## A scanning transmon qubit for strong coupling circuit quantum electrodynamics

Like a quantum computer designed for a particular class of problems, a quantum simulator enables quantitative modeling of quantum systems that is computationally intractable with a classical computer. Quantum simulations of quantum many-body systems have been performed using ultracold atoms and trapped ions among other systems.

## Circuit quantum electrodynamics with a spin qubit

Electron spins trapped in quantum dots have been proposed as basic building blocks of a future quantum processor. Although fast, 180-picosecond, two-quantum-bit (two-qubit) operations can be realized using nearest-neighbour exchange coupling, a scalable, spin-based quantum computing architecture will almost certainly require long-range qubit interactions.

## Symmetries and collective excitations in large superconducting circuits

The intriguing appeal of circuits lies in their modularity and ease of fabrication. Based on a toolbox of simple building blocks, circuits present a powerful framework for achieving new functionality by combining circuit elements into larger networks. It is an open question to what degree modularity also holds for quantum circuits -- circuits made of superconducting material, in which electric voltages and currents are governed by the laws of quantum physics.

## Anomalous Hall Effects of Light and Chiral Edge Modes on the Kagome Lattice

We theoretically investigate a photonic Kagome lattice which can be realized in microwave cavity arrays using current technology. The Kagome lattice exhibits an exotic band structure with three bands one of which can be made completely flat. The presence of artificial gauge fields allows to emulate topological phases and induce chiral edge modes which can coexist inside the energy gap with the flat band that is topologically trivial.

## On-chip quantum simulation with superconducting circuits

Using a well-controlled quantum system to simulate complex quantum matter is an idea that has been around for 30 years and put into practice in systems of ultracold atoms for more than a decade. Much recent excitement has focused on a new implementation of quantum simulators using superconducting circuits, where conventional microchip fabrication can be used to take design concepts to experimental reality, quickly and flexibly.

## Low-Disorder Microwave Cavity Lattices for Quantum Simulation with Photons

We assess experimentally the suitability of coupled transmission line resonators for studies of quantum phase transitions of light. We have measured devices with low photon hopping rates t/2pi = 0.8MHz to quantify disorder in individual cavity frequencies. The observed disorder is consistent with small imperfections in fabrication. We studied the dependence of the disorder on transmission line geometry and used our results to fabricate devices with disorder less than two parts in 10^4.