Encoding a bosonic mode into qubits for simulating boson-matter interactions

Abstract

We explore the space-time cost of encoding of a bosonic mode into a set of qubits via various encodings, and their resilience to noise. In particular, we compare the performance of the unary Fock state encoding, an unexplored encoding of Fock states into Dicke states (``Dicke'' encoding), and the binary quadrature encoding. We do so by considering a displacement as well as a simulation of a Dicke model, coupling a bosonic mode to a set of atoms represented as qubits. Using classical simulations, we assess the accuracy and optimized space-time costs in terms of number of qubits, circuit depth and CNOT count of a quantum simulation of the time dynamics using these encodings. Although our study is far from comprehensive, we find that the binary quadrature encoding is overall most favorable in terms of being very space-efficient and relatively time-efficient due to the use of the quantum Fourier transform. Our novel Dicke encoding leads to very shallow circuits, but pays in terms of using many more qubits. We probe the use of an H2-2 Quantinuum trapped-ion qubit device (56 qubits) for displacement and Dicke model simulation in the low boson-number regime, where we find that noise leads to visible deviations from ideal circuit dynamics.