Bosonic Hamiltonian Learning with the Help of Engineered Dissipation
Learning the dynamics of bosonic quantum systems is essential for the characterization and benchmarking of continuous-variable quantum devices, yet remains largely unexplored due to their infinite-dimensional Hilbert spaces and unbounded operators. We propose a framework for efficient Hamiltonian learning in such systems by combining coherent state preparation, heterodyne detection, and engineered dissipation. Central to our approach is a moment criterion based on the particle number operator, which enables the derivation of Lieb-Robinson-type bounds and allows learning strategies from finite-dimensional systems to be extended to bosonic m-mode Hamiltonians defined by polynomials in the annihilation and creation operators. This criterion can be enforced through photon dissipation inspired by the bosonic cat code.