Symmetry, Phases of Matter, and Resources in Quantum Computing

Our conference covers three related subjects: quantum fault-tolerance, magic states and resource theories, and quantum computational phases of matter. The linking elements between them are (a) on the phenomenological side, the persistence of computational power under perturbations, and (b) on the theory side, symmetry. The latter is necessary for the working of all three. The subjects are close but not identical, and we expect cross-fertilization between them. Fault tolerance is an essential component of universal scalable quantum computing. However, known practical methods of achieving fault tolerance are extremely resource intensive. Distillation of magic states is, in the current paradigm of fault-tolerance, the costliest operational component, by a large margin. It is therefore pertinent to improve the efficiency of such procedures, study theoretical limits of efficiency, and more generally, to establish a resource theory of quantum state magic. During the workshop, we will focus on a fundamental connection between fault-tolerant protocols and symmetries. "Computational phases of matter’’ are a surprising link between quantum computation and condensed matter physics. Namely, in the presence of suitable symmetries, the ground states of spin Hamiltonians have computational power within the scheme of measurement-based quantum computation, and this power is uniform across physical phases. Several computationally universal phases have to date been discovered. This subject is distinct from the above, but linked to them by the feature of persistence of computational power under deformations and deviations.