Quantum simulation with arrays of transmon qubits: Ising dynamics*

Chains of coupled qubits are known to realize the transverse-field Ising Hamiltonian in the two-level approximation. In this model, the qubit transition frequencies map onto the external magnetic field, so the ground and excited states play the role of spin-up and spin-down atoms. We implement this structure in a planar, on-chip architecture, with a one dimensional linear array of capacitively-coupled transmon qubits, where the two terminal qubits are dispersively coupled to microwave independent resonators for state readout. We present spectroscopic data and describe coherent manipulations in the array.