Strategies for digital quantum simulation of bosons

Many prominent bosonic simulation problems are thought to be intractable on a classical computer, including the Bose-Hubbard model, quantum photonics, and molecular vibronics. The behavior of such systems would be efficiently studied on a quantum computer. Before such a simulation is performed, one must choose how to encode the bosonic degrees of freedom into a set of qubits. We present a general methodology for encoding truncated bosons into arrays of qubits, and consider several encoding types. We study the quantum operations and qubit counts for local and composite operators. Importantly, we also consider the utility of interconverting between mappings in the middle of a simulation. These methods lower the quantum resource requirements compared to previous encoding strategies, which may allow for larger problems to be simulated on near-term quantum devices.