The Bethe Ansatz as a Quantum Circuit

The Bethe ansatz is an analytical method to address exactly solvable models in quantum mechanics. If the models have global symmetry, the trial wave functions of the Bethe ansatz consist of superpositions of plane waves. It has been shown that the Bethe ansatz can be recast as a deterministic quantum circuit. Quantum gates were determined numerically. In this talk, we shall share our progress in realising the Bethe ansatz as a quantum circuit, and present the analytical expressions of the quantum gates. Formulae rely upon diagrammatic rules that define the matrix-product-state network of the wave functions of the Bethe ansatz. Our results shed new light on the equivalence between the coordinate and algebraic Bethe ansatze.