def schmidt_decomposition_tensornetwork(bipartitepurestate_tensor):
""" Calculate the Schmidt decomposition of the given discrete bipartite quantum system
This is called by :func:`schmidt_decomposition`. This runs tensornetwork.
:param bipartitepurestate_tensor: tensor describing the bi-partitite states, with each elements the coefficients for :math:`|ij\\rangle`
:return: list of tuples containing the Schmidt coefficient, eigenmode for first subsystem, and eigenmode for second subsystem
:type bipartitepurestate_tensor: numpy.ndarray
:rtype: list
"""
state_dims = bipartitepurestate_tensor.shape
mindim = np.min(state_dims)
node = tn.Node(bipartitepurestate_tensor)
vecs1, diags, vecs2_h, _ = tn.split_node_full_svd(node, [node[0]],
[node[1]])
decomposition = [(diags.tensor[k,
k], vecs1.tensor[:,
k], vecs2_h.tensor[k, :])
for k in range(mindim)]
decomposition = sorted(decomposition, key=lambda dec: dec[0], reverse=True)
return decomposition
def update_dis(hamiltonian, state, isometry, disentangler):
"""Updates the disentangler with the aim of reducing the energy.
Args:
hamiltonian: The hamiltonian (rank-6 tensor) defined at the bottom of the
MERA layer.
state: The 3-site reduced state (rank-6 tensor) defined at the top of the
MERA layer.
isometry: The isometry tensor (rank 3) of the binary MERA.
disentangler: The disentangler tensor (rank 4) of the binary MERA.
Returns:
The updated disentangler.
"""
env = env_dis(hamiltonian, state, isometry, disentangler)
nenv = tensornetwork.Node(
env, axis_names=["bl", "br", "tl", "tr"], backend="jax")
output_edges = [nenv["bl"], nenv["br"], nenv["tl"], nenv["tr"]]
nu, _, nv, _ = tensornetwork.split_node_full_svd(
nenv, [nenv["bl"], nenv["br"]], [nenv["tl"], nenv["tr"]],
left_edge_name="s1",
right_edge_name="s2")
nu["s1"].disconnect()
nv["s2"].disconnect()
tensornetwork.connect(nu["s1"], nv["s2"])
nres = tensornetwork.contract_between(nu, nv, output_edge_order=output_edges)
return np.conj(nres.get_tensor())
def convert_mps(state, dia=False):
n = len(state.tensor.shape)
S = [tn.Node(np.array([0])) for i in range(n)]
if (dia):
D = [tn.Node(np.array([0])) for i in range(n - 1)]
S[0], D[0], P, _ = tn.split_node_full_svd(state,
state[:1],
state[1:],
max_truncation_err=10e-5)
for i in range(1, n - 1):
S[i], D[i], P, _ = tn.split_node_full_svd(
P, P[:2], P[2:], max_truncation_err=10e-5)
S[-1] = P
del state, n, P, i, dia
return S, D
else:
S[0], D, P, _ = tn.split_node_full_svd(state,
state[:1],
state[1:],
max_truncation_err=10e-5)
P = D @ P
for i in range(1, n - 1):
S[i], D, P, _ = tn.split_node_full_svd(
P, P[:2], P[2:], max_truncation_err=10e-5)
P = D @ P
S[-1] = P
del state, n, P, i, dia, D
return S
def convert_mpo(ope, dia=False):
n = int(len(ope.tensor.shape) * 0.5)
O = [tn.Node(np.array([0.0])) for i in range(n)]
if (dia):
D = [tn.Node(np.array([0.0])) for i in range(n - 1)]
O[0], D[0], P, _ = tn.split_node_full_svd(ope,
ope[:2],
ope[2:],
max_truncation_err=10e-5)
for i in range(1, n - 1):
O[i], D[i], P, _ = tn.split_node_full_svd(
P, P[:3], P[3:], max_truncation_err=10e-5)
