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fermion_2d.py
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fermion_2d.py
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"""Classes and algorithms related to Fermionic 2D tensor networks.
"""
import re
import functools
from operator import add
from itertools import product
from collections import defaultdict
from ..utils import check_opt, pairwise
from .tensor_core import (
bonds,
rand_uuid,
oset,
tags_to_oset
)
from .tensor_2d import (
Rotator2D,
TensorNetwork2D,
TensorNetwork2DVector,
TensorNetwork2DFlat,
TensorNetwork2DOperator,
PEPS,
PEPO,
is_lone_coo,
gen_long_range_path,
calc_plaquette_sizes,
calc_plaquette_map
)
from .fermion import (
FermionTensor,
FermionTensorNetwork,
tensor_contract
)
from .block_gen import rand_all_blocks, ones_single_block
INVERSE_CUTOFF = 1e-10
class FermionTensorNetwork2D(FermionTensorNetwork, TensorNetwork2D):
"""A subclass of ``quimb.tensor.tensor_2d.TensorNetwork2D`` that overrides methods
that depend on ordering of the tensors. Reorder method is added to aid row/column-wise
operations. Environments are now computed as an entire FermionTensorNetwork so that the
plaquettes are placed correctly
"""
_EXTRA_PROPS = (
'_site_tag_id',
'_row_tag_id',
'_col_tag_id',
'_Lx',
'_Ly',
)
def _compatible_2d(self, other):
"""Check whether ``self`` and ``other`` are compatible 2D tensor
networks such that they can remain a 2D tensor network when combined.
"""
return (
isinstance(other, FermionTensorNetwork2D) and
all(getattr(self, e) == getattr(other, e)
for e in FermionTensorNetwork2D._EXTRA_PROPS)
)
def __and__(self, other):
new = super().__and__(other)
if self._compatible_2d(other):
new.view_as_(FermionTensorNetwork2D, like=self)
return new
def __or__(self, other):
new = super().__or__(other)
if self._compatible_2d(other):
new.view_as_(FermionTensorNetwork2D, like=self)
return new
def flatten(self, fuse_multibonds=True, inplace=False):
raise NotImplementedError
def reorder(self, direction, layer_tags=None, inplace=False):
r"""Reorder all tensors either row/column-wise
If ``direction == 'row'`` then::
| | | | | | |
Row 0: ─●─>●─>●─>●─>●─>●─>●─ then Row 1
| | | | | | |
Row 1: ─●─>●─>●─>●─>●─>●─>●─ then Row 2
| | | | | | |
Row 2: ─●─>●─>●─>●─>●─>●─>●─
| | | | | | |
If ``direction == 'col'`` then::
v v v v v v v
─●──●──●──●──●──●──●─
v v v v v v v
─●──●──●──●──●──●──●─
v v v v v v v
─●──●──●──●──●──●──●─
v v v v v v v
Parameters
----------
direction : {"row", "col"}
The direction to reorder the entire network
layer_tags : optional
The relative order within a single coordinate
inplace : bool, optional
Whether to perform the operation inplace
"""
Lx, Ly = self._Lx, self._Ly
tid_map = dict()
current_position = 0
if direction == "row":
iterator = product(range(Lx), range(Ly))
elif direction == "col":
iterator = product(range(Ly), range(Lx))
else:
raise KeyError("direction not supported")
for i, j in iterator:
x, y = (i, j) if direction=="row" else (j, i)
site_tag = self.site_tag(x, y)
tids = self._get_tids_from_tags(site_tag)
