matrix_product_state(input_tensor, rank, verbose=False)[source]

MPS decomposition via recursive SVD

Decomposes input_tensor into a sequence of order-3 tensors (factors) – also known as Tensor-Train decomposition [R13].

input_tensor : tensorly.tensor

rank : {int, int list}

maximum allowable MPS rank of the factors if int, then this is the same for all the factors if int list, then rank[k] is the rank of the kth factor

verbose : boolean, optional

level of verbosity


factors : MPS factors

order-3 tensors of the MPS decomposition


[R13](1, 2) Ivan V. Oseledets. “Tensor-train decomposition”, SIAM J. Scientific Computing, 33(5):2295–2317, 2011.