A key challenge in quantum simulation on quantum devices is the efficient preparation of eigenstates of quantum many-body systems which typically span exponentially large Hilbert spaces. A popular and powerful approach to address this complexity is the use of exponential ansätze (like in the Unitary Coupled-Cluster method) that attempt to capture the essential structural features of the corresponding wavefunctions. However, their operational form is, in general, system-dependent, making it difficult to draw broad conclusions across different physical systems. In this talk, I will present a universal methodology for learning the exact ansatz of quantum many-body systems that can be implemented on quantum devices. This novel approach is based on a generalization of the contracted Schrödinger equation for electronic systems, which allows the ansatz to retain the same number of degrees of freedom as the original many-body Hamiltonian. In addition to discussing the theoretical foundations of the approach, I will provide explicit numerical examples, including molecular systems interacting with light and quantum systems made up of bosons. These examples will show how well the new method performs compared to traditional approaches, like the (polaritonic) coupled-cluster method. At the end of the talk, I will introduce a machine learning technique that can learn the parameters of the ansatz, regardless of the specific type of particles the system contains.