if len(tids) == 1:
tid, = tids
if tid not in tid_map:
tid_map[tid] = current_position
current_position +=1
else:
if layer_tags is None:
_tags = [self.tensor_map[ix].tags for ix in tids]
_tmp_tags = _tags[0].copy()
for itag in _tags[1:]:
_tmp_tags &= itag
_layer_tags = sorted([list(i-_tmp_tags)[0] for i in _tags])
else:
_layer_tags = layer_tags
for tag in _layer_tags:
tid, = self._get_tids_from_tags((site_tag, tag))
if tid not in tid_map:
tid_map[tid] = current_position
current_position += 1
return self._reorder_from_tid(tid_map, inplace)
def _contract_boundary_full_bond(
self,
xrange,
yrange,
from_which,
max_bond,
cutoff=0.0,
method='eigh',
renorm=True,
optimize='auto-hq',
opposite_envs=None,
contract_boundary_opts=None,
):
raise NotImplementedError
def compute_environments(
self,
from_which,
xrange=None,
yrange=None,
max_bond=None,
*,
cutoff=1e-10,
canonize=True,
mode='mps',
layer_tags=None,
dense=False,
compress_opts=None,
envs=None,
**contract_boundary_opts
):
"""Compute the ``self.Lx`` 1D boundary tensor networks describing
the environments of rows and columns. The returned tensor network
also contains the original plaquettes
"""
direction = {"left": "col",
"right": "col",
"top": "row",
"bottom": "row"}[from_which]
tn = self.reorder(direction, layer_tags=layer_tags)
r2d = Rotator2D(tn, xrange, yrange, from_which)
sweep, row_tag = r2d.vertical_sweep, r2d.row_tag
contract_boundary_fn = r2d.get_contract_boundary_fn()
if envs is None:
envs = {}
if mode == 'full-bond':
# set shared storage for opposite env contractions
contract_boundary_opts.setdefault('opposite_envs', {})
envs[from_which, sweep[0]] = FermionTensorNetwork([])
first_row = row_tag(sweep[0])
envs['mid', sweep[0]] = tn.select(first_row).copy()
if len(sweep)==1:
return envs
if dense:
tn ^= first_row
envs[from_which, sweep[1]] = tn.select(first_row).copy()
for i in sweep[2:]:
iprevprev = i - 2 * sweep.step
iprev = i - sweep.step
envs['mid', iprev] = tn.select(row_tag(iprev)).copy()
if dense:
tn ^= (row_tag(iprevprev), row_tag(iprev))
else:
contract_boundary_fn(
iprevprev, iprev,
max_bond=max_bond,
cutoff=cutoff,
mode=mode,
canonize=canonize,
layer_tags=layer_tags,
compress_opts=compress_opts,
**contract_boundary_opts,
)
envs[from_which, i] = tn.select(first_row).copy()
return envs
compute_bottom_environments = functools.partialmethod(
compute_environments, from_which='bottom')
compute_top_environments = functools.partialmethod(
compute_environments, from_which='top')
compute_left_environments = functools.partialmethod(
compute_environments, from_which='left')
compute_right_environments = functools.partialmethod(
compute_environments, from_which='right')
def _compute_plaquette_environments_row_first(
self,
x_bsz,
y_bsz,
max_bond=None,
cutoff=1e-10,
canonize=True,
layer_tags=None,
second_dense=None,
row_envs=None,
**compute_environment_opts
):
if second_dense is None:
second_dense = x_bsz < 2
# first we contract from either side to produce column environments
if row_envs is None:
row_envs = self.compute_row_environments(
