Discrete and continuous variables oftentimes require different treatments in many learning tasks. Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quantum learning theory. While previous works mostly focused on quantum spin systems, where quantum states can be seen as superpositions of discrete bit-strings, relatively little is known about Hamiltonian learning for continuous-variable quantum systems. In this work we focus on learning the Hamiltonian of a bosonic quantum system, a common type of continuous-variable quantum system. In this talk, I will introduce an analytic framework to study the effects of strong dissipation in such systems, enabling the development of Heisenberg-limited algorithms for learning general bosonic Hamiltonians with higher-order terms of the creation and annihilation operators. On a theoretical level, we derive a new quantitative adiabatic approximation estimate for general Lindbladian evolutions with unbounded generators. This is based on joint work with Tim Möbus, Andreas Bluhm, Tuvia Gefen, Yu Tong and Albert H Werner, arXiv:2506.00606.
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