Quantum simulation of Bose-Hubbard ladders on superconducting qubits

Superconducting qubits provide a promising platform for quantum simulation due to their natural implementation of the Bose-Hubbard Hamiltonian and flexibility in tuning system parameters. In these systems, the combination of on-site interactions and interference effects from synthetic magnetic fields gives rise to interesting quantum many body dynamics and phases. Ladders built from coupled one-dimensional chains are among the simplest lattices where effects from a magnetic field can be observed; in addition, their reduced dimensionality maximizes the impact of on-site interactions. Within a single device, a combination of fixed and tunable qubit couplings allows precise control over the ratio of hoppings along the parallel and perpendicular edges of the ladder. Additionally, changing the sign of the hopping implements a synthetic magnetic field equivalent to 0 or 𝜋 flux threaded through each plaquette of the ladder. The tunability of both hopping and flux enables access of various quantum many body phases and correlations. Here, we present the design and implementation of a ladder realized with superconducting qubits and demonstrate control over the Hamiltonian parameters necessary to explore these fascinating quantum phases.