O[-1] = P
del ope, dia, n, P, i
return O, D
else:
O[0], D, P, _ = tn.split_node_full_svd(ope,
ope[:2],
ope[2:],
max_truncation_err=10e-5)
P = D @ P
for i in range(1, n - 1):
O[i], D, P, _ = tn.split_node_full_svd(
P, P[:3], P[3:], max_truncation_err=10e-5)
P = D @ P
O[-1] = P
del ope, dia, n, P, i, D
return O
def test_split_node_full_svd_relative_tolerance(backend):
absolute = tn.Node(np.diag([2.0, 1.0, 0.2, 0.1]), backend=backend)
relative = tn.Node(np.diag([2.0, 1.0, 0.2, 0.1]), backend=backend)
max_truncation_err = 0.2
_, _, _, trunc_sv_absolute, = tn.split_node_full_svd(
node=absolute,
left_edges=[absolute[0]],
right_edges=[absolute[1]],
max_truncation_err=max_truncation_err,
relative=False)
_, _, _, trunc_sv_relative, = tn.split_node_full_svd(
node=relative,
left_edges=[relative[0]],
right_edges=[relative[1]],
max_truncation_err=max_truncation_err,
relative=True)
np.testing.assert_almost_equal(trunc_sv_absolute, [0.1])
np.testing.assert_almost_equal(trunc_sv_relative, [0.2, 0.1])
def test_split_node_full_svd(backend):
unitary1 = np.array([[1.0, 1.0], [1.0, -1.0]]) / np.sqrt(2.0)
unitary2 = np.array([[0.0, 1.0], [1.0, 0.0]])
singular_values = np.array([9.1, 7.5], dtype=np.float32)
val = np.dot(unitary1, np.dot(np.diag(singular_values), (unitary2.T)))
a = tn.Node(val, backend=backend)
e1 = a[0]
e2 = a[1]
_, s, _, _, = tn.split_node_full_svd(a, [e1], [e2])
tn.check_correct(tn.reachable(s))
np.testing.assert_allclose(s.tensor, np.diag([9.1, 7.5]), rtol=1e-5)
def update_bond(psi,
b,
wf,
ortho,
normalize=True,
max_truncation_error=None,
max_bond_dim=None):
"""Update the MPS tensors at bond b using the two-site wave-function wf.
If the MPS orthogonality center is at site b or b+1,the canonical form
will be preserved with the new orthogonality center position depending on the value
of ortho.
Args:
psi: The MPS for which the.
b: The bond to update.
wf: The two-site wave-function, it is assumed that wf is a tensornetwork.Node of the form
s_b s_b+1
| |
bond b-1 ---- wf ----- bond b+1
where the edges order of wf is [bond b-1 , s_b, s_b+1, bond b+1]
ortho: 'left' or 'right', on which side of the bond should the orthogonality center
be located after the update.
normalize: Whether to keep the wave-function normalized after update.
max_truncation_error: The maximal allowed truncation error when discarding singular values.
max_bond_dim: An upper bound on the number of kept singular values values.
Returns:
trunc_svals: A list of discarded singular values.
"""
U, S, V, trunc_svals = tn.split_node_full_svd(
wf, [wf[0], wf[1]], [wf[2], wf[3]],
max_truncation_err=max_truncation_error,
max_singular_values=max_bond_dim)
S.set_tensor(S.tensor / tn.norm(S))
if ortho == 'left':
U = U @ S
if psi.center_position == b + 1:
psi.center_position -= 1
elif ortho == 'right':
V = S @ V
if psi.center_position == b:
psi.center_position += 1
else:
raise ValueError("ortho must be 'left' or 'right'")
tn.disconnect(U[-1])
psi.nodes[b] = U
psi.nodes[b + 1] = V
return trunc_svals
def schmidt_decomposition_tensornetwork(bipartitepurestate_tensor):
