An example of a tensor network.

The number of edges (or wires) connecting to a tensor is equal to that tensor’s rank. When an index (edge) is contracted by combining two tensors according to Eq 1, the two tensor are replaced by a new one. The number of scalar entries in the tensor scales exponentially in the number of edges to which it connects. In general it is not trivial to choose an efficient contraction ordering that minimizes the total number of floating point operations.