def test_steady_state(chi, dtype):
isometry = misc_mera.w_update_svd_numpy(
np.random.rand(chi, chi, chi).astype(dtype.as_numpy_dtype))
unitary = misc_mera.u_update_svd_numpy(
np.random.rand(chi, chi, chi, chi).astype(dtype.as_numpy_dtype))
rho = tf.reshape(
tf.eye(chi * chi * chi, dtype=dtype), (chi, chi, chi, chi, chi, chi))
rho_ss = bml.steady_state_density_matrix(
nsteps=60, rho=rho, isometry=isometry, unitary=unitary)
rho_test = bml.descending_super_operator(rho_ss, isometry, unitary)
np.testing.assert_array_less(rho_ss - rho_test, 1E-6)
def test_isometry_envs(chi, dtype):
isometry = misc_mera.w_update_svd_numpy(
np.random.rand(chi, chi, chi).astype(dtype.as_numpy_dtype))
unitary = misc_mera.u_update_svd_numpy(
np.random.rand(chi, chi, chi, chi).astype(dtype.as_numpy_dtype))
rho = tf.random_uniform(shape=[chi, chi, chi, chi, chi, chi], dtype=dtype)
ham = tf.random_uniform(shape=[chi, chi, chi, chi, chi, chi], dtype=dtype)
envs = {}
envs[0] = bml.get_env_isometry_1(ham, rho, isometry, unitary)
envs[1] = bml.get_env_isometry_3(ham, rho, isometry, unitary)
envs[2] = bml.get_env_isometry_5(ham, rho, isometry, unitary)
envs[3] = bml.get_env_isometry_2(ham, rho, isometry, unitary)
envs[4] = bml.get_env_isometry_4(ham, rho, isometry, unitary)
envs[5] = bml.get_env_isometry_6(ham, rho, isometry, unitary)
t_a = [tn.ncon([envs[n], isometry], [[1, 2, 3], [1, 2, 3]]) for n in range(3)]
t_b = [
tn.ncon([envs[n], isometry], [[1, 2, 3], [1, 2, 3]]) for n in range(3, 6)
]
np.testing.assert_allclose(t_a, t_a[0])
np.testing.assert_allclose(t_b, t_b[0])
def optimize_mod_binary_mera(hamAB_0,
hamBA_0,
rhoAB_0,
rhoBA_0,
wC,
vC,
uC,
numiter=1000,
refsym=True,
nsteps_steady_state=8,
verbose=0,
opt_u=True,
opt_vw=True,
numpy_update=True,
opt_all_layers=False,
opt_u_after=9):
"""
optimization of a scale invariant modified binary MERA tensor network
Args:
hamAB_0 (tf.Tensor): bottom-layer Hamiltonians in AB lattices
hamBA_0 (tf.Tensor): bottom-layer Hamiltonians in BA lattices
rhoAB_0 (tf.Tensor): reduced densit matrix on a-b lattice
rhoBA_0 (tf.Tensor): reduced densit matrix on b-a lattice
wC (list of tf.Tensor): isometries of the MERA, with
vC (list of tf.Tensor): isometries of the MERA, with
uC (list of tf.Tensor): disentanglers of the MERA
numiter (int): number of iteration steps
refsym (bool): if `True`, impose reflection symmetry
nsteps_steady_state (int): number of power-method iteration steps for calculating the
steady state density matrices
verbose (int): verbosity flag
opt_u (bool): if `False`, skip disentangler optimization
opt_vw (bool): if `False`, skip isometry optimization
numpy_update (bool): if `True`, use numpy svd to calculate updates
opt_all_layers (bool): if `True`, optimize all layers
if `False`, optimize only truncating layers
opt_u_after (int): start optimizing disentangler only after `opt_u_after` initial optimization steps
Returns:
wC (list of tf.Tensor): optimized isometries
vC (list of tf.Tensor): optimized isometries
uC (list of tf.Tensor): optimized disentanglers
rhoAB (tf.Tensor): steady state density matrices on the A-B lattice at the top layer
rhoBA (tf.Tensor): steady state density matrices on the B-A lattice at the top layer
run_times (list of float): run times per iteration step
Energies (list of float): energies per iteration step
"""