state_dims = bipartitepurestate_tensor.shape
mindim = np.min(state_dims)
node = tn.Node(bipartitepurestate_tensor)
vecs1, diags, vecs2_h, _ = tn.split_node_full_svd(node, [node[0]],
[node[1]])
decomposition = [(diags.tensor[k,
k], vecs1.tensor[:,
k], vecs2_h.tensor[k, :])
for k in range(mindim)]
decomposition = sorted(decomposition, key=lambda dec: dec[0], reverse=True)
return decomposition
def test_split_node_full_svd_names(backend):
a = tn.Node(np.random.rand(10, 10), backend=backend)
e1 = a[0]
e2 = a[1]
left, s, right, _, = tn.split_node_full_svd(a, [e1], [e2],
left_name='left',
middle_name='center',
right_name='right',
left_edge_name='left_edge',
right_edge_name='right_edge')
assert left.name == 'left'
assert s.name == 'center'
assert right.name == 'right'
assert left.edges[-1].name == 'left_edge'
assert s[0].name == 'left_edge'
assert s[1].name == 'right_edge'
assert right.edges[0].name == 'right_edge'
def test_split_node_full_svd_names(num_charges):
np.random.seed(10)
a = tn.Node(get_random((10, 10), num_charges=num_charges),
backend='symmetric')
e1 = a[0]
e2 = a[1]
left, s, right, _, = tn.split_node_full_svd(a, [e1], [e2],
left_name='left',
middle_name='center',
right_name='right',
left_edge_name='left_edge',
right_edge_name='right_edge')
assert left.name == 'left'
assert s.name == 'center'
assert right.name == 'right'
assert left.edges[-1].name == 'left_edge'
assert s[0].name == 'left_edge'
assert s[1].name == 'right_edge'
assert right.edges[0].name == 'right_edge'
def getRenyiEntropy(psi: List[tn.Node], n: int, ASize: int, maxBondDim=1024):
psiCopy = copyState(psi)
for k in [len(psiCopy) - 1 - i for i in range(len(psiCopy) - ASize - 1)]:
psiCopy = shiftWorkingSite(psiCopy, k, '<<')
M = multiContraction(psiCopy[ASize - 1], psiCopy[ASize], [2], [0])
leftEdges = M.edges[:2]
rightEdges = M.edges[2:]
maxBondDim = getAppropriateMaxBondDim(maxBondDim, leftEdges, rightEdges)
[U, S, V,
truncErr] = tn.split_node_full_svd(M,
leftEdges,
rightEdges,
max_singular_values=maxBondDim)
eigenvaluesRoots = np.diag(S.tensor)
result = sum([l**(2 * n) for l in eigenvaluesRoots])
removeState(psiCopy)
return result
def svdTruncation(node: tn.Node, leftEdges: List[tn.Edge], rightEdges: List[tn.Edge], \
dir: str, maxBondDim=1024, leftName='U', rightName='V', edgeName=None):
maxBondDim = getAppropriateMaxBondDim(maxBondDim, leftEdges, rightEdges)
if dir == '>>':
leftEdgeName = edgeName
rightEdgeName = None
else:
leftEdgeName = None
rightEdgeName = edgeName
[U, S, V, truncErr] = tn.split_node_full_svd(node, leftEdges, rightEdges, max_singular_values=maxBondDim, \
left_name=leftName, right_name=rightName, \
left_edge_name=leftEdgeName, right_edge_name=rightEdgeName)
if dir == '>>':
l = copyState([U])[0]
r = copyState([tn.contract_between(S, V, name=V.name)])[0]
else:
l = copyState([tn.contract_between(U, S, name=U.name)])[0]
r = copyState([V])[0]
tn.remove_node(U)
tn.remove_node(S)
tn.remove_node(V)
return [l, r, truncErr]
def test_split_node_full_svd_orig_shape(backend):
n1 = tn.Node(np.random.rand(3, 4, 5), backend=backend)
