find_embedding(S, T, **params)¶
Heuristically attempt to find a minor-embedding of a graph representing an Ising/QUBO into a target graph.
S: an iterable of label pairs representing the edges in the source graph, or a NetworkX Graph T: an iterable of label pairs representing the edges in the target graph, or a NetworkX Graph **params (optional): see below
When return_overlap = False (the default), returns a dict that maps labels in S to lists of labels in T. If the heuristic fails to find an embedding, an empty dictionary is returned When return_overlap = True, returns a tuple consisting of a dict that maps labels in S to lists of labels in T and a bool indicating whether or not a valid embedding was found When interrupted by Ctrl-C, returns the best embedding found so far Note that failure to return an embedding does not prove that no embedding exists
max_no_improvement: Maximum number of failed iterations to improve the current solution, where each iteration attempts to find an embedding for each variable of S such that it is adjacent to all its neighbours. Integer >= 0 (default = 10) random_seed: Seed for the random number generator that find_embedding uses. Integer >=0 (default is randomly set) timeout: Algorithm gives up after timeout seconds. Number >= 0 (default is approximately 1000 seconds, stored as a double) max_beta: Qubits are assigned weight according to a formula (beta^n) where n is the number of chains containint that qubit. This value should never be less than or equal to 1. (default is effectively infinite, stored as a double) tries: Number of restart attempts before the algorithm stops. On D-WAVE 2000Q, a typical restart takes between 1 and 60 seconds. Integer >= 0 (default = 10) inner_rounds: the algorithm takes at most this many iterations between restart attempts; restart attempts are typically terminated due to max_no_improvement. Integer >= 0 (default = effectively infinite) chainlength_patience: Maximum number of failed iterations to improve chainlengths in the current solution, where each iteration attempts to find an embedding for each variable of S such that it is adjacent to all its neighbours. Integer >= 0 (default = 10) max_fill: Restricts the number of chains that can simultaneously incorporate the same qubit during the search. Integer >= 0, values above 63 are treated as 63 (default = effectively infinite) threads: Maximum number of threads to use. Note that the parallelization is only advantageous where the expected degree of variables is significantly greater than the number of threads. Integer >= 1 (default = 1) return_overlap: This function returns an embedding whether or not qubits are used by multiple variables. Set this value to 1 to capture both return values to determine whether or not the returned embedding is valid. Logical 0/1 integer (default = 0) skip_initialization: Skip the initialization pass. Note that this only works if the chains passed in through initial_chains and fixed_chains are semi-valid. A semi-valid embedding is a collection of chains such that every adjacent pair of variables (u,v) has a coupler (p,q) in the hardware graph where p is in chain(u) and q is in chain(v). This can be used on a valid embedding to immediately skip to the chainlength improvement phase. Another good source of semi-valid embeddings is the output of this function with the return_overlap parameter enabled. Logical 0/1 integer (default = 0) verbose: Level of output verbosity. Integer < 4 (default = 0). When set to 0, the output is quiet until the final result. When set to 1, output looks like this: initialized max qubit fill 3; num maxfull qubits=3 embedding trial 1 max qubit fill 2; num maxfull qubits=21 embedding trial 2 embedding trial 3 embedding trial 4 embedding trial 5 embedding found. max chain length 4; num max chains=1 reducing chain lengths max chain length 3; num max chains=5 When set to 2, outputs the information for lower levels and also reports progress on minor statistics (when searching for an embedding, this is when the number of maxfull qubits decreases; when improving, this is when the number of max chains decreases) When set to 3, report before each before each pass. Look here when tweaking `tries`, `inner_rounds`, and `chainlength_patience` When set to 4, report additional debugging information. By default, this package is built without this functionality. In the c++ headers, this is controlled by the CPPDEBUG flag Detailed explanation of the output information: max qubit fill: largest number of variables represented in a qubit num maxfull: the number of qubits that has max overfill max chain length: largest number of qubits representing a single variable num max chains: the number of variables that has max chain size initial_chains: Initial chains inserted into an embedding before fixed_chains are placed, which occurs before the initialization pass. These can be used to restart the algorithm in a similar state to a previous embedding; for example, to improve chainlength of a valid embedding or to reduce overlap in a semi-valid embedding (see skip_initialization) previously returned by the algorithm. Missing or empty entries are ignored. A dictionary, where initial_chains[i] is a list of qubit labels. fixed_chains: Fixed chains inserted into an embedding before the initialization pass. As the algorithm proceeds, these chains are not allowed to change. Missing or empty entries are ignored. A dictionary, where fixed_chains[i] is a list of qubit labels. restrict_chains: Throughout the algorithm, we maintain the condition that chain[i] is a subset of restrict_chains[i] for each i, except those with missing or empty entries. A dictionary, where restrict_chains[i] is a list of qubit labels. suspend_chains: This is a metafeature that is only implemented in the Python interface. suspend_chains[i] is an iterable of iterables; for example suspend_chains[i] = [blob_1, blob_2], with each blob_j an iterable of target node labels. this enforces the following: for each suspended variable i, for each blob_j in the suspension of i, at least one qubit from blob_j will be contained in the chain for i we accomplish this trhough the following problem transformation for each iterable blob_j in suspend_chains[i], * add an auxiliary node Zij to both source and target graphs * set fixed_chains[Zij] = [Zij] * add the edge (i,Zij) to the source graph * add the edges (q,Zij) to the target graph for each q in blob_j