This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.
From a quantum information perspective, we will study universal features of chaotic quantum systems.
Quantum error correction -- originally invented for quantum computing -- has proven itself useful in a variety of non-computational physical systems, as the ideas of QEC are broadly applicable.
Generally speaking, physicists still experience that computing with paper and pencil is in most cases simpler than computing with a Computer Algebra System.
The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes, and even by braiding engineered Majorana modes using twist defects. Here, we present a unified framework to describe these methods, which can be used to better compare different schemes and to facilitate the design of hybrid schemes.
We present an in-depth study of the domain walls available in the color code. We begin by presenting new boundaries which gives rise to a new family of color codes. Interestingly, the smallest example of such a code consists of just 4 qubits and weight three parity check measurements, making it an accessible playground for today's experimentalists interested in small scale experiments on topological codes. Secondly, we catalogue the twist defects that are accessible with the color code model.
We first summarize background on the quantum capacity of a quantum channel, and explain why we know very little about this fundamental quantity, even for the qubit depolarizing channel (the quantum analogue of the binary symmetric channel) despite 20 years of effort by the community.
While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT), indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy-compression and approximate quantum error correction, both of which are predicted in holography.
The theory of alphabits is a natural generalisation of approximate quantum error correction that proves fundamental to the study of asymptotic quantum resources. In particular, it leads to an asymptotically reversible variation on quantum teleportation, called zerobit teleportation, which decomposes qubits of communication into correlation and transmission components. They also naturally arise in the study of black holes with significant consequences for the nature of quantum error correction in AdS/CFT.
Transversality is one of the most desirable features of fault-tolerant circuits because it automatically limits the propagation of errors. However, it was shown by Eastin & Knill that no universal set of quantum gates on any quantum code is transversal. In this talk, we strengthen this result for stabilizer codes to say that transversal gates must in fact be contained in the Clifford hierarchy. Moreover, we present new circuits on Bacon-Shor codes that saturate our bounds.
A recent breakthrough in the condensed matter community is the identification and characterization of a rich set of ordered states, known as symmetry protected topological (SPT) phases. These phases are not only fascinating from the perspective of fundamental physics but have also found powerful applications in quantum computation. Very little is known about the thermal stability of SPT ordered systems, or whether their associated computational properties may survive at non-zero temperature.