tn.split_node_full_svd(n1, [n1[0], n1[2]], [n1[1]])
np.testing.assert_allclose(n1.shape, (3, 4, 5))
def test_split_node_full_svd_of_node_without_backend_raises_error():
node = np.random.rand(3, 3, 3)
with pytest.raises(AttributeError):
tn.split_node_full_svd(node, left_edges=[], right_edges=[])
def svdTruncation(node: tn.Node,
leftEdges: List[int],
rightEdges: List[int],
dir: str,
maxBondDim=128,
leftName='U',
rightName='V',
edgeName='default',
normalize=False,
maxTrunc=8):
maxBondDim = getAppropriateMaxBondDim(maxBondDim,
[node.edges[e] for e in leftEdges],
[node.edges[e] for e in rightEdges])
if dir == '>>':
leftEdgeName = edgeName
rightEdgeName = None
else:
leftEdgeName = None
rightEdgeName = edgeName
[U, S, V,
truncErr] = tn.split_node_full_svd(node,
[node.edges[e] for e in leftEdges],
[node.edges[e] for e in rightEdges],
max_singular_values=maxBondDim,
left_name=leftName,
right_name=rightName,
left_edge_name=leftEdgeName,
right_edge_name=rightEdgeName)
s = S
S = tn.Node(np.diag(S.tensor))
tn.remove_node(s)
norm = np.sqrt(sum(S.tensor**2))
if maxTrunc > 0:
meaningful = sum(np.round(S.tensor / norm, maxTrunc) > 0)
S.tensor = S.tensor[:meaningful]
U.tensor = np.transpose(np.transpose(U.tensor)[:meaningful])
V.tensor = V.tensor[:meaningful]
if normalize:
S = multNode(S, 1 / norm)
for e in S.edges:
e.name = edgeName
if dir == '>>':
l = copyState([U])[0]
r = multiContraction(S,
V,
'1',
'0',
cleanOr1=True,
cleanOr2=True,
isDiag1=True)
elif dir == '<<':
l = multiContraction(U,
S, [len(U.edges) - 1],
'0',
cleanOr1=True,
cleanOr2=True,
isDiag2=True)
r = copyState([V])[0]
elif dir == '>*<':
v = V
V = copyState([V])[0]
tn.remove_node(v)
u = U
U = copyState([U])[0]
tn.remove_node(u)
return [U, S, V, truncErr]
tn.remove_node(U)
tn.remove_node(S)
tn.remove_node(V)
return [l, r, truncErr]
def zip_up(
self,
array: Any,
axes: Optional[List[Tuple]] = None,
left_index: Optional[int] = None,
right_index: Optional[int] = None,
direction: Optional[Text] = "right",
max_singular_values: Optional[int] = None,
max_truncation_err: Optional[float] = None,
relative: Optional[bool] = False,
copy: Optional[bool] = True) -> List[Tuple]:
"""
...................................................................
| |
| | | | | B~~B | | |
~~A~~A~~A~~ , B~~B ==> | | | = ~~C~~C~~C~~
| | ~~A~~A~~A~~
self , array ==> new self
...................................................................
| |
| | | | | B~~B~~ | | |
~~A~~A~~A , B~~B~~ ==> | | | = ~~C~~C~~C~~
| | ~~A~~A~~A
self , array ==> new self
...................................................................
"""
# -- input parsing --
if axes is None:
axes = [(0,0)]
assert self.rank + array.rank - 2*len(axes) > 0, \
"This contraction would lead to nodes with no legs. " \
+ "To fully contract node use NodeArray.contract()."
_left_index, _right_index = _parse_left_right_index(self,
array,
left_index,
right_index)
b = array.copy() if copy else array
# -- handle left and right edges --
if b.left:
assert _left_index == 0
assert not self.left
self.left_edge = b.left_edge
if b.right:
