标题： 一维量子格点模型中的对偶性的低深度酉量子电路 显示英文标题

标题： Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models

摘要： 一种系统的方法来研究对称的(1+1)d量子格点模型中的对偶性，最近已被提出，这是通过在对称融合范畴上的模范畴来表述的。 通过描述对偶性如何以非平凡的方式交织闭合边界条件和电荷子域，这些对偶性可以通过幺正矩阵乘积算符来实现。 在本文中，我们解释了如何通过引入辅助自由度来构建线性深度的幺正量子电路，这些辅助自由度可以跟踪各个子域。 线性深度与这些对偶性改变其作用状态的相位这一事实是一致的。 当补充测量时，我们证明相对于编码到幂零融合范畴中的对称性的对偶性可以在常数深度中实现。 这些电路可以用来高效地制备短程和长程纠缠态，或者在(2+1)d拓扑模型的不同能隙边界之间进行映射。 显示英文摘要

摘要： A systematic approach to dualities in symmetric (1+1)d quantum lattice models has recently been proposed in terms of module categories over the symmetry fusion categories. By characterizing the non-trivial way in which dualities intertwine closed boundary conditions and charge sectors, these can be implemented by unitary matrix product operators. In this manuscript, we explain how to turn such duality operators into unitary linear depth quantum circuits via the introduction of ancillary degrees of freedom that keep track of the various sectors. The linear depth is consistent with the fact that these dualities change the phase of the states on which they act. When supplemented with measurements, we show that dualities with respect to symmetries encoded into nilpotent fusion categories can be realised in constant depth. The resulting circuits can for instance be used to efficiently prepare short- and long-range entangled states or map between different gapped boundaries of (2+1)d topological models.