max_bond=max_bond, cutoff=cutoff, canonize=canonize,
layer_tags=layer_tags, **compute_environment_opts)
# next we form vertical strips and contract from both top and bottom
# for each column
col_envs = dict()
for i in range(self.Lx - x_bsz + 1):
#
# ●━━━●━━━●━━━●━━━●━━━●━━━●━━━●━━━●━━━●
# ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲
# o─o─o─o─o─o─o─o─o─o─o─o─o─o─o─o─o─o─o─o ┬
# | | | | | | | | | | | | | | | | | | | | ┊ x_bsz
# o─o─o─o─o─o─o─o─o─o─o─o─o─o─o─o─o─o─o─o ┴
# ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱ ╲ ╱
# ●━━━●━━━●━━━●━━━●━━━●━━━●━━━●━━━●━━━●
#
row_i = FermionTensorNetwork((
row_envs['bottom', i],
*[row_envs['mid', i+x] for x in range(x_bsz)],
row_envs['top', i + x_bsz - 1],
)).view_as_(FermionTensorNetwork2D, like=self)
#
# y_bsz
# <--> second_dense=True
# ●── ──●
# │ │ ╭── ──╮
# ●── . . ──● │╭─ . . ─╮│ ┬
# │ │ or ● ● ┊ x_bsz
# ●── . . ──● │╰─ . . ─╯│ ┴
# │ │ ╰── ──╯
# ●── ──●
# 'left' 'right' 'left' 'right'
#
col_envs[i] = row_i.compute_col_environments(
xrange=(max(i - 1, 0), min(i + x_bsz, self.Lx - 1)),
max_bond=max_bond, cutoff=cutoff,
canonize=canonize, layer_tags=layer_tags,
dense=second_dense, **compute_environment_opts)
# then range through all the possible plaquettes, selecting the correct
# boundary tensors from either the column or row environments
plaquette_envs = dict()
for i0, j0 in product(range(self.Lx - x_bsz + 1),
range(self.Ly - y_bsz + 1)):
# we want to select bordering tensors from:
#
# L──A──A──R <- A from the row environments
# │ │ │ │
# i0+1 L──●──●──R
# │ │ │ │ <- L, R from the column environments
# i0 L──●──●──R
# │ │ │ │
# L──B──B──R <- B from the row environments
#
# j0 j0+1
#
env_ij = FermionTensorNetwork((
col_envs[i0]['left', j0],
*[col_envs[i0]['mid', ix] for ix in range(j0, j0+y_bsz)],
col_envs[i0]['right', j0 + y_bsz - 1]
), check_collisions=False)
plaquette_envs[(i0, j0), (x_bsz, y_bsz)] = env_ij
return plaquette_envs
def _compute_plaquette_environments_col_first(
self,
x_bsz,
y_bsz,
max_bond=None,
cutoff=1e-10,
canonize=True,
layer_tags=None,
second_dense=None,
col_envs=None,
**compute_environment_opts
):
if second_dense is None:
second_dense = y_bsz < 2
# first we contract from either side to produce column environments
if col_envs is None:
col_envs = self.compute_col_environments(
max_bond=max_bond, cutoff=cutoff, canonize=canonize,
layer_tags=layer_tags, **compute_environment_opts)
# next we form vertical strips and contract from both top and bottom
# for each column
row_envs = dict()
for j in range(self.Ly - y_bsz + 1):
#
# y_bsz
# <-->
#
# ╭─╱o─╱o─╮
# ●──o|─o|──●
# ┃╭─|o─|o─╮┃
# ●──o|─o|──●
# ┃╭─|o─|o─╮┃
# ●──o|─o|──●
# ┃╭─|o─|o─╮┃
# ●──o╱─o╱──●
# ┃╭─|o─|o─╮┃
# ●──o╱─o╱──●
#
col_j = FermionTensorNetwork((
col_envs['left', j],
*[col_envs['mid', j+jn] for jn in range(y_bsz)],
col_envs['right', j + y_bsz - 1],
)).view_as_(FermionTensorNetwork2D, like=self)
#
# y_bsz
# <--> second_dense=True
# ●──●──●──● ╭──●──╮
# │ │ │ │ or │ ╱ ╲ │ 'top'
# . . . . ┬
# ┊ x_bsz
# . . . . ┴
# │ │ │ │ or │ ╲ ╱ │ 'bottom'
# ●──●──●──● ╰──●──╯
#
row_envs[j] = col_j.compute_row_environments(
