Dual unitary gates are highly non-local two-qudit unitary gates that have been studied extensively in quantum many-body physics and quantum information in the recent past. A special class of dual unitary gates consists of rank-four perfect tensors that are equivalent to highly entangled multipartite pure states called absolutely maximally entangled (AME) states. In this work, numerical and analytical constructions of dual unitary gates and perfect tensors that are diagonal in a special maximally entangled basis are presented. The main ingredient in our construction is a phase-valued (unimodular) two-dimensional array whose discrete Fourier transform is also unimodular. We obtain perfect tensors for several local Hilbert space dimensions, particularly, in dimension six. A perfect tensor in local dimension six is equivalent to an AME state of four qudits, denoted as AME(4,6). Such a state cannot be constructed from existing constructions of AME states based on error-correcting codes and graph states. An explicit construction of AME(4,6) states is provided in this work using two-qudit controlled and single-qudit gates making it feasible to generate such states experimentally.

中文翻译：

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使用双单模向量构建完美张量


双酉门是高度非局部的双量子酉门，近年来在量子多体物理学和量子信息中得到了广泛的研究。一类特殊的双酉门由四阶完美张量组成，这些张量相当于高度纠缠的多部分纯态，称为绝对最大纠缠 （AME） 状态。在这项工作中，提出了在特殊最大纠缠基中对角线的双酉门和完美张量的数值和解析结构。我们构造的主要成分是一个相位值（单模）二维数组，其离散傅里叶变换也是单模的。我们获得了几个局部希尔伯特空间维度的完美张量，特别是在第六维。局部维度 6 中的完美张量相当于四个 qudit 的 AME 状态，表示为 AME（4,6）。这样的状态不能基于纠错码和图形状态从 AME 状态的现有构造中构造出来。这项工作使用双 qudit 控制和单 qudit 门提供了 AME（4,6） 状态的显式构造，使得通过实验生成此类状态成为可能。