def initialize_mod_binary_MERA(phys_dim, chi, dtype=tf.float64):
"""
Parameters:
-------------------
phys_dim: int
Hilbert space dimension of the bottom layer
chi: int
maximum bond dimension
dtype: tensorflow dtype
dtype of the MERA tensors
Returns:
-------------------
(wC, vC, uC, rhoAB, rhoBA)
wC, vC, uC: list of tf.Tensor
rhoAB, rhoBA: tf.Tensor
"""
wC = []
vC = []
uC = []
n = 0
while True:
wC.append(
tf.reshape(
tf.eye(
min(phys_dim**(2**(n + 1)), chi**2),
min(phys_dim**(2**(n + 1)), chi),
dtype=dtype),
(min(phys_dim**(2**n), chi), min(phys_dim**(2**n), chi),
min(phys_dim**(2**(n + 1)), chi))))
vC.append(
tf.reshape(
tf.eye(
min(phys_dim**(2**(n + 1)), chi**2),
min(phys_dim**(2**(n + 1)), chi),
dtype=dtype),
(min(phys_dim**(2**n), chi), min(phys_dim**(2**n), chi),
min(phys_dim**(2**(n + 1)), chi))))
uC.append(
tf.reshape(
tf.eye(min(phys_dim**(2**(n + 1)), chi**2), dtype=dtype),
(min(phys_dim**(2**n), chi), min(phys_dim**(2**n), chi),
min(phys_dim**(2**n), chi), min(phys_dim**(2**n), chi))))
n += 1
if misc_mera.all_same_chi(wC[-1]):
break
chi_top = wC[-1].shape[2]
rhoAB = tf.reshape(
tf.eye(chi_top * chi_top, dtype=dtype),
(chi_top, chi_top, chi_top, chi_top))
rhoBA = tf.reshape(
tf.eye(chi_top * chi_top, dtype=dtype),
(chi_top, chi_top, chi_top, chi_top))
return wC, vC, uC, rhoAB, rhoBA
def increase_bond_dimension_by_adding_layers(chi_new, wC, vC, uC):
"""
deprecated
increase the bond dimension of the MERA to `chi_new`
by padding tensors in the last layer with zeros. If the desired `chi_new` cannot
be obtained from padding, adds layers of Tensors
the last layer is guaranteed to have uniform bond dimension
Parameters:
--------------------------------
chi_new: int
new bond dimenion
wC, vC, uC: list of tf.Tensor
MERA isometries and disentanglers
Returns:
--------------------------------
(wC, vC, uC): list of tf.Tensors
"""
if misc_mera.all_same_chi(wC[-1], vC[-1],
uC[-1]) and (wC[-1].shape[2] >= chi_new):
#nothing to do here
return wC, vC, uC
elif misc_mera.all_same_chi(wC[-1], vC[-1],
uC[-1]) and (wC[-1].shape[2] < chi_new):
chi = min(chi_new, wC[-1].shape[0] * wC[-1].shape[1])
wC[-1] = misc_mera.pad_tensor(wC[-1],
[wC[-1].shape[0], wC[-1].shape[1], chi])
vC[-1] = misc_mera.pad_tensor(vC[-1],
[vC[-1].shape[0], vC[-1].shape[1], chi])
wC_temp = copy.deepcopy(wC[-1])
vC_temp = copy.deepcopy(vC[-1])
uC_temp = copy.deepcopy(uC[-1])
wC.append(misc_mera.pad_tensor(wC_temp, [chi, chi, chi]))
vC.append(misc_mera.pad_tensor(vC_temp, [chi, chi, chi]))
uC.append(misc_mera.pad_tensor(uC_temp, [chi, chi, chi, chi]))
return increase_bond_dimension_by_adding_layers(chi_new, wC, vC, uC)
elif not misc_mera.all_same_chi(wC[-1], vC[-1], uC[-1]):
raise ValueError('chis of last layer have to be all the same!')
