Clifford Circuits Augmented Grassmann Matrix Product States

Abstract

Recent advances in combining Clifford circuits with tensor-network (TN) methods have shown that classically simulable disentanglers can suppress substantial portions of the entanglement structure, effectively alleviating the bond-dimension bottleneck in TN simulations. In this work, we develop a variational TN framework based on Grassmann tensor networks, which natively encode fermionic statistics while preserving locality. By incorporating locally defined Clifford circuits within the fermionic formalism, we simulate benchmark models including the tight-binding and $t$-$V$ models. Our results show that Clifford disentangling removes the classically simulable component of entanglement, leading to a reduced bond dimension and improved accuracy in ground-state energy estimates. Interestingly, once the natural Grassmann-evenness requirement of the fermionic formulation is taken into account and Clifford gates with identical entanglement action are grouped together, the original set of 11520 two-qubit Clifford gates reduces to only 12 distinct gates. This strong reduction leads to a more efficient disentangling scheme within the fermionic framework. These findings highlight the potential of Clifford-augmented Grassmann TNs as a scalable and accurate tool for studying strongly correlated fermionic systems, particularly in higher dimensions.