Module pathfinding_and_contraction 

Pathfinding and Contraction

Pathfinding

To contract a tensor network, we need to specify the order in which the contractions should appear. This is passed as a list of pairs of tensor indices. There are different formats / interpretions of contraction paths; this library uses what we call the “replace left” format:

Format	Action for a single contraction (i, j)	Example for 4 tensors
SSA	Contract tensor i and j, then append resulting tensor at end	[(0, 2), (1, 3), (4, 5)], result in 6
opt-einsum	Pop tensors i and j, then contract and append resulting tensor at end	[(0, 2), (0, 2), (0, 1)], result in 0
Replace left	Contract tensor i and j, then replace i by the resulting tensor	[(0, 2), (1, 3), (0, 1)], result in 0

The rationale behind this format is that it can operate in-place without modifying the size of the tensors list, hence avoiding moving of elements and reallocations.

To find contraction paths for a given tensor network, the library offers various contraction path finders. The best choice is usually to use Cotengrust, which integrates a Rust port of path finders from the Python library cotengra. It has three variants specified by OptMethod.

Contraction

To contract the tensor network locally, just use contract_tensor_network and pass in the tensor network and a contraction path.

Re-exports

pub use crate::_tutorial as table_of_contents;