标题： 贝特假设，量子电路，和F基 显示英文标题

标题： Bethe Ansatz, Quantum Circuits, and the F-basis

摘要： Bethe假设是一种构造量子可积自旋链精确本征态的方法。 最近，确定性量子算法，称为“代数Bethe电路”，已被开发出来，用于制备自旋-1/2 XXZ模型的Bethe态。 这些电路表示标准代数Bethe假设的幺正形式，使用作用于自旋链和辅助空间上的矩阵乘积态来表达。 在本工作中，我们系统化了这些先前的结果，并表明代数Bethe电路可以通过辅助空间中的基变换得到。 新的基与来自量子可积模型理论的“F基”相同，它生成了坐标Bethe假设所特有的平面波的线性叠加。 我们解释了这种联系，强调F基的某些性质（即自旋的交换对称性）对于代数Bethe电路的构造至关重要。 我们通过为非均匀自旋-1/2 XXZ模型提出新的量子电路来展示我们的方法。 显示英文摘要

摘要： 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.