Posts Tagged With 'tensor network'
Matrix multiplication and tensor contraction cost
The computational cost of a matrix multiplication \(A\cdot{B}\) reads \(\mathfrak{C}\left(A\cdot{B}\right)=d_{0}d_{1}d_{2}\) with \(A\) is a \(d_{0}\times{d}_{1}\) matrix and \(B\) is a \(d_{1}\times{d}_{2}\) matrix …
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Preliminary
From a many-body operator (MBO) to a matrix product operator (MPO)
We are talking about quantum many-body models on a lattice \(\Lambda\).
A lattice \(\Lambda\) is a graph consisting of \(|\Lambda|\) sites, which are always labeled in a one-dimensional array \(\left\{0, \dots, |\Lambda|-1\right\}\) in a specific …
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Introduction
Tensors and their contraction
Tensor is a higher-dimensional generalization of the matrix, which has two indices such as \(M_{ij}\).
For example, a four-dimensional tensor can be obtained by the tensor product of two matrices \(\left(A\otimes B\right)\_{ij}=C_{ij}=C_{k\cdot d_{l}+l …
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