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·费曼推测，可以对量子计算机进行编程，以比经典计算机更有效地模拟某些量子系统。这种令人着迷的可能性启发了目前的研究计划，我们将建立一个基于超导器件的多用途量子处理器。超导材料可以很容易地在硅片上生长成薄膜，并形成复杂的微电路。当冷却到绝对零度以上几万度的温度时，适当设计的超导微电路可以表现为量子比特(或量子比特)。与只能取值为0或1的经典比特不同，量子比特可以在0和1的任何叠加中制备。此外，可以在所谓的纠缠状态下准备成对的量子比特，从而实现量子机上的连接。我们将实现一种量子机，其中一组四个量子比特，每个量子比特与一个共同的辅助量子比特相互作用，形成一个二维(2D)晶格的一个单位单元，或表面代码。表面代码将使实现量子存储成为可能，在这种存储中，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自然会导致拓扑有序和非平凡多粒子量子系统的模拟。因此，我们的研究将从基础物理角度和技术应用两方面都具有相关性。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编码单元的基态冷却，并执行单元对之间的相关测量。这些将代表着对量子计算和凝聚态物理领域的开创性贡献。此外，加拿大作为一个国家将从表面代码的开发中受益，这既是为了支持关键的科学和技术探索，也是为了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.