1.2. tnpy.matrix_product_state.MatrixProductState

class tnpy.matrix_product_state.MatrixProductState(*args, **kwargs)

Bases: quimb.tensor.tensor_1d.MatrixProductState

Matrix product state (MPS) for a finite size system.

Parameters

• *args – Positional arguments for quimb.tensor.MatrixProductState.

• **kwargs – Keyword arguments for quimb.tensor.MatrixProductState.

Note

This class inherits directly from quimb.tensor.MatrixProductState, with some added features. But, note that the underlying tensors are in the shape ‘lpr’, which differs from the parent class quimb.tensor.MatrixProductState.

__init__(*args, **kwargs)

Matrix product state (MPS) for a finite size system.

Parameters

• *args – Positional arguments for quimb.tensor.MatrixProductState.

• **kwargs – Keyword arguments for quimb.tensor.MatrixProductState.

Note

This class inherits directly from quimb.tensor.MatrixProductState, with some added features. But, note that the underlying tensors are in the shape ‘lpr’, which differs from the parent class quimb.tensor.MatrixProductState.

Methods

__init__(*args, **kwargs)	Matrix product state (MPS) for a finite size system.
add(t[, virtual, check_collisions])	Add Tensor, TensorNetwork or sequence thereof to self.
add_MPS(other[, inplace, compress])	Add another MatrixProductState to this one.
add_MPS_(other, *[, inplace, compress])
add_tag(tag[, where, which])	Add tag to every tensor in this network, or if where is specified, the tensors matching those tags -- i.e. adds the tag to all tensors in self.select_tensors(where, which=which).
add_tensor(tensor[, tid, virtual])	Add a single tensor to this network - mangle its tid if neccessary.
add_tensor_network(tn[, virtual, ...])
align(*[, ind_ids, inplace])	Align an arbitrary number of tensor networks in a stack-like geometry.
align_(*[, ind_ids, inplace])
all_inds()	Return a tuple of all indices (with repetition) in this network.
amplitude(b)	Compute the amplitude of configuration b.
antidiag_gauge([output_inds, atol, cache, ...])	Flip the order of any bonds connected to antidiagonal tensors.
antidiag_gauge_([output_inds, atol, cache, ...])
apply_to_arrays(fn)	Modify every tensor's array inplace by applying fn to it.
as_cyclic([inplace])	Convert this flat, 1D, TN into cyclic form by adding a dummy bond between the first and last sites.
aslinearoperator(left_inds, right_inds[, ...])	View this TensorNetwork as a TNLinearOperator.
astype(dtype[, inplace])	Convert the type of all tensors in this network to dtype.
astype_(dtype, *[, inplace])
balance_bonds([inplace])	Apply tensor_balance_bond() to all bonds in this tensor network.
balance_bonds_(*[, inplace])
bipartite_schmidt_state(sz_a[, get, cur_orthog])	Compute the reduced state for a bipartition of an OBC MPS, in terms of the minimal left/right schmidt basis.
bond(i, j)	Get the name of the index defining the bond between sites i and j.
bond_size(i, j)	Return the size of the bond between site i and j.
bond_sizes()
calc_current_orthog_center()	Calculate the site(s) of the current orthogonality center.
canonize(where[, cur_orthog, bra])	Mixed canonize this TN. If this is a MPS, this implies that::.
canonize_around(tags[, which, min_distance, ...])	Expand a locally canonical region around tags.
canonize_around_(tags[, which, ...])
canonize_between(tags1, tags2[, absorb])	'Canonize' the bond between the two single tensors in this network specified by tags1 and tags2 using tensor_canonize_bond.
canonize_cyclic(i[, bra, method, inv_tol])	Bring this MatrixProductState into (possibly only approximate) canonical form at site(s) i.
column_reduce([output_inds, atol, cache, ...])	Find bonds on this tensor network which have tensors where all but one column (of the respective index) is non-zero, allowing the 'cutting' of that bond.
column_reduce_([output_inds, atol, cache, ...])
compress([form])	Compress this 1D Tensor Network, possibly into canonical form.
compress_all([inplace])	Inplace compress all bonds in this network.
compress_all_(*[, inplace])
compress_between(tags1, tags2[, max_bond, ...])	Compress the bond between the two single tensors in this network specified by tags1 and tags2 using tensor_compress_bond().
compress_simplify([output_inds, atol, ...])
compress_simplify_([output_inds, atol, ...])
compress_site(i[, canonize, cur_orthog, bra])	Compress the bonds adjacent to site i, by default first setting the orthogonality center to that site.