yrange=(max(j - 1, 0), min(j + y_bsz, self.Ly - 1)),
max_bond=max_bond, cutoff=cutoff, canonize=canonize,
layer_tags=layer_tags, dense=second_dense,
**compute_environment_opts)
# then range through all the possible plaquettes, selecting the correct
# boundary tensors from either the column or row environments
plaquette_envs = dict()
for i0, j0 in product(range(self.Lx - x_bsz + 1),
range(self.Ly - y_bsz + 1)):
# we want to select bordering tensors from:
#
# A──A──A──A <- A from the row environments
# │ │ │ │
# i0+1 L──●──●──R
# │ │ │ │ <- L, R from the column environments
# i0 L──●──●──R
# │ │ │ │
# B──B──B──B <- B from the row environments
#
# j0 j0+1
#
env_ij = FermionTensorNetwork((
row_envs[j0]['bottom', i0],
*[row_envs[j0]['mid', ix] for ix in range(i0, i0+x_bsz)],
row_envs[j0]['top', i0 + x_bsz - 1]
), check_collisions=False)
plaquette_envs[(i0, j0), (x_bsz, y_bsz)] = env_ij
return plaquette_envs
def gate_string_split_(TG, where, string, original_ts, bonds_along,
reindex_map, site_ix, info, **compress_opts):
# by default this means singuvalues are kept in the string 'blob' tensor
compress_opts.setdefault('absorb', 'right')
loc_info = dict([t.get_fermion_info() for t in original_ts])
# the outer, neighboring indices of each tensor in the string
neighb_inds = []
# tensors we are going to contract in the blob, reindex some to attach gate
contract_ts = []
fermion_info = []
qpn_infos = []
for t, coo in zip(original_ts, string):
neighb_inds.append(tuple(ix for ix in t.inds if ix not in bonds_along))
contract_ts.append(t.reindex_(reindex_map) if coo in where else t)
fermion_info.append(t.get_fermion_info())
qpn_infos.append(t.data.dq)
blob = tensor_contract(*contract_ts, TG, inplace=True)
regauged = []
work_site = blob.get_fermion_info()[1]
fs = blob.fermion_owner[0]
# one by one extract the site tensors again from each end
inner_ts = [None] * len(string)
i = 0
j = len(string) - 1
while True:
lix = neighb_inds[i]
if i > 0:
lix += (bonds_along[i - 1],)
# the original bond we are restoring
bix = bonds_along[i]
# split the blob!
qpn_info = [blob.data.dq - qpn_infos[i], qpn_infos[i]]
lix = tuple(oset(blob.inds)-oset(lix))
blob, *maybe_svals, inner_ts[i] = blob.split(
left_inds=lix, get='tensors', bond_ind=bix, qpn_info=qpn_info, **compress_opts)
# if singular values are returned (``absorb=None``) check if we should
# return them via ``info``, e.g. for ``SimpleUpdate`
if maybe_svals and info is not None:
s = next(iter(maybe_svals)).data
#coo_pair = tuple(sorted((string[i], string[i + 1])))
coo_pair = (string[i], string[i+1])
info['singular_values', coo_pair] = s
# regauge the blob but record so as to unguage later
if i != j - 1:
blob.multiply_index_diagonal_(bix, s, location="back")
regauged.append((i + 1, bix, "back", s))
# move inwards along string, terminate if two ends meet
i += 1
if i == j:
inner_ts[i] = blob
break
# extract at end of string
lix = neighb_inds[j]
if j < len(string) - 1:
lix += (bonds_along[j],)
# the original bond we are restoring
bix = bonds_along[j - 1]
