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Can the Matrix Product State (MPS) simulator of the QISKIT be used to solve (2+1) D problems? I have seen this paper using the MPS simulator for a (2+1) D problem. However, my understanding is that an MPS can only work efficiently for 1+1 D problems due to the issue of entanglement. My question is whether or not the results obtained from the MPS simulator in a (2+1) D model can be trusted?

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    $\begingroup$ It's a good question. In that paper they are looking at a 1D boundary, but seem to be expecting (and numerically finding) a power-law decay in correlations on that boundary. It's not clear how they find that with an MPS simulation because no real details are provided. $\endgroup$
    – ChrisD
    Feb 20 at 21:36

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After discussing the topic with more experienced individuals, including Yael Ben-Haim in the Qiskit Slack channel, I gained some insight into why Matrix Product States (MPS) can be utilized in higher dimensions. Even though MPS is efficient in 1D systems, it has the potential to function in any dimension. However, it appears that the bond dimension must be increased in cases of increased entanglement, such as near critical points or, as in this case, simply due to the increased connectivity in higher dimensions. Consequently, this will likely make the MPS more time-consuming in higher dimensions, potentially negating any advantages it may have over other classical techniques.

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