quimb.experimental.belief_propagation.d2bp¶

Classes¶

D2BP

Dense (as in one tensor per site) 2-norm (as in for wavefunctions and

Functions¶

`contract_d2bp`(tn[, messages, output_inds, optimize, ...])	Estimate the norm squared of `tn` using dense 2-norm belief
`compress_d2bp`(tn, max_bond[, cutoff, cutoff_mode, ...])	Compress the tensor network `tn` using dense 2-norm belief
`sample_d2bp`(tn[, output_inds, messages, ...])	Sample a configuration from `tn` using dense 2-norm belief

Module Contents¶

class quimb.experimental.belief_propagation.d2bp.D2BP(tn, messages=None, output_inds=None, optimize='auto-hq', damping=0.0, update='sequential', local_convergence=True, **contract_opts)¶

Bases: quimb.experimental.belief_propagation.bp_common.BeliefPropagationCommon

Dense (as in one tensor per site) 2-norm (as in for wavefunctions and operators) belief propagation. Allows messages reuse. This version assumes no hyper indices (i.e. a standard PEPS like tensor network).

Potential use cases for D2BP and a PEPS like tensor network are:

globally compressing it from bond dimension D to D'

eagerly applying gates and locally compressing back to D

sampling configurations

estimating the norm of the tensor network

Parameters:

tn (TensorNetwork) – The tensor network to form the 2-norm of and run BP on.
messages (dict[(str, int), array_like], optional) – The initial messages to use, effectively defaults to all ones if not specified.
output_inds (set[str], optional) – The indices to consider as output (dangling) indices of the tn. Computed automatically if not specified.
optimize (str or PathOptimizer, optional) – The path optimizer to use when contracting the messages.
damping (float, optional) – The damping factor to use, 0.0 means no damping.
update ({'parallel', 'sequential'}, optional) – Whether to update all messages in parallel or sequentially.
local_convergence (bool, optional) – Whether to allow messages to locally converge - i.e. if all their input messages have converged then stop updating them.
contract_opts – Other options supplied to cotengra.array_contract.

tn¶

contract_opts¶

damping¶

local_convergence¶

update¶

backend¶

_abs¶

_sum¶

_normalize¶

_distance¶

touch_map¶

touched¶

exprs¶

update_touched_from_tids(*tids)¶: Specify that the messages for the given tids have changed.

update_touched_from_tags(tags, which='any')¶: Specify that the messages for the messages touching tags have changed.

update_touched_from_inds(inds, which='any')¶: Specify that the messages for the messages touching inds have changed.

iterate(tol=5e-06)¶: Perform a single iteration of dense 2-norm belief propagation.

compute_marginal(ind)¶: Compute the marginal for the index ind.

contract(strip_exponent=False)¶

Estimate the total contraction, i.e. the 2-norm.

Parameters:: strip_exponent (bool, optional) – Whether to strip the exponent from the final result. If True then the returned result is (mantissa, exponent).
Return type:: scalar or (scalar, float)

compress(max_bond, cutoff=0.0, cutoff_mode=4, renorm=0, inplace=False)¶: Compress the initial tensor network using the current messages.

quimb.experimental.belief_propagation.d2bp.contract_d2bp(tn, messages=None, output_inds=None, optimize='auto-hq', damping=0.0, update='sequential', local_convergence=True, max_iterations=1000, tol=5e-06, strip_exponent=False, info=None, progbar=False, **contract_opts)¶

Estimate the norm squared of tn using dense 2-norm belief propagation.

Parameters:

tn (TensorNetwork) – The tensor network to form the 2-norm of and run BP on.
messages (dict[(str, int), array_like], optional) – The initial messages to use, effectively defaults to all ones if not specified.
max_iterations (int, optional) – The maximum number of iterations to perform.
tol (float, optional) – The convergence tolerance for messages.
output_inds (set[str], optional) – The indices to consider as output (dangling) indices of the tn. Computed automatically if not specified.
optimize (str or PathOptimizer, optional) – The path optimizer to use when contracting the messages.
damping (float, optional) – The damping parameter to use, defaults to no damping.
update ({'parallel', 'sequential'}, optional) – Whether to update all messages in parallel or sequentially.
local_convergence (bool, optional) – Whether to allow messages to locally converge - i.e. if all their input messages have converged then stop updating them.
strip_exponent (bool, optional) – Whether to strip the exponent from the final result. If True then the returned result is (mantissa, exponent).
info (dict, optional) – If specified, update this dictionary with information about the belief propagation run.
progbar (bool, optional) – Whether to show a progress bar.
contract_opts – Other options supplied to cotengra.array_contract.

Return type:

scalar or (scalar, float)

quimb.experimental.belief_propagation.d2bp.compress_d2bp(tn, max_bond, cutoff=0.0, cutoff_mode='rsum2', renorm=0, messages=None, output_inds=None, optimize='auto-hq', damping=0.0, update='sequential', local_convergence=True, max_iterations=1000, tol=5e-06, inplace=False, info=None, progbar=False, **contract_opts)¶

Compress the tensor network tn using dense 2-norm belief propagation.

Parameters:

tn (TensorNetwork) – The tensor network to form the 2-norm of, run BP on and then compress.
max_bond (int) – The maximum bond dimension to compress to.
cutoff (float, optional) – The cutoff to use when compressing.
cutoff_mode (int, optional) – The cutoff mode to use when compressing.
messages (dict[(str, int), array_like], optional) – The initial messages to use, effectively defaults to all ones if not specified.
max_iterations (int, optional) – The maximum number of iterations to perform.
tol (float, optional) – The convergence tolerance for messages.
output_inds (set[str], optional) – The indices to consider as output (dangling) indices of the tn. Computed automatically if not specified.
optimize (str or PathOptimizer, optional) – The path optimizer to use when contracting the messages.
damping (float, optional) – The damping parameter to use, defaults to no damping.
update ({'parallel', 'sequential'}, optional) – Whether to update all messages in parallel or sequentially.
local_convergence (bool, optional) – Whether to allow messages to locally converge - i.e. if all their input messages have converged then stop updating them.
inplace (bool, optional) – Whether to perform the compression inplace.
info (dict, optional) – If specified, update this dictionary with information about the belief propagation run.
progbar (bool, optional) – Whether to show a progress bar.
contract_opts – Other options supplied to cotengra.array_contract.

Return type:

TensorNetwork

quimb.experimental.belief_propagation.d2bp.sample_d2bp(tn, output_inds=None, messages=None, max_iterations=100, tol=0.01, bias=None, seed=None, local_convergence=True, progbar=False, **contract_opts)¶

Sample a configuration from tn using dense 2-norm belief propagation.

Parameters:

tn (TensorNetwork) – The tensor network to sample from.
output_inds (set[str], optional) – Which indices to sample.
messages (dict[(str, int), array_like], optional) – The initial messages to use, effectively defaults to all ones if not specified.
max_iterations (int, optional) – The maximum number of iterations to perform, per marginal.
tol (float, optional) – The convergence tolerance for messages.
bias (float, optional) – Bias the sampling towards more locally likely bit-strings. This is done by raising the probability of each bit-string to this power.
seed (int, optional) – A random seed for reproducibility.
local_convergence (bool, optional) – Whether to allow messages to locally converge - i.e. if all their input messages have converged then stop updating them.
progbar (bool, optional) – Whether to show a progress bar.
contract_opts – Other options supplied to cotengra.array_contract.

Returns:

config (dict[str, int]) – The sampled configuration, a mapping of output indices to values.
tn_config (TensorNetwork) – The tensor network with the sampled configuration applied.
omega (float) – The BP probability of the sampled configuration.