# split the blob!
qpn_info = [qpn_infos[j], blob.data.dq - qpn_infos[j]]
inner_ts[j], *maybe_svals, blob= blob.split(
left_inds=lix, get='tensors', bond_ind=bix, qpn_info=qpn_info, **compress_opts)
# if singular values are returned (``absorb=None``) check if we should
# return them via ``info``, e.g. for ``SimpleUpdate`
if maybe_svals and info is not None:
s = next(iter(maybe_svals)).data
coo_pair = (string[j-1], string[j])
info['singular_values', coo_pair] = s
# regauge the blob but record so as to ungauge later
if j != i + 1:
blob.multiply_index_diagonal_(bix, s, location="front")
regauged.append((j - 1, bix, "front", s))
# move inwards along string, terminate if two ends meet
j -= 1
if j == i:
inner_ts[j] = blob
break
# SVD funcs needs to be modify and make sure S has even parity
for i, bix, location, s in regauged:
snew = inv_with_smudge(s, INVERSE_CUTOFF, gauge_smudge=0)
t = inner_ts[i]
t.multiply_index_diagonal_(bix, snew, location=location)
revert_index_map = {v: k for k, v in reindex_map.items()}
for to, tn in zip(original_ts, inner_ts):
to.reindex_(revert_index_map)
tn.transpose_like_(to)
to.modify(data=tn.data)
for i, (tid, _) in enumerate(fermion_info):
if i==0:
fs.replace_tensor(work_site, original_ts[i], tid=tid, virtual=True)
else:
fs.insert_tensor(work_site+i, original_ts[i], tid=tid, virtual=True)
fs._reorder_from_dict(dict(fermion_info))
def gate_string_reduce_split_(TG, where, string, original_ts, bonds_along,
reindex_map, site_ix, info, **compress_opts):
compress_opts.setdefault('absorb', 'right')
# indices to reduce, first and final include physical indices for gate
inds_to_reduce = [(bonds_along[0], site_ix[0])]
for b1, b2 in pairwise(bonds_along):
inds_to_reduce.append((b1, b2))
inds_to_reduce.append((bonds_along[-1], site_ix[-1]))
# tensors that remain on the string sites and those pulled into string
outer_ts, inner_ts = [], []
fermion_info = []
fs = TG.fermion_owner[0]
tid_lst = []
for coo, rix, t in zip(string, inds_to_reduce, original_ts):
tq, tr = t.split(left_inds=None, right_inds=rix,
method='qr', get='tensors', absorb="right")
fermion_info.append(t.get_fermion_info())
outer_ts.append(tq)
inner_ts.append(tr.reindex_(reindex_map) if coo in where else tr)
for tq, tr, t in zip(outer_ts, inner_ts, original_ts):
isite = t.get_fermion_info()[1]
fs.replace_tensor(isite, tr, virtual=True)
fs.insert_tensor(isite+1, tq, virtual=True)
blob = tensor_contract(*inner_ts, TG, inplace=True)
work_site = blob.get_fermion_info()[1]
regauged = []
# extract the new reduced tensors sequentially from each end
i = 0
j = len(string) - 1
while True:
# extract at beginning of string
lix = bonds(blob, outer_ts[i])
if i == 0:
lix.add(site_ix[0])
else:
lix.add(bonds_along[i - 1])
# the original bond we are restoring
bix = bonds_along[i]
# split the blob!
lix = tuple(oset(blob.inds)-oset(lix))
blob, *maybe_svals, inner_ts[i] = blob.split(
left_inds=lix, get='tensors', bond_ind=bix, **compress_opts)
# if singular values are returned (``absorb=None``) check if we should
# return them via ``info``, e.g. for ``SimpleUpdate`
if maybe_svals and info is not None:
s = next(iter(maybe_svals)).data
coo_pair = (string[i], string[i + 1])
info['singular_values', coo_pair] = s
# regauge the blob but record so as to unguage later
if i != j - 1:
blob.multiply_index_diagonal_(bix, s, location="back")
regauged.append((i + 1, bix, "back", s))
# move inwards along string, terminate if two ends meet
i += 1
if i == j:
inner_ts[i] = blob
break
# extract at end of string
lix = bonds(blob, outer_ts[j])
if j == len(string) - 1:
lix.add(site_ix[-1])
else:
lix.add(bonds_along[j])
# the original bond we are restoring
bix = bonds_along[j - 1]
