A Systematic Construction of Clifford Perfect Tensors

Perfect tensors are essential building blocks for holographic quantum states, which provide an intriguing platform of combining quantum information theory and physics of spacetime. Network of perfect tensors generated from stabilizer codes can be efficiently analyzed. To our knowledge, the full classification of such perfect tensors is still unknown. In this work, we demonstrate a systematic approach of constructing a large class of perfect tensors, with some existing construction schemes as special cases. Moreover, we investigate their operator generalization to continuous variable systems and identify the differences between the construction schemes in discrete variable and continuous variable systems.