标题： 克利福德电路增强的格雷姆矩阵乘积态 显示英文标题

标题： Clifford Circuits Augmented Grassmann Matrix Product States

摘要： 最近将Clifford电路与张量网络(TN)态结合的进展表明，经典可模拟的解纠缠器可以显著减少纠缠，缓解TN模拟中的键维数瓶颈。 在本工作中，我们开发了一个基于Grassmann张量网络的变分TN框架，该框架原生地编码了费米统计特性同时保持了局域性。 通过在费米形式主义中引入局部定义的Clifford电路，我们模拟了包括紧束缚和$t$-$V$模型在内的基准模型。 我们的结果表明，Clifford解纠缠移除了纠缠的经典可模拟部分，导致键维数减少，并提高了基态能量估计的准确性。 有趣的是，在Clifford电路上施加自然的Grassmann偶性约束显著减少了解纠缠门的数量，从720个减少到仅32个，从而实现了更高效的实现。 这些发现突显了Clifford增强的Grassmann TN在研究强关联费米系统中的潜力，尤其是在高维情况下。 显示英文摘要

摘要： Recent advances in combining Clifford circuits with tensor network (TN) states have shown that classically simulable disentanglers can significantly reduce entanglement, mitigating 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, imposing the natural Grassmann-evenness constraint on the Clifford circuits significantly reduces the number of disentangling gates, from 720 to just 32, yielding a far more efficient implementation. 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.