标题： 贝特_ansatz, 量子电路, 和 F-基底 显示英文标题

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

摘要： 贝特_ansatz 是一种用于构造量子可积自旋链精确本征态的方法。最近，确定性的量子算法，被称为“代数贝特电路”，已被开发出来以准备自旋-1/2 XXZ 模型的贝特态。这些电路代表了标准代数贝特_ansatz 的幺正表述，使用作用于自旋链和辅助空间上的矩阵乘积态来表示。在这项工作中，我们系统化了这些先前的结果，并表明代数贝特电路可以通过辅助空间中的基变换来推导。新的基与量子可积模型理论中已知的“F-基”相同，生成了坐标贝特_ansatz 特有的平面波线性叠加。我们解释了这种联系，强调指出 F-基的某些性质（即自旋的交换对称性）对于构建代数贝特电路至关重要。我们通过展示无均匀自旋-1/2 XXZ 模型的新量子电路来演示我们的方法。 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.