dtype = rhoAB_0.dtype
hamAB = [0 for x in range(len(vC) + 1)]
hamBA = [0 for x in range(len(vC) + 1)]
rhoAB = [0 for x in range(len(vC) + 1)]
rhoBA = [0 for x in range(len(vC) + 1)]
hamAB[0] = hamAB_0
hamBA[0] = hamBA_0
chi1 = hamAB[0].shape[0]
bias = tf.math.reduce_max(
tf.linalg.eigvalsh(tf.reshape(hamAB[0], (chi1 * chi1, chi1 * chi1))))
hamAB[0] = hamAB[0] - bias * tf.reshape(tf.eye(chi1 * chi1, dtype=dtype),
(chi1, chi1, chi1, chi1))
hamBA[0] = hamBA[0] - bias * tf.reshape(tf.eye(chi1 * chi1, dtype=dtype),
(chi1, chi1, chi1, chi1))
skip_layer = [misc_mera.skip_layer(w) for w in wC]
for p in range(len(wC)):
if skip_layer[p]:
hamAB[p + 1], hamBA[p + 1] = ascending_super_operator(
hamAB[p], hamBA[p], wC[p], vC[p], uC[p], refsym)
Energies = []
run_times = []
for k in range(numiter):
t1 = time.time()
rhoAB_0, rhoBA_0 = steady_state_density_matrices(
nsteps_steady_state, rhoAB_0, rhoBA_0, wC[-1], vC[-1], uC[-1],
refsym)
rhoAB[-1] = rhoAB_0
rhoBA[-1] = rhoBA_0
for p in range(len(rhoAB) - 2, -1, -1):
rhoAB[p], rhoBA[p] = descending_super_operator(
rhoAB[p + 1], rhoBA[p + 1], wC[p], vC[p], uC[p], refsym)
if verbose > 0:
if np.mod(k, 10) == 1:
Energies.append(
(tn.ncon([rhoAB[0], hamAB[0]], [[1, 2, 3, 4], [1, 2, 3, 4]]
) + tn.ncon([rhoBA[0], hamBA[0]],
[[1, 2, 3, 4], [1, 2, 3, 4]])) / 4 +
bias / 2)
stdout.write(
'\rIteration: %i of %i: E = %.8f, err = %.16f at D = %i with %i layers'
% (int(k), int(numiter), float(Energies[-1]),
float(Energies[-1] + 4 / np.pi, ), int(
wC[-1].shape[2]), len(wC)))
stdout.flush()
for p in range(len(wC)):
if (not opt_all_layers) and skip_layer[p]:
continue
if k >= opt_u_after:
uEnv = get_env_disentangler(hamAB[p], hamBA[p], rhoBA[p + 1],
wC[p], vC[p], uC[p], refsym)
if opt_u:
if refsym:
uEnv = uEnv + tf.transpose(uEnv, (1, 0, 3, 2))
if numpy_update:
uC[p] = misc_mera.u_update_svd_numpy(uEnv)
else:
uC[p] = misc_mera.u_update_svd(uEnv)
wEnv = get_env_w_isometry(hamAB[p], hamBA[p], rhoBA[p + 1],
rhoAB[p + 1], wC[p], vC[p], uC[p])
if opt_vw:
if numpy_update:
wC[p] = misc_mera.w_update_svd_numpy(wEnv)
else:
wC[p] = misc_mera.w_update_svd(wEnv)
if refsym:
vC[p] = wC[p]
else:
vEnv = get_env_v_isometry(hamAB[p], hamBA[p], rhoBA[p + 1],
rhoAB[p + 1], wC[p], vC[p],
uC[p])
vC[p] = misc_mera.w_update_svd(vEnv)
hamAB[p + 1], hamBA[p + 1] = ascending_super_operator(
hamAB[p], hamBA[p], wC[p], vC[p], uC[p], refsym)
run_times.append(time.time() - t1)
if verbose > 2:
print('time per iteration: ', run_times[-1])
return wC, vC, uC, rhoAB[-1], rhoBA[-1], run_times, Energies
def optimize_mod_binary_mera(hamAB_0,
hamBA_0,
rhoAB_0,
rhoBA_0,
wC,
vC,
uC,
numiter=1000,
refsym=True,
nsteps_steady_state=8,
verbose=0,
opt_u=True,
opt_vw=True,
numpy_update=True,
opt_all_layers=False,
opt_u_after=9):
"""
------------------------
adapted from Glen Evenbly (c) for www.tensors.net, (v1.1) - last modified 24/1/2019
------------------------
optimization of a scale invariant modified binary MERA tensor network
Parameters:
----------------------------
hamAB_0, hamBA_0: tf.Tensor
bottom-layer Hamiltonians in AB and BA sublattices
rhoAB_0, rhoBA_0: tf.Tensor
initial values for steady-state density matrices
wC, vC, uC: list of tf.Tensor
isometries (wC, vC) and disentanglers (uC) of the MERA, with
bottom layers first
numiter: int
number of iteration steps
refsym: bool
impose reflection symmetry