# split the blob!
inner_ts[j], *maybe_svals, blob = blob.split(
left_inds=lix, get='tensors', bond_ind=bix, **compress_opts)
# if singular values are returned (``absorb=None``) check if we should
# return them via ``info``, e.g. for ``SimpleUpdate`
if maybe_svals and info is not None:
s = next(iter(maybe_svals)).data
coo_pair = (string[j - 1], string[j])
info['singular_values', coo_pair] = s
# regauge the blob but record so as to unguage later
if j != i + 1:
blob.multiply_index_diagonal_(bix, s, location="front")
regauged.append((j - 1, bix, "front", s))
# move inwards along string, terminate if two ends meet
j -= 1
if j == i:
inner_ts[j] = blob
break
for i, (tid, _) in enumerate(fermion_info):
if i==0:
fs.replace_tensor(work_site, inner_ts[i], tid=tid, virtual=True)
else:
fs.insert_tensor(work_site+i, inner_ts[i], tid=tid, virtual=True)
new_ts = [
tensor_contract(ts, tr, inplace=True).transpose_like_(to)
for to, ts, tr in zip(original_ts, outer_ts, inner_ts)
]
for i, bix, location, s in regauged:
snew = inv_with_smudge(s, INVERSE_CUTOFF, gauge_smudge=0)
t = new_ts[i]
t.multiply_index_diagonal_(bix, snew, location=location)
for (tid, _), to, t in zip(fermion_info, original_ts, new_ts):
site = t.get_fermion_info()[1]
to.modify(data=t.data)
fs.replace_tensor(site, to, tid=tid, virtual=True)
fs._reorder_from_dict(dict(fermion_info))
class FermionTensorNetwork2DVector(FermionTensorNetwork2D,
FermionTensorNetwork,
TensorNetwork2DVector):
"""Mixin class for a 2D square lattice vector TN, i.e. one with a single
physical index per site.
"""
_EXTRA_PROPS = (
'_site_tag_id',
'_row_tag_id',
'_col_tag_id',
'_Lx',
'_Ly',
'_site_ind_id',
)
def to_dense(self, *inds_seq, **contract_opts):
raise NotImplementedError
def make_norm(
self,
mangle_append='*',
layer_tags=('KET', 'BRA'),
return_all=False,
):
ket = self.copy()
ket.add_tag(layer_tags[0])
bra = ket.retag({layer_tags[0]: layer_tags[1]})
bra = bra.H
if mangle_append:
bra.mangle_inner_(mangle_append)
norm = ket & bra
if return_all:
return norm, ket, bra
return norm
def gate(
self,
G,
where,
contract=False,
tags=None,
inplace=False,
info=None,
long_range_use_swaps=False,
long_range_path_sequence=None,
**compress_opts
):
check_opt("contract", contract, (False, True, 'split', 'reduce-split'))
psi = self if inplace else self.copy()
if is_lone_coo(where):
where = (where,)
else:
where = tuple(where)
ng = len(where)
tags = tags_to_oset(tags)
# allow a matrix to be reshaped into a tensor if it factorizes
# i.e. (4, 4) assumed to be two qubit gate -> (2, 2, 2, 2)
site_ix = [psi.site_ind(i, j) for i, j in where]
# new indices to join old physical sites to new gate
bnds = [rand_uuid() for _ in range(ng)]
reindex_map = dict(zip(site_ix, bnds))
TG = FermionTensor(G.copy(), inds=site_ix+bnds, tags=tags, left_inds=site_ix) # [bnds first, then site_ix]
if contract is False:
#
# │ │ <- site_ix
# GGGGG
# │╱ │╱ <- bnds
# ──●───●──
# ╱ ╱
#
psi.reindex_(reindex_map)
psi |= TG
return psi
elif (contract is True) or (ng == 1):
#
# │╱ │╱
# ──GGGGG──
# ╱ ╱
#
psi.reindex_(reindex_map)
input_tids = psi._get_tids_from_inds(bnds, which='any')
isite = [psi.tensor_map[itid].get_fermion_info()[1] for itid in input_tids]
psi.fermion_space.add_tensor(TG, virtual=True)
# get the sites that used to have the physical indices
site_tids = psi._get_tids_from_inds(bnds, which='any')
# pop the sites, contract, then re-add
pts = [psi._pop_tensor(tid) for tid in site_tids]
out = tensor_contract(*pts, TG, inplace=True)
psi |= out
psi.fermion_space.move(out.get_fermion_info()[0], min(isite))
return psi
# following are all based on splitting tensors to maintain structure
ij_a, ij_b = where
# parse the argument specifying how to find the path between
# non-nearest neighbours
if long_range_path_sequence is not None:
# make sure we can index
long_range_path_sequence = tuple(long_range_path_sequence)
