"Learning how to create and control highly-entangled many-body systems is a central challenge of modern quantum science, with promising applications from quantum computing to many-body physics and quantum-enhanced metrology. Analog quantum simulators provide a rich playground for exploring the emergent collective phenomena in synthetic quantum systems, and how to harness these many-body effects for future quantum technologies.

In this talk, I will describe various approaches for assembling and probing quantum matter from strongly interacting microwave photons using superconducting circuits. Our platform consists of an array of capacitively coupled transmon qubits acting as a Hubbard model for photons. Capitalizing on the precise time- and space-resolved control of the lattice potential landscape has played a pivotal role in our platform for adiabatically preparing quantum fluids of light and investigating many-body quantum dynamics. While these techniques have thus far relied entirely on the classical control of the lattice, harnessing the actual quantum nature of our sites unlocks a new capability for evolving our synthetic material under a quantum superposition of different lattice configurations. We showcase this principle with a quantum-controlled photonic transistor by employing ancilla-conditioned many-body transport, whereby the orchestrated interference and freezing of the dynamics yield highly entangled cat states useful for quantum information and metrology. Furthermore, we introduce a new tool for efficiently characterizing these long-range correlated states using many-body Ramsey interferometry, extracting the information of our many-body eigenstates from the relative phase accumulated in the ancilla qubit."