Automated Fermionic signs in tensor networks via Z₂ graded tensors

Fermionic signs in one-dimensional (1D) systems are taken care of by a Jordan-Wigner transformation. In 2D lattice models,this is generalized in the construction of fermionic projected entangled pair state (fPEPS; Corboz et al., PRB 2010). This demonstrated that fermionic signs can also be treated efficiently locally beyond 1D systems, albeit with organizational overhead to properly include fermionic parity. To deal with that overhead in a systematic manner, it was argued more recently (Mortier et al, SciPost 2024; Gao et al., quant-ph/2024 ) that fermionic signs can be treated automatically in the tensor framework in an algorithmic manner via Z₂-graded tensors. I will briefly discuss its current implementation in the open-source QSpace tensor library.