We discuss the trace problem and stable rank for tracialy complete C*-algebras
In the category of operator systems, identification comes via complete order isomorphisms, and so an operator system can be identified with a C*-algebra without itself being an algebra. So, when is an operator system a C*-algebra? This question has floated around the community for some time. From Choi and Effros, we know that injectivity is sufficient, but certainly not necessary outside of the finite-dimensional setting. In this talk, I will give a characterization in the separable nuclear setting coming from C*-encoding systems. This comes from joint work with Galke, van Lujik, and Stottmeister.
Quantum computers are becoming a reality and current generations of machines are already well beyond the 50-qubit frontier. However, hardware imperfections still overwhelm these devices and it is generally believed the fault-tolerant, error-corrected systems will not be within reach in the near term: a single logical qubit needs to be encoded into potentially thousands of physical qubits which is prohibitive.
Due to limited resources, in the near term, hybrid quantum-classical protocols are the most promising candidates for achieving early quantum advantage and these need to resort to quantum error mitigation techniques. I will explain the basic concepts and introduce hybrid quantum-classical protocols are the most promising candidates for achieving early quantum advantage. These have the potential to solve real-world problems---including optimisation or ground-state search---but they suffer from a large number of circuit repetitions required to extract information from the quantum state. I will finally identify the most likely areas where quantum computers may deliver a true advantage in the near term.
Bálint Koczor
Associate Professor in Quantum Information Theory
Mathematical Institute, University of Oxford
Barrie Juniper, a former member of the Department of Biology established a collection of 100 different sorts of apple in the Wytham Walled Garden when he and Stephen Harris were working on the genetics of apples. Many of these still survive, although some have died out.
The Walled Garden is not normally accessible, but on a couple of afternoons in the autumn it is open for anyone to come and pick the fruit (though taste them first, some are rather bitter).