A class of highly entangled many-body states that can be efficiently simulated

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The reduced density matrix for n n contiguous wires, as well as n n -point correlators, can also be computed with a cost that scales exponentially in n n but is still efficient in the number N N of wires

Cited in the paper.

Lemma 2 also applies to the state | Ψ [ i 1 i 2 ⋯ i N ] ⟩ |\Psi[i_{1}i_{2}\cdots i_{N}]\rangle

Cited in the paper.

Another interesting case is when all the gates are repetition of a finite set of gates, in which case O ⁡ ( χ 4 ) O(\chi^{4}) parameters completely specifies the ansatz. Notice that then we can consider the thermodynamic limit, N → ∞ N\rightarrow\infty . An efficient computation of local expectation values is still possible by considering the fixed-point(s) of the non-linear map ρ t ⊗ 2 → ρ t + 1 \rho_{t}^{\otimes 2}\rightarrow\rho_{t+1} in Fig. 3

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