Bethe Ansatz, Quantum Circuits, and F-basis

Octubre 23, 2024
De 11:30am hasta 12:30pm

Grey Room 3

Specialist level
Speaker: 
Roberto Ruiz (IFT)
Location&Place: 

Grey Room 3

Abstract: 

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.