. This fascinating possibility inspires the present research program, where we will build a multi-purpose quantum processor based on superconducting devices. Superconducting materials can readily be grown as thin films on silicon wafers, and patterned into complex microcircuits. When cooled down to temperatures of a few tens of thousandths of a degree above absolute zero, suitably designed superconducting microcircuits can behave as quantum bits (or qubits). Behaving differently than a classical bit, which can assume only a value of zero or one, a qubit can be prepared in any superposition of zero and one. Additionally, pairs of qubits can be prepared in so-called entangled states, enabling connectivity on the quantum machine. We will implement a quantum machine where a set of four qubits, each interacting with a common auxiliary qubit, forms a one unit cell of a two-dimensional (2D) lattice, or surface code. Surface codes will make it possible to realize quantum memories where quantum information can be stored, for a virtually unlimited time, in clusters of unit cells in the 2D lattice. In addition, the four-body interaction on each surface code cell will naturally lead to the emulation of topological order and of nontrivial many-particle quantum systems. Our research will thus be relevant both from a fundamental physics perspective and for technological applications. We believe the experimental testing of a long-lived quantum memory on a small size surface code is achievable within the next five years. In a similar time window it will be possible to reach ground state cooling of a few surface code cells and to perform correlation measurements between pairs of cells. These will represent seminal contributions to the fields of quantum computing and condensed matter physics. Additionally, Canada as a country will profit from the development of surface codes, both for supporting a critical scientific and technological quest and for helping educate the next generation of top researchers.