# if the first element is a str specifying move sequence, e.g.
# ('v', 'h')
# ('av', 'bv', 'ah', 'bh') # using swaps
manual_lr_path = not isinstance(long_range_path_sequence[0], str)
# otherwise assume a path has been manually specified, e.g.
# ((1, 2), (2, 2), (2, 3), ... )
# (((1, 1), (1, 2)), ((4, 3), (3, 3)), ...) # using swaps
else:
manual_lr_path = False
psi.fermion_space.add_tensor(TG, virtual=True)
# check if we are not nearest neighbour and need to swap first
if long_range_use_swaps:
raise NotImplementedError
string = tuple(gen_long_range_path(
*where, sequence=long_range_path_sequence))
# the tensors along this string, which will be updated
original_ts = [psi[coo] for coo in string]
# the len(string) - 1 indices connecting the string
bonds_along = [next(iter(bonds(t1, t2)))
for t1, t2 in pairwise(original_ts)]
if contract == 'split':
#
# │╱ │╱ │╱ │╱
# ──GGGGG── ==> ──G┄┄┄G──
# ╱ ╱ ╱ ╱
#
gate_string_split_(
TG, where, string, original_ts, bonds_along,
reindex_map, site_ix, info, **compress_opts)
elif contract == 'reduce-split':
#
# │ │ │ │
# GGGGG GGG │ │
# │╱ │╱ ==> ╱│ │ ╱ ==> ╱│ │ ╱ │╱ │╱
# ──●───●── ──>─●─●─<── ──>─GGG─<── ==> ──G┄┄┄G──
# ╱ ╱ ╱ ╱ ╱ ╱ ╱ ╱
# <QR> <LQ> <SVD>
#
gate_string_reduce_split_(
TG, where, string, original_ts, bonds_along,
reindex_map, site_ix, info, **compress_opts)
return psi
gate_ = functools.partialmethod(gate, inplace=True)
def compute_local_expectation(
self,
terms,
max_bond=None,
*,
cutoff=1e-10,
canonize=True,
mode='mps',
layer_tags=('KET', 'BRA'),
normalized=False,
autogroup=True,
contract_optimize='auto-hq',
return_all=False,
plaquette_envs=None,
plaquette_map=None,
**plaquette_env_options,
):
norm, ket, bra = self.make_norm(return_all=True, layer_tags=layer_tags)
plaquette_env_options["max_bond"] = max_bond
plaquette_env_options["cutoff"] = cutoff
plaquette_env_options["canonize"] = canonize
plaquette_env_options["mode"] = mode
plaquette_env_options["layer_tags"] = layer_tags
# factorize both local and global phase on the operator tensors
new_terms = dict()
for where, op in terms.items():
if is_lone_coo(where):
_where = (where,)
else:
_where = tuple(where)
ng = len(_where)
site_ix = [bra.site_ind(i, j) for i, j in _where]
bnds = [rand_uuid() for _ in range(ng)]
TG = FermionTensor(op.copy(), inds=site_ix+bnds, left_inds=site_ix)
new_terms[where] = bra.fermion_space.move_past(TG).data
if plaquette_envs is None:
plaquette_envs = dict()
for x_bsz, y_bsz in calc_plaquette_sizes(terms.keys(), autogroup):
plaquette_envs.update(norm.compute_plaquette_environments(
x_bsz=x_bsz, y_bsz=y_bsz, **plaquette_env_options))
if plaquette_map is None:
# work out which plaquettes to use for which terms
plaquette_map = calc_plaquette_map(plaquette_envs)
# now group the terms into just the plaquettes we need
plaq2coo = defaultdict(list)
for where, G in new_terms.items():
p = plaquette_map[where]
plaq2coo[p].append((where, G))
expecs = dict()
for p in plaq2coo:
# site tags for the plaquette
tn = plaquette_envs[p]
