# Struct find_embedding::frozen_chain¶

struct frozen_chain

This class stores chains for embeddings, and performs qubit-use accounting.

The label is the index number for the variable represented by this chain. The links member of a chain is an unordered map storing the linking information for this chain. The data member of a chain stores the connectivity information for the chain.

Links: If u and v are variables which are connected by an edge, the following must be true: either chain_u or chain_v is empty,

or

chain_u.links[v] is a key in chain_u.data, chain_v.links[u] is a key in chain_v.data, and (chain_u.links[v], chain_v.links[u]) are adjacent in the qubit graph

Moreover, (chain_u.links[u]) must exist if chain_u is not empty, and this is considered the root of the chain.

Data: The data member stores the connectivity information. More precisely, data is a mapping qubit->(parent, refs) where: parent is also contained in the chain refs is the total number of references to qubit, counting both parents and links the chain root is its own parent.