论文标题
代数伯特电路
Algebraic Bethe Circuits
论文作者
论文摘要
代数Bethe Ansatz（ABA）是一种非常成功的分析方法，用于精确解决统计力学和凝结物理学的几种物理模型。在这里，我们将ABA成为统一形式，以直接在量子计算机上实施。这是通过使用QR分解将ABA构成一级工人的非独立$ r $矩阵来实现的。我们的算法是确定性的，可用于伯特方程的真实和复杂根。我们在旋转 - $ \ frac {1} {2} $ xx和xxz型号上说明了我们的方法。我们表明，使用这种方法可以在量子计算机上有效地准备XX模型的特征状态，并具有量子资源，该量子资源符合先前的最新方法。我们在IBM量子计算机上运行小规模的错误减少实现，包括在$ 4 $站点上为XX和XXZ型号的基态制备。最后，我们使用统一矩阵得出了一种新形式的Yang-Baxter方程式，并在量子计算机上对其进行了验证。
The Algebraic Bethe Ansatz (ABA) is a highly successful analytical method used to exactly solve several physical models in both statistical mechanics and condensed-matter physics. Here we bring the ABA into unitary form, for its direct implementation on a quantum computer. This is achieved by distilling the non-unitary $R$ matrices that make up the ABA into unitaries using the QR decomposition. Our algorithm is deterministic and works for both real and complex roots of the Bethe equations. We illustrate our method on the spin-$\frac{1}{2}$ XX and XXZ models. We show that using this approach one can efficiently prepare eigenstates of the XX model on a quantum computer with quantum resources that match previous state-of-the-art approaches. We run small-scale error-mitigated implementations on the IBM quantum computers, including the preparation of the ground state for the XX and XXZ models on $4$ sites. Finally, we derive a new form of the Yang-Baxter equation using unitary matrices, and also verify it on a quantum computer.