def initialize_mod_binary_MERA(phys_dim, chi, dtype=tf.float64):
"""
initialize a modified binary MERA network
Args:
phys_dim (int): Hilbert space dimension of the bottom layer
chi (int): maximum bond dimension
dtype (tensorflow dtype): dtype of the MERA tensors
Returns:
wC (list of tf.Tensor): padded MERA isometries and disentanglers
vC (list of tf.Tensor): MERA isometries and disentanglers
uC (list of tf.Tensor): padded MERA isometries and disentanglers
rhoAB (tf.Tensor): reduced density on the AB lattice
rhoBA (tf.Tensor): reduced density on the BA lattice
"""
wC = []
vC = []
uC = []
n = 0
while True:
wC.append(
tf.reshape(
tf.eye(min(phys_dim**(2**(n + 1)), chi**2),
min(phys_dim**(2**(n + 1)), chi),
dtype=dtype),
(min(phys_dim**(2**n), chi), min(
phys_dim**(2**n), chi), min(phys_dim**(2**(n + 1)), chi))))
vC.append(
tf.reshape(
tf.eye(min(phys_dim**(2**(n + 1)), chi**2),
min(phys_dim**(2**(n + 1)), chi),
dtype=dtype),
(min(phys_dim**(2**n), chi), min(
phys_dim**(2**n), chi), min(phys_dim**(2**(n + 1)), chi))))
uC.append(
tf.reshape(
tf.eye(min(phys_dim**(2**(n + 1)), chi**2), dtype=dtype),
(min(phys_dim**(2**n), chi), min(phys_dim**(2**n), chi),
min(phys_dim**(2**n), chi), min(phys_dim**(2**n), chi))))
n += 1
if misc_mera.all_same_chi(wC[-1]):
break
chi_top = wC[-1].shape[2]
rhoAB = tf.reshape(tf.eye(chi_top * chi_top, dtype=dtype),
(chi_top, chi_top, chi_top, chi_top))
rhoBA = tf.reshape(tf.eye(chi_top * chi_top, dtype=dtype),
(chi_top, chi_top, chi_top, chi_top))
return wC, vC, uC, rhoAB, rhoBA
def get_scaling_dims(loadname, savename, use_gpu=False, k=11):
with open(loadname, 'rb') as f:
wC, uC = pickle.load(f)
fname = 'binary_mera_optimization'
rootdir = os.getcwd()
if not os.path.exists(fname):
os.mkdir(fname)
os.chdir(fname)
DEVICES = tf.contrib.eager.list_devices()
print("Available devices:")
for i, device in enumerate(DEVICES):
print("%d) %s" % (i, device))
CPU = '/device:CPU:0'
GPU = '/job:localhost/replica:0/task:0/device:GPU:0'
if use_gpu:
specified_device_type = GPU
name = 'GPU'
else:
specified_device_type = CPU
name = 'CPU'
filename = savename
scaling_dims = {}
# with open(filename, 'rb') as f:
# scaling_dims = pickle.load(f)
with tf.device(device):
for n in reversed(range(len(wC) - 2, len(wC))):
print(np.array(wC[n].shape))
if not misc_mera.all_same_chi(wC[n]):
continue
scaling_dims[n] = bml.get_scaling_dimensions(wC[n], uC[n], k=k)
print(scaling_dims[n])
with open(filename, 'wb') as f:
pickle.dump(scaling_dims, f)
def pad_mera_tensors(chi_new, wC, vC, uC, noise=0.0):
"""
increase the bond dimension of the MERA to `chi_new`
by padding tensors in all layers with zeros. If the desired `chi_new` cannot
be obtained from padding, adds layers of Tensors
the last layer is guaranteed to have uniform bond dimension
Args:
chi_new (int): new bond dimenion
wC (list of tf.Tensor): MERA isometries and disentanglers
vC (list of tf.Tensor): MERA isometries and disentanglers
uC (list of tf.Tensor): MERA isometries and disentanglers
noise (float): amplitude of uniform noise added to the padded tensors
Returns:
wC (list of tf.Tensor): padded MERA isometries and disentanglers
vC (list of tf.Tensor): MERA isometries and disentanglers
uC (list of tf.Tensor): padded MERA isometries and disentanglers
"""
all_chis = [t.shape[n] for t in wC for n in range(len(t.shape))]
if not np.all([c <= chi_new for c in all_chis]):
#nothing to increase
return wC, vC, uC
chi_0 = wC[0].shape[0]
wC[0] = misc_mera.pad_tensor(wC[0], [chi_0, chi_0, min(chi_new, chi_0**2)])
vC[0] = misc_mera.pad_tensor(vC[0], [chi_0, chi_0, min(chi_new, chi_0**2)])
for n in range(1, len(wC)):
wC[n] = misc_mera.pad_tensor(wC[n], [
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**(n + 1)))
])
vC[n] = misc_mera.pad_tensor(vC[n], [
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**(n + 1)))
])
uC[n] = misc_mera.pad_tensor(uC[n], [
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**n))
])
wC[n] += (tf.random_uniform(shape=wC[n].shape, dtype=wC[n].dtype) *
noise)
vC[n] += (tf.random_uniform(shape=vC[n].shape, dtype=vC[n].dtype) *
noise)
uC[n] += (tf.random_uniform(shape=uC[n].shape, dtype=uC[n].dtype) *
noise)
n = len(wC)
while not misc_mera.all_same_chi(wC[-1]):
wC.append(
misc_mera.pad_tensor(wC[-1], [
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**(n + 1)))
]))
vC.append(
misc_mera.pad_tensor(vC[-1], [
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**(n + 1)))
]))
uC.append(
misc_mera.pad_tensor(uC[-1], [
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**n)),
min(chi_new, chi_0**(2**n))
]))
wC[-1] += (tf.random_uniform(
shape=wC[-1].shape, minval=-1, maxval=1, dtype=wC[-1].dtype) *
noise)
vC[-1] += (tf.random_uniform(
shape=vC[-1].shape, minval=-1, maxval=1, dtype=vC[-1].dtype) *
noise)
uC[-1] += (tf.random_uniform(
shape=uC[-1].shape, minval=-1, maxval=1, dtype=uC[-1].dtype) *
noise)
n += 1
return wC, vC, uC