Learning the Exact Universal Ansatz of Quantum Many-body Systems

The efficient preparation of quantum many-body states on quantum devices is a major challenge, as they typically exhibit an exponentially large number of amplitudes. One of the most popular approaches to managing this complexity is using exponential ansätze, such as the Coupled-Cluster method, that capture the corresponding wavefunction's essential structural features. However, these ansätze are often system-dependent, making generalizing findings across different physical systems challenging. Here, we develop a strategy to learn the universal, exact exponential ansatz parameters for quantum many-body physics. Our approach generalizes the contracted Schrödinger equation for electronic systems, which, quite remarkably, allows the ansatz to retain the same degrees of freedom as the original many-body Hamiltonian. Inspired by architectures previously applied in operator learning, particularly in the context of driven-dissipative quantum mechanics, the learning process leverages these advancements to achieve efficient state preparation. We illustrate the power of this approach with numerical examples, including molecular systems interacting with light and mixtures of bosonic quantum systems, highlighting its superior performance over traditional methods, such as the (polaritonic) coupled-cluster approach.