compute_centralities()
compute_contracted_inds(*tids[, output_inds])	Get the indices describing the tensor contraction of tensors corresponding to tids.
compute_hierarchical_linkage([tids, method, ...])
compute_hierarchical_ordering([tids, ...])
compute_hierarchical_ssa_path([tids, ...])
compute_shortest_distances([tids, exclude_inds])	Compute the minimum graph distances between all or some nodes tids.
conj([mangle_inner, mangle_outer])	Create a conjugated copy of this MatrixProductState instance.
conj_([mangle_inner, inplace])
contract([tags, inplace])	Contract some, or all, of the tensors in this network.
contract_([tags, inplace])
contract_around(tags[, which, min_distance, ...])	Perform a compressed contraction inwards towards the tensors identified by tags.
contract_around_(tags[, which, ...])
contract_around_center(**opts)
contract_around_corner(**opts)
contract_between(tags1, tags2, **contract_opts)	Contract the two tensors specified by tags1 and tags2 respectively.
contract_compressed(optimize[, output_inds, ...])
contract_compressed_(optimize[, ...])
contract_cumulative(tags_seq[, inplace])	Cumulative contraction of tensor network.
contract_ind(ind[, output_inds])	Contract tensors connected by ind.
contract_structured(tag_slice[, ...])	Perform a structured contraction, translating tag_slice from a slice or ... to a cumulative sequence of tags.
contract_tags(tags[, which, inplace])	Contract the tensors that match any or all of tags.
contraction_cost([optimize])	Compute the 'contraction cost' of this tensor network.
contraction_info([optimize])	Compute the opt_einsum.PathInfo object decsribing the contraction of this entire tensor network using path optimizer optimize.
contraction_path([optimize])	Compute the contraction path, a sequence of (int, int), for the contraction of this entire tensor network using path optimizer optimize.
contraction_tree([optimize, output_inds])	Return the cotengra.ContractionTree corresponding to contracting this entire tensor network with path finder optimize.
contraction_width([optimize])	Compute the 'contraction width' of this tensor network.
convert_to_zero()	Inplace conversion of this network to an all zero tensor network.
copy([virtual, deep])	Copy this TensorNetwork.
correlation(A, i, j[, B])	Correlation of operator A between i and j.
count_canonized()
cut_between(left_tags, right_tags, left_ind, ...)	Cut the bond between the tensors specified by left_tags and right_tags, giving them the new inds left_ind and right_ind respectively.
cut_iter(*inds)	Cut and iterate over one or more indices in this tensor network.
delete(tags[, which])	Delete any tensors which match all or any of tags.
diagonal_reduce([output_inds, atol, cache, ...])	Find tensors with diagonal structure and collapse those axes.
diagonal_reduce_([output_inds, atol, cache, ...])
distance(tnB[, xAA, xAB, xBB, method])	Compute the Frobenius norm distance between two tensor networks:
distribute_exponent()	Distribute the exponent p of this tensor network (i.e.
draw([color, output_inds, highlight_inds, ...])	Plot this tensor network as a networkx graph using matplotlib, with edge width corresponding to bond dimension.
draw_tree_span(tags[, which, min_distance, ...])	Visualize a generated tree span out of the tensors tagged by tags.
drop_tags(tags)	Remove a tag from any tensors in this network which have it.
enlarge_bond_dim(new_bond_dim, method)
entropy(i[, cur_orthog, method])	The entropy of bipartition between the left block of i sites and the rest.
equalize_norms([value, inplace])	Make the Frobenius norm of every tensor in this TN equal without changing the overall value if value=None, or set the norm of every tensor to value by scalar multiplication only.
equalize_norms_([value, inplace])
expand_bond_dimension(new_bond_dim[, ...])	Expand the bond dimensions of this 1D tensor network to at least new_bond_dim.
expec(*[, compress, eps])	Compute the expectation of several 1D TNs, using transfer matrix compression if any are periodic.
fit(tn_target[, method, tol, inplace, progbar])	Optimize the entries of this tensor network with respect to a least squares fit of tn_target which should have the same outer indices.
fit_(tn_target[, method, tol, inplace, progbar])
flip(inds[, inplace])	Flip the dimension corresponding to indices inds on all tensors that share it.
flip_(inds, *[, inplace])
