On the complexity of integrable eigenstates

Eigenstate preparation remains a central challenge in using quantum computing to study many-body physics. Integrable models, known for their exactly solvable nature, offer a promising avenue due to the relative simplicity of their eigenstates. These models exhibit fully elastic and factorized scattering processes, yet they remain essential for understanding complex many-body phenomena. In this seminar, we discuss how the celebrated Bethe Ansatz, a method for constructing eigenstates of a broad class of integrable systems, can be translated into a quantum circuit. We will analyze the complexity of the resulting circuits, focusing on the number of elementary quantum gates required and how this resource scales with system size and particle number.