if normalized:
norm_i0j0 = tn.contract(all, optimize=contract_optimize)
else:
norm_i0j0 = None
for where, G in plaq2coo[p]:
newtn = tn.copy()
if is_lone_coo(where):
_where = (where,)
else:
_where = tuple(where)
ng = len(_where)
site_ix = [bra.site_ind(i, j) for i, j in _where]
bnds = [rand_uuid() for _ in range(ng)]
reindex_map = dict(zip(site_ix, bnds))
TG = FermionTensor(G.copy(), inds=site_ix+bnds, left_inds=site_ix)
ntsr = len(newtn.tensor_map)
fs = newtn.fermion_space
tids = newtn._get_tids_from_inds(site_ix, which='any')
for tid_ in tids:
tsr = newtn.tensor_map[tid_]
if layer_tags[0] in tsr.tags:
tsr.reindex_(reindex_map)
newtn.add_tensor(TG, virtual=True)
expec_ij = newtn.contract(all, optimize=contract_optimize)
expecs[where] = expec_ij, norm_i0j0
if return_all:
return expecs
if normalized:
return functools.reduce(add, (e / n for e, n in expecs.values()))
return functools.reduce(add, (e for e, _ in expecs.values()))
class FermionTensorNetwork2DOperator(FermionTensorNetwork2D,
FermionTensorNetwork,
TensorNetwork2DOperator):
_EXTRA_PROPS = (
'_site_tag_id',
'_row_tag_id',
'_col_tag_id',
'_Lx',
'_Ly',
'_upper_ind_id',
'_lower_ind_id',
)
def to_dense(self, *inds_seq, **contract_opts):
raise NotImplementedError
class FermionTensorNetwork2DFlat(FermionTensorNetwork2D,
FermionTensorNetwork,
TensorNetwork2DFlat):
"""Mixin class for a 2D square lattice tensor network with a single tensor
per site, for example, both PEPS and PEPOs.
"""
_EXTRA_PROPS = (
'_site_tag_id',
'_row_tag_id',
'_col_tag_id',
'_Lx',
'_Ly',
)
def expand_bond_dimension(self, new_bond_dim, inplace=True, bra=None,
rand_strength=0.0):
raise NotImplementedError
class FPEPS(FermionTensorNetwork2DVector,
FermionTensorNetwork2DFlat,
FermionTensorNetwork2D,
FermionTensorNetwork,
PEPS):
_EXTRA_PROPS = (
'_site_tag_id',
'_row_tag_id',
'_col_tag_id',
'_Lx',
'_Ly',
'_site_ind_id',
)
def __init__(self, arrays, *, shape='urdlp', tags=None,
site_ind_id='k{},{}', site_tag_id='I{},{}',
row_tag_id='ROW{}', col_tag_id='COL{}', **tn_opts):
if isinstance(arrays, FPEPS):
super().__init__(arrays)
return
tags = tags_to_oset(tags)
self._site_ind_id = site_ind_id
self._site_tag_id = site_tag_id
self._row_tag_id = row_tag_id
self._col_tag_id = col_tag_id
arrays = tuple(tuple(x for x in xs) for xs in arrays)
self._Lx = len(arrays)
self._Ly = len(arrays[0])
tensors = []
# cache for both creating and retrieving indices
ix = defaultdict(rand_uuid)
for i, j in product(range(self.Lx), range(self.Ly)):
array = arrays[i][j]
# figure out if we need to transpose the arrays from some order
# other than up right down left physical
array_order = shape
if i == self.Lx - 1:
array_order = array_order.replace('u', '')
if j == self.Ly - 1:
array_order = array_order.replace('r', '')
if i == 0:
array_order = array_order.replace('d', '')
if j == 0:
array_order = array_order.replace('l', '')
# allow convention of missing bonds to be singlet dimensions
if len(array.shape) != len(array_order):