Centro de Excelencia Severo Ochoa
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The Bethe Ansatz is a method to construct the eigenstates of quantum-integrable models. We report our progress in systematising the quantum circuits to prepare the states of the Bethe Ansatz called 'Algebraic Bethe Circuits'. The key element is the F-basis in the auxiliary space of the tensor network of the algebraic Bethe Ansatz. The F-basis defines a matrix-product state invariant under exchange of ancillae connected to the coordinate Bethe Ansatz. Unitarisation of the matrix-product state, together with the elimination of ancillae, leads to closed formulae for the unitaries of the circuit thanks to the symmetry of the F-basis. We illustrate our results with a new circuit for the inhomogeneous spin-1/2 XXZ model with periodic boundaries.
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