论文标题
费米子量子细胞自动机和广义矩阵产品一级
Fermionic quantum cellular automata and generalized matrix product unitaries
论文作者
论文摘要
我们研究矩阵产品统一操作员（MPU）用于费米子一维（1D）链。与1D QUDIT系统的情况形成鲜明对比的是，我们表明（i）费米子MPU不一定具有严格的因果锥体，并且（ii）并非所有费米子量子量子细胞自动机（QCA）都可以表示为费米子MPU。然后，我们引入了后者的自然概括，通过允许在其辅助空间上作用的其他操作员获得。我们表征了一个具有地方性的广义MPU的家族，并表明，除了附加惰性辅助辅助费米斯的自由度，该家族的任何代表都是Fermionic QCA和Viceversa。最后，我们证明了通用MPU的索引定理，在一个维度中恢复了Fermionic QCA最近得出的分类。作为我们分析的技术工具，我们还为费米子矩阵产品状态引入了分级的规范形式，证明了其独特性达到相似性转换。
We study matrix product unitary operators (MPUs) for fermionic one-dimensional (1D) chains. In stark contrast with the case of 1D qudit systems, we show that (i) fermionic MPUs do not necessarily feature a strict causal cone and (ii) not all fermionic Quantum Cellular Automata (QCA) can be represented as fermionic MPUs. We then introduce a natural generalization of the latter, obtained by allowing for an additional operator acting on their auxiliary space. We characterize a family of such generalized MPUs that are locality-preserving, and show that, up to appending inert ancillary fermionic degrees of freedom, any representative of this family is a fermionic QCA and viceversa. Finally, we prove an index theorem for generalized MPUs, recovering the recently derived classification of fermionic QCA in one dimension. As a technical tool for our analysis, we also introduce a graded canonical form for fermionic matrix product states, proving its uniqueness up to similarity transformations.
