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）推测，通过编程，量子计算机可以比传统计算机更有效地模拟某些量子系统。这种迷人的可能性激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分之一度的温度时，适当设计的超导微电路可以表现为量子比特（或量子位）。量子比特的行为与经典比特不同，经典比特只能假设0或1的值，量子比特可以在0和1的任何叠加中制备。此外，可以在所谓的纠缠态中制备成对的量子比特，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）晶格或表面代码的一个单元格。表面编码将使量子存储成为可能，量子信息可以存储在二维晶格中的单位细胞簇中，几乎无限时间。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秩序和非平凡多粒子量子系统的模拟。因此，我们的研究无论从基础物理学的角度还是从技术应用的角度都是相关的。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。在一个相似的时间窗口内，将有可能达到几个表面编码单元的基态冷却，并在单元对之间进行相关测量。这些将代表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受益于表面代码的发展，既支持关键的科学和技术探索，又有助于培养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.