TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.6.187
TI  - Bethe Ansatz, quantum circuits, and the F-basis
PY  - 2025/06/12
UR  - https://scipost.org/SciPostPhys.18.6.187
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 6
SP  - 187
A1  - Ruiz, Roberto
AU  - Sopena, Alejandro
AU  - López, Esperanza
AU  - Sierra, German
AU  - Pozsgay, Balázs
AB  - The Bethe Ansatz is a method for constructing exact eigenstates of quantum-integrable spin chains. Recently, deterministic quantum algorithms, referred to as "algebraic Bethe circuits", have been developed to prepare Bethe states for the spin-$1/2$ XXZ model. These circuits represent a unitary formulation of the standard algebraic Bethe Ansatz, expressed using matrix-product states that act on both the spin chain and an auxiliary space. In this work, we systematize these previous results, and show that algebraic Bethe circuits can be derived by a change of basis in the auxiliary space. The new basis, identical to the "F-basis" known from the theory of quantum-integrable models, generates the linear superposition of plane waves that is characteristic of the coordinate Bethe Ansatz. We explain this connection, highlighting that certain properties of the F-basis (namely, the exchange symmetry of the spins) are crucial for the construction of algebraic Bethe circuits. We demonstrate our approach by presenting new quantum circuits for the inhomogeneous spin-$1/2$ XXZ model.
ER  -

@Article{10.21468/SciPostPhys.18.6.187,
	title={{Bethe Ansatz, quantum circuits, and the F-basis}},
	author={Roberto Ruiz and Alejandro Sopena and Esperanza López and Germán Sierra and Balázs Pozsgay},
	journal={SciPost Phys.},
	volume={18},
	pages={187},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.6.187},
	url={https://scipost.org/10.21468/SciPostPhys.18.6.187},
}