QuICS

Recently an algorithm has been constructed that shows the binary icosahedral group 2I together with a T-like gate forms the most efficient single-qubit universal gate set. To carry out the algorithm fault tolerantly requires a code that implements 2I transversally. We fill this void by constructing a family of distance d = 3 codes that all implement 2I transversally. To do this, we introduce twisted unitary t-groups, a generalization of unitary t-groups under a twisting by an irreducible representation.

A set of universal fault-tolerant logical gates in quantum error correcting codes is necessary for quantum computing. Transversal operations applied independently on each qubit in a code block are naturally fault-tolerant and easy to implement, but the Eastin-Knill theorem states that the resulting discrete gate set cannot be universal. Circumventing this requires complex protocols such as magic state distillation, code switching, etc. Surface code error correction has been demonstrated on several experimental platforms.

The Eastin-Knill theorem shows that the transversal gates of a quantum code, which are naturally fault-tolerant, form a finite group G. We show that G is an invariant of equivalent quantum codes and thus can be considered as a well defined symmetry. This thesis studies how the symmetry G dictates the existence and parameters of quantum codes using representation theory. We focus on qubit quantum codes that have symmetry coming from finite subgroups of SU(2). We examine two different methods of deriving quantum codes from these symmetries.

In [1] we constructed a family of two-dimensional topological stabilizer codes on continuous variable (CV) degrees of freedom, which generalize homological rotor codes and the toric-GKP code. Our topological codes are built using the concept of boson condensation -- we start from a parent stabilizer code based on an R gauge theory and condense various bosonic excitations. This produces a large class of topological CV stabilizer codes, including ones that are characterized by the anyon theories of U(1)2n×U(1)−2m Chern-Simons theories, for arbitrary pairs of positive integers (n,m).

In 1994, the field of quantum computing had a significant breakthrough when Peter Shor introduced a quantum algorithm that factors integers in (probabilistic) polynomial time.  In these talks, I'll explain the mathematical aspects of Shor's algorithm.
Part II will follow on 3/5.

One approach to ion-photon entanglement relies on transitions from 2P3/2 to the low-lying 2D3/2 and 2D5/2 states at 1345 nm and 1650 nm in Yb+ [1]. Here Purcell enhancement is crucial for achieving good performance in the context of quantum networking. In support of this effort, we developed a monolithic, fiber-coupled Fabry–Pérot cavity integrated with a blade trap that operates at cryogenic temperatures. One of the cavity mirrors is bonded to a metalens that mode-matches cavity light to a single-mode fiber.