from_TN(tn[, like, inplace])	Construct a specific tensor network subclass (i.e.
from_dense(psi, dims[, site_ind_id, site_tag_id])	Create a MatrixProductState directly from a dense vector
full_simplify([seq, output_inds, atol, ...])	Perform a series of tensor network 'simplifications' in a loop until there is no more reduction in the number of tensors or indices.
full_simplify_([seq, output_inds, atol, ...])
fuse_multibonds([inplace])	Fuse any multi-bonds (more than one index shared by the same pair of tensors) into a single bond.
fuse_multibonds_(*[, inplace])
gate(G, where[, contract, tags, ...])	Act with the gate g on sites where, maintaining the outer indices of the 1D tensor netowork.
gate_(G, where[, contract, tags, ...])
gate_inds(G, inds[, contract, tags, info, ...])	Apply the 'gate' G to indices inds, propagating them to the outside, as if applying G @ x.
gate_inds_(G, inds[, contract, tags, info, ...])
gate_split(G, where[, inplace])	Apply a two-site gate and then split resulting tensor to retrieve a MPS form.
gate_split_(G, where, *[, inplace])
gate_with_auto_swap(G, where[, inplace, ...])	Perform a two site gate on this MPS by, if necessary, swapping and compressing the sites until they are adjacent, using gate_split, then unswapping the sites back to their original position.
gauge_all_canonize([max_iterations, absorb, ...])	Iterative gauge all the bonds in this tensor network with a basic 'canonization' strategy.
gauge_all_canonize_([max_iterations, ...])
gauge_all_random([iterations, unitary, inplace])	Gauge all the bonds in this network randomly.
gauge_all_random_([iterations, unitary, inplace])
gauge_all_simple([max_iterations, tol, ...])	Iterative gauge all the bonds in this tensor network with a 'simple update' like strategy.
gauge_all_simple_([max_iterations, tol, ...])
gauge_local(tags[, which, max_distance, ...])	Iteratively gauge all bonds in the tagged sub tensor network according to one of several strategies.
gauge_local_(tags[, which, max_distance, ...])
gauge_simple_insert(gauges[, smudge])	Insert the simple update style bond gauges found in gauges if they are present in this tensor network.
gauge_simple_remove([outer, inner])	Remove the simple update style bond gauges inserted by gauge_simple_insert.
gauge_simple_temp(gauges[, smudge, ...])	Context manager that temporarily inserts simple update style bond gauges into this tensor network, before optionally ungauging them.
gen_loops([max_loop_length])	Generate sequences of tids that represent loops in the TN.
gen_site_coos()
geometry_hash([output_inds, strict_index_order])	A hash of this tensor network's shapes & geometry.
get_equation([output_inds])	Get the 'equation' describing this tensor network, in einsum style with a single unicode letter per index.
get_inputs_output_size_dict([output_inds])	Get a tuple of inputs, output and size_dict suitable for e.g.
get_symbol_map()	Get the mapping of the current indices to einsum style single unicode characters.
get_tree_span(tids[, min_distance, ...])	Generate a tree on the tensor network graph, fanning out from the tensors identified by tids, up to a maximum of max_distance away.
graph([color, output_inds, highlight_inds, ...])	Plot this tensor network as a networkx graph using matplotlib, with edge width corresponding to bond dimension.
graph_tree_span(tags[, which, min_distance, ...])	Visualize a generated tree span out of the tensors tagged by tags.
hyperinds_resolve([mode, sorter, inplace])	Convert this into a regular tensor network, where all indices appear at most twice, by inserting COPY tensor or tensor networks for each hyper index.
hyperinds_resolve_([mode, sorter, inplace])
ind_size(ind)	Find the size of ind.
ind_sizes()	Get dict of each index mapped to its size.
inner_inds()	Tuple of interior indices, assumed to be any indices that appear twice or more (this only holds generally for non-hyper tensor networks).
insert_gauge(U, where1, where2[, Uinv, tol])	Insert the gauge transformation U^-1 @ U into the bond between the tensors, T1 and T2, defined by where1 and where2.
insert_operator(A, where1, where2[, tags, ...])	Insert an operator on the bond between the specified tensors, e.g..
insert_operator_(A, where1, where2[, tags, ...])
iscomplex()
isel(selectors[, inplace])	Select specific values for some dimensions/indices of this tensor network, thereby removing them.
isel_(selectors, *[, inplace])
