Quantum Computational Resources in the Presence of Symmetry

Summary

Fault-tolerance is essential to the performance of quantum technologies, but known schemes are extremely resource intensive. Thus, improving existing schemes or inventing new schemes is of central importance. This joint project is based on the realization that fault-tolerance schemes make use of symmetries in fundamental ways, and that studying the problem of fault tolerance broadly from a symmetry perspective may offer valuable insights. We will do so by focusing on fault-tolerance and control-error mitigation primitives that make explicit use of symmetries, and unveil fundamental connections between the two. This involves the study of decoherence and error control, and measures that counteract them in two settings: fault-tolerant universal quantum computation (FTQC) using magic state distillation; and computational phases of matter. We will address which types of symmetries lead to computationally universal phases of matter, and the minimum operational cost of fault-tolerant universal quantum computation. This work is a collaboration between the research groups of David Poulin, Robert Raussendorf, and Beni Yoshida from the Université de Sherbrooke, University of British Columbia and the Perimeter Institute, respectively. Results from this project will shed light on which order parameters of condensed matter systems are important for quantum information processing and quantum sensing, and how to assess and reduce the overhead requirements for fault-tolerant quantum computation via understanding the process of magic-state distillation.

Figure 1. (a) Heat plot for the non-classicality measure mana, for a single qutrit. The grey region is completely classical, and it contains the stabilizer polytope (with dashed boundary) as a strict subset. (b) The working of quantum computation in SPT phases rest on the presence of symmetry. Shown here is a symmetry that enables quantum computational wire, a computational primitive for computation.