nsteps_steady_state: int
number of power-methodf iteration steps for calculating the
steady state density matrices
verbose: int
verbosity flag
opt_u, opt_uv: bool
if False, skip unitary or isometry optimization
numpy_update: bool
if True, use numpy svd to calculate update of disentanglers
opt_all_layers: bool
if True, optimize all layers
if False, optimize only truncating layers
opt_u_after: int
start optimizing disentangler only after `opt_u_after` initial optimization steps
Returns:
-------------------------------
(wC, vC, uC, rhoAB, rhoBA, run_times, Energies)
wC, vC, uC: list of tf.Tensor
obtimized MERA tensors
rhoAB, rhoBA: tf.Tensor
steady state density matrices at the top layer
run_times: list
run times per iteration step
Energies: list
energies at each iteration step
"""
dtype = rhoAB_0.dtype
hamAB = [0 for x in range(len(vC) + 1)]
hamBA = [0 for x in range(len(vC) + 1)]
rhoAB = [0 for x in range(len(vC) + 1)]
rhoBA = [0 for x in range(len(vC) + 1)]
hamAB[0] = hamAB_0
hamBA[0] = hamBA_0
chi1 = hamAB[0].shape[0]
bias = tf.math.reduce_max(
tf.linalg.eigvalsh(tf.reshape(hamAB[0], (chi1 * chi1, chi1 * chi1))))
hamAB[0] = hamAB[0] - bias * tf.reshape(
tf.eye(chi1 * chi1, dtype=dtype), (chi1, chi1, chi1, chi1))
hamBA[0] = hamBA[0] - bias * tf.reshape(
tf.eye(chi1 * chi1, dtype=dtype), (chi1, chi1, chi1, chi1))
skip_layer = [misc_mera.skip_layer(w) for w in wC]
for p in range(len(wC)):
if skip_layer[p]:
hamAB[p + 1], hamBA[p + 1] = ascending_super_operator(
hamAB[p], hamBA[p], wC[p], vC[p], uC[p], refsym)
Energies = []
run_times = []
for k in range(numiter):
t1 = time.time()
rhoAB_0, rhoBA_0 = steady_state_density_matrices(
nsteps_steady_state, rhoAB_0, rhoBA_0, wC[-1], vC[-1], uC[-1],
refsym)
rhoAB[-1] = rhoAB_0
rhoBA[-1] = rhoBA_0
for p in range(len(rhoAB) - 2, -1, -1):
rhoAB[p], rhoBA[p] = descending_super_operator(
rhoAB[p + 1], rhoBA[p + 1], wC[p], vC[p], uC[p], refsym)
if verbose > 0:
if np.mod(k, 10) == 1:
Energies.append(
(tn.ncon([rhoAB[0], hamAB[0]],
[[1, 2, 3, 4], [1, 2, 3, 4]]) + tn.
ncon([rhoBA[0], hamBA[0]], [[1, 2, 3, 4], [1, 2, 3, 4]])) /
4 + bias / 2)
stdout.write(
'\rIteration: %i of %i: E = %.8f, err = %.16f at D = %i with %i layers'
% (int(k), int(numiter), float(Energies[-1]),
float(Energies[-1] + 4 / np.pi,), int(wC[-1].shape[2]),
len(wC)))
stdout.flush()
for p in range(len(wC)):
if (not opt_all_layers) and skip_layer[p]:
continue
if k >= opt_u_after:
uEnv = get_env_disentangler(hamAB[p], hamBA[p], rhoBA[p + 1],
wC[p], vC[p], uC[p], refsym)
if opt_u:
if refsym:
uEnv = uEnv + tf.transpose(uEnv, (1, 0, 3, 2))
if numpy_update:
uC[p] = misc_mera.u_update_svd_numpy(uEnv)
else:
uC[p] = misc_mera.u_update_svd(uEnv)
wEnv = get_env_w_isometry(hamAB[p], hamBA[p], rhoBA[p + 1],
rhoAB[p + 1], wC[p], vC[p], uC[p])
if opt_vw:
if numpy_update:
wC[p] = misc_mera.w_update_svd_numpy(wEnv)
else:
wC[p] = misc_mera.w_update_svd(wEnv)
if refsym:
vC[p] = wC[p]
else:
vEnv = get_env_v_isometry(hamAB[p], hamBA[p], rhoBA[p + 1],
rhoAB[p + 1], wC[p], vC[p], uC[p])
vC[p] = misc_mera.w_update_svd(vEnv)
hamAB[p + 1], hamBA[p + 1] = ascending_super_operator(
hamAB[p], hamBA[p], wC[p], vC[p], uC[p], refsym)
run_times.append(time.time() - t1)
if verbose > 2:
print('time per iteration: ', run_times[-1])
return wC, vC, uC, rhoAB[-1], rhoBA[-1], run_times, Energies