assert _right_index == len(self) - 1
assert not self.right
self.right_edge = b.right_edge
# -- set variables for directions --
# Variables reappear in comments below.
if direction == "right":
from_index = _left_index
to_index = _right_index
sign = +1
reverse = False
ia_start_border = 0
outer_start = self.left
outer_start_edge = self.left_edge
outer_bond = -1
inner_bond = 0
elif direction == "left":
reverse = False
from_index = _right_index
to_index = _left_index
sign = -1
reverse = True
ia_start_border = len(self)-1
outer_start = self.right
outer_start_edge = self.right_edge
outer_bond = 0
inner_bond = -1
else:
raise ValueError()
carry_node = None
singular_values = []
# sign ( 1 / -1 )
ias = range(from_index, to_index + sign, sign)
# reverse ( False / True )
ibs = reversed(range(len(b))) if reverse else range(len(b))
for ia, ib in zip(ias, ibs):
ax_a_list = []
ax_b_list = []
for ax_a, ax_b in axes:
self.array_edges[ia][ax_a] ^ b.array_edges[ib][ax_b]
ax_a_list.append(ax_a)
ax_b_list.append(ax_b)
for ax_a in sorted(ax_a_list, reverse=True):
del self.array_edges[ia][ax_a]
for ax_b in sorted(ax_b_list, reverse=True):
del b.array_edges[ib][ax_b]
self.array_edges[ia].extend(b.array_edges[ib])
contraction_nodes = [self.nodes[ia], b.nodes[ib]]
if carry_node is not None:
contraction_nodes.append(carry_node)
contracted_node = tn.contractors.greedy(contraction_nodes,
ignore_edge_order=True)
# to_index (_right_index / _left_index)
if ia == to_index:
self.nodes[ia] = contracted_node
else:
u_edges = []
# ia_start_border (0 / len(self)-1)
if ia == ia_start_border:
# outer_start (self.left / self.right)
if outer_start:
# outer_start_edge (self.left_edge / self.right_edge)
u_edges.append(outer_start_edge)
else:
# outer_bond (-1 / 0)
u_edges.append(self.bond_edges[ia + outer_bond])
u_edges.extend(self.array_edges[ia])
# inner_bond (0 / -1)
v_edges = [self.bond_edges[ia + inner_bond],
b.bond_edges[ib + inner_bond]]
u, s, vh, trun_vals = tn.split_node_full_svd(
node=contracted_node,
left_edges=u_edges,
right_edges=v_edges,
max_singular_values=max_singular_values,
max_truncation_err=max_truncation_err,
relative=relative)
singular_values.append((s.tensor.diagonal(),trun_vals))
self.nodes[ia] = u
# inner_bond (0 / -1)
self.bond_edges[ia + inner_bond] = s[0]
carry_node = s @ vh
return singular_values
def svd_sweep(
self,
from_index: Optional[int] = 0,
to_index: Optional[int] = -1,
max_singular_values: Optional[int] = None,
max_truncation_err: Optional[float] = None,
relative: Optional[bool] = False) -> None:
"""
...................................................................
| | | | | | | | | | | |
--A1~~A2~~A3~~A4~~A5~~A6-- ==> --A1~~A2~~a3~~a4~~a5~~A6--
self ==> new self
...................................................................
"""
_from_index = len(self) + from_index if from_index<0 else from_index
_to_index = len(self) + to_index if to_index<0 else to_index
if _from_index < 0 or _from_index >= len(self):
raise IndexError("Index out of range.")
if _to_index < 0 or _to_index >= len(self):
raise IndexError("Index out of range.")
singular_values = []
if _from_index < _to_index:
for i in range(_from_index, _to_index):
u_edges = []
if i == 0:
if self.left:
u_edges.append(self.left_edge)
else:
u_edges.append(self.bond_edges[i-1])
u_edges.extend(self.array_edges[i])
v_edges = [self.bond_edges[i]]
u, s, vh, trun_vals = tn.split_node_full_svd(
node=self.nodes[i],
left_edges=u_edges,
right_edges=v_edges,
max_singular_values=max_singular_values,
max_truncation_err=max_truncation_err,
relative=relative)
singular_values.append((s.tensor.diagonal(),trun_vals))
self.nodes[i] = u
self.bond_edges[i] = s[0]
svh = s @ vh
self.nodes[i+1] = svh @ self.nodes[i+1]
elif _to_index < _from_index:
for i in range(_from_index, _to_index, -1):
u_edges = []
u_edges.extend(self.array_edges[i])
if i == len(self)-1:
if self.right:
u_edges.append(self.right_edge)
else:
u_edges.append(self.bond_edges[i])
v_edges = [self.bond_edges[i-1]]
u, s, vh, trun_vals = tn.split_node_full_svd(
node=self.nodes[i],
left_edges=u_edges,
right_edges=v_edges,
max_singular_values=max_singular_values,
max_truncation_err=max_truncation_err,
relative=relative)
singular_values.append((s.tensor.diagonal(),trun_vals))
self.nodes[i] = u
self.bond_edges[i-1] = s[0]
svh = s @ vh
self.nodes[i-1] = svh @ self.nodes[i-1]
return singular_values