largest_element()	Return the 'largest element', in terms of absolute magnitude, of this tensor network.
least_central_tid()
left_canonize([stop, start, normalize, bra])	Left canonize all or a portion of this TN. If this is a MPS, this implies that::.
left_canonize_site(i[, bra])	Left canonize this TN's ith site, inplace.
left_compress([start, stop, bra])	Compress this 1D TN, from left to right, such that it becomes left-canonical (unless absorb != 'right').
left_compress_site(i[, bra])	Left compress this 1D TN's ith site, such that the site is then left unitary with its right bond (possibly) reduced in dimension.
load(filename)	Initialize the underlying tensors of MatrixProductState from a file.
logneg_subsys(sysa, sysb[, compress_opts, ...])	Compute the logarithmic negativity between subsytem blocks, e.g..
loop_simplify([output_inds, ...])	Try and simplify this tensor network by identifying loops and checking for low-rank decompositions across groupings of the loops outer indices.
loop_simplify_([output_inds, ...])
magnetization(i[, direction, cur_orthog])	Compute the magnetization at site i.
make_norm([mangle_append, layer_tags, ...])	Make the norm tensor network of this tensor network tn.H & tn.
make_tids_consecutive([tid0])	Reset the tids - node identifies - to be consecutive integers.
mangle_inner_([append, which])	Generate new index names for internal bonds, meaning that when this tensor network is combined with another, there should be no collisions.
max_bond()	Return the size of the largest bond in this network.
maybe_convert_coo(x)	Check if x is an integer and convert to the corresponding site tag if so.
measure(site[, remove, outcome, renorm, ...])	Measure this MPS at site, including projecting the state.
measure_(site[, remove, outcome, renorm, ...])
most_central_tid()
multiply(x[, inplace, spread_over])	Scalar multiplication of this tensor network with x.
multiply_(x, *[, inplace, spread_over])
multiply_each(x[, inplace])	Scalar multiplication of each tensor in this tensor network with x.
multiply_each_(x, *[, inplace])
new_bond(tags1, tags2, **opts)	Inplace addition of a dummmy (size 1) bond between the single tensors specified by by tags1 and tags2.
norm(**contract_opts)	Frobenius norm of this tensor network.
normalize([bra, eps, insert])	Normalize this MPS, optional with co-vector bra.
outer_dims_inds()	Get the 'outer' pairs of dimension and indices, i.e. as if this tensor network was fully contracted.
outer_inds()	Tuple of exterior indices, assumed to be any lone indices (this only holds generally for non-hyper tensor networks).
pair_simplify([cutoff, output_inds, ...])
pair_simplify_([cutoff, output_inds, ...])
partial_trace(keep[, upper_ind_id, ...])	Partially trace this matrix product state, producing a matrix product operator.
partial_trace_compress(sysa, sysb[, eps, ...])	Perform a compressed partial trace using singular value lateral then vertical decompositions of transfer matrix products.
partition(tags[, which, inplace])	Split this TN into two, based on which tensors have any or all of tags.
partition_tensors(tags[, inplace, which])	Split this TN into a list of tensors containing any or all of tags and a TensorNetwork of the the rest.
permute_arrays([shape])	Permute the indices of each tensor in this MPS to match shape.
ptr(keep[, upper_ind_id, rescale_sites])	Alias of partial_trace().
random(n, bond_dim, phys_dim, **kwargs)	Create a randomly initialized MatrixProductState.
randomize([dtype, seed, inplace])	Randomize every tensor in this TN - see quimb.tensor.tensor_core.Tensor.randomize().
randomize_([dtype, seed, inplace])
rank_simplify([output_inds, equalize_norms, ...])	Simplify this tensor network by performing contractions that don't increase the rank of any tensors.
rank_simplify_([output_inds, ...])
reduce_inds_onto_bond(inda, indb[, tags, ...])	Use QR factorization to 'pull' the indices inda and indb off of their respective tensors and onto the bond between them.
reindex(index_map[, inplace])	Rename indices for all tensors in this network, optionally in-place.
reindex_(index_map, *[, inplace])
reindex_all(new_id[, inplace])	Reindex all physical sites and change the site_ind_id.
reindex_all_(new_id, *[, inplace])
reindex_sites(new_id[, where, inplace])	Update the physical site index labels to a new string specifier.
reindex_sites_(new_id[, where, inplace])
