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

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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.