Scalable chains of coupled superconducting transmission line resonators

The investigation of many-body Hamiltonians is relevant to understand collective quantum behavior in solid state physics. However, solving these many-body Hamiltonians can be challenging on a classical computer. For this reason, quantum simulations are an attractive approach to simulate such complex Hamiltonians with experimentally easily accessible and well-controlled systems. In our experiment, we use superconducting circuits to take the first steps towards this direction. More precisely, we characterize chains of up to four coupled transmission line resonators in a scalable layout. After introducing nonlinearities in the form of Josephson junctions and scaling to longer chains, our system can become a quantum simulator for Bose-Hubbard-type Hamiltonians.