replace_section_with_svd(start, stop, eps, ...)	Take a 1D tensor network, and replace a section with a SVD.
replace_with_identity(where[, which, inplace])	Replace all tensors marked by where with an identity. E.g. if X denote where tensors::.
replace_with_svd(where, left_inds, eps, *[, ...])	Replace all tensors marked by where with an iteratively constructed SVD. E.g. if X denote where tensors::.
replace_with_svd_(where, left_inds, eps, *)
retag(tag_map[, inplace])	Rename tags for all tensors in this network, optionally in-place.
retag_(tag_map, *[, inplace])
retag_sites(new_id[, where, inplace])	Modify the site tags for all or some tensors in this 1D TN (without changing the site_tag_id).
right_canonize([stop, start, normalize, bra])	Right canonize all or a portion of this TN. If this is a MPS, this implies that::.
right_canonize_site(i[, bra])	Right canonize this TN's ith site, inplace.
right_compress([start, stop, bra])	Compress this 1D TN, from right to left, such that it becomes right-canonical (unless absorb != 'left').
right_compress_site(i[, bra])	Right compress this 1D TN's ith site, such that the site is then right unitary with its left bond (possibly) reduced in dimension.
save(filename)	Save the underlying tensors of this MatrixProductState in the order of indices 'lpr' into file.
schmidt_gap(i[, cur_orthog, method])	The schmidt gap of bipartition between the left block of i sites and the rest.
schmidt_values(i[, cur_orthog, method])	Find the schmidt values associated with the bipartition of this MPS between sites on either site of i. In other words, i is the number of sites in the left hand partition::.
select(tags[, which, virtual])	Get a TensorNetwork comprising tensors that match all or any of tags, inherit the network properties/structure from self.
select_all(tags, *[, which, virtual])
select_any(tags, *[, which, virtual])
select_local(tags[, which, max_distance, ...])	Select a local region of tensors, based on graph distance max_distance to any tagged tensors.
select_neighbors(tags[, which])	Select any neighbouring tensors to those specified by tags.self
select_tensors(tags[, which])	Return the sequence of tensors that match tags.
shift_orthogonality_center(current, new[, bra])	Move the orthogonality center of this MPS.
show([max_width])
singular_values(i[, cur_orthog, method])	Find the singular values associated with the ith bond.
site_ind(i)	Get the physical index name of site i.
site_tag(i)	The name of the tag specifiying the tensor at site i.
slice2sites(tag_slice)	Take a slice object, and work out its implied start, stop and step, taking into account cyclic boundary conditions.
split(left_inds[, method, get, absorb, ...])	Decompose this tensor into two tensors.
split_simplify([atol, equalize_norms, ...])	Find tensors which have low rank SVD decompositions across any combination of bonds and perform them.
split_simplify_([atol, equalize_norms, ...])
split_tensor(site, direction)	Split the tensor at given site into two tensors, and multiply the one on left or right direction into its neighbouring tensor.
squeeze([fuse, inplace])	Drop singlet bonds and dimensions from this tensor network.
squeeze_([fuse, inplace])
strip_exponent(tid_or_tensor[, value])	Scale the elements of tensor corresponding to tid so that the norm of the array is some value, which defaults to 1.
subgraphs([virtual])	Split this tensor network into disconneceted subgraphs.
swap_site_to(i, f[, cur_orthog, inplace])	Swap site i to site f, compressing the bond after each swap.
swap_sites_with_compress(i, j[, cur_orthog, ...])	Swap sites i and j by contracting, then splitting with the physical indices swapped.
tensors_sorted()	Return a tuple of tensors sorted by their respective tags, such that the tensors of two networks with the same tag structure can be iterated over pairwise.
tids_are_connected(tids)	Check whether nodes tids are connected.
to_dense(*inds_seq, **contract_opts)	Return the dense ket version of this 1D vector, i.e. a qarray with shape (-1, 1).
trace(left_inds, right_inds, **contract_opts)	Trace over left_inds joined with right_inds
unitize([method, allow_no_left_inds, inplace])
unitize_([method, allow_no_left_inds, inplace])
view_as(cls[, inplace])	View this tensor network as subclass cls.
view_as_(cls, *[, inplace])
view_like(like[, inplace])	View this tensor network as the same subclass cls as like inheriting its extra properties as well.
view_like_(like, *[, inplace])

Attributes

H	Conjugate all the tensors in this network (leaves all indices).
L	The number of sites.
arrays	Get the tuple of raw arrays containing all the tensor network data.
bond_dim	The bond dimensions.
dtype	The dtype of this TensorNetwork, this is the minimal common type of all the tensors data.
n_sites
nsites	The number of sites.
num_indices	The total number of indices in the tensor network.
num_tensors	The total number of tensors in the tensor network.
phys_dim	Physical dimensions of local state.
shape	Actual, i.e. exterior, shape of this TensorNetwork.
site_ind_id	The string specifier for the physical indices
site_inds	An ordered tuple of the actual physical indices.
site_tag_id	The string specifier for tagging each site of this 1D TN.
site_tags	An ordered tuple of the actual site tags.
sites
tags
tensors	Get the tuple of tensors in this tensor network.

__init__(*args, **kwargs)

Matrix product state (MPS) for a finite size system.

Parameters

• *args – Positional arguments for quimb.tensor.MatrixProductState.

• **kwargs – Keyword arguments for quimb.tensor.MatrixProductState.

Note

This class inherits directly from quimb.tensor.MatrixProductState, with some added features. But, note that the underlying tensors are in the shape ‘lpr’, which differs from the parent class quimb.tensor.MatrixProductState.

property n_sites: int

property phys_dim: int

Physical dimensions of local state.

property bond_dim: int

The bond dimensions.

Notes

The actual bond dimensions can be smaller than this one at the boundaries.

permute_arrays(shape='lrp')

Permute the indices of each tensor in this MPS to match shape. This doesn’t change how the overall object interacts with other tensor networks but may be useful for extracting the underlying arrays consistently. This is an inplace operation.

Parameters

shape (str) – A permutation of 'lrp' specifying the desired order of the left, right, and physical indices respectively.

conj(mangle_inner=False, mangle_outer=False)

Create a conjugated copy of this MatrixProductState instance.

Parameters

• mangle_inner (bool) – Whether to rename the inner indices, so that there will be no conflict with the original one when contracting the network.

• mangle_outer (bool) – Whether to rename the outer indices, so that there will be no conflict with the original one when contracting the network.

Return type

conj_mps

save(filename)

Save the underlying tensors of this MatrixProductState in the order of indices 'lpr' into file. Only accepts suffix '.hdf5' or '.npz' as file extension.

Parameters

filename (str) – Absolute path to file in local disk.

Returns:

classmethod load(filename)

Initialize the underlying tensors of MatrixProductState from a file. Tensors in the file should take the order of indices 'lpr'. Only accepts suffix '.hdf5' or '.npz' as file extension.

Parameters

filename (str) – Absolute path to file in local disk.

Return type

mps

classmethod random(n, bond_dim, phys_dim, **kwargs)

Create a randomly initialized MatrixProductState.

Parameters

• n (int) – The system size.

• bond_dim (int) – The bond dimensions.

• phys_dim (int) – Physical dimensions of local state.

Return type

tnpy.matrix_product_state.MatrixProductState

Returns:

split_tensor(site, direction)

Split the tensor at given site into two tensors, and multiply the one on left or right direction into its neighbouring tensor. This is an inplace operation.

Parameters

• site (int) –

• direction (tnpy.matrix_product_state.Direction) –

Returns:

enlarge_bond_dim(new_bond_dim, method)

Parameters

• new_bond_dim (int) –

• method (str) –