def test_realistic(self):
seed_rand(42)
ham = MPO_ham_heis(20)
dmrg = DMRG2(ham, bond_dims=[2, 4])
dmrg.solve()
rho_ab = dmrg.state.ptr(range(6, 14))
xf = approx_spectral_function(rho_ab, lambda x: x,
tol=0.1, verbosity=2)
assert_allclose(1.0, xf, rtol=0.6, atol=0.001)
def construct_lanczos_tridiag_MPO(A,
K,
v0=None,
initial_bond_dim=None,
beta_tol=1e-6,
max_bond=None,
seed=False,
v0_opts=None,
k_min=10):
"""
"""
if initial_bond_dim is None:
initial_bond_dim = 8
if max_bond is None:
max_bond = 8
if v0 is None:
if seed:
# needs to be truly random so MPI processes don't overlap
qu.seed_rand(random.SystemRandom().randint(0, 2**32 - 1))
V = MPO_rand(A.nsites,
initial_bond_dim,
phys_dim=A.phys_dim(),
dtype=A.dtype)
else: # normalize
V = v0 / (v0.H @ v0)**0.5
Vm1 = MPO_zeros_like(V)
alpha = np.zeros(K + 1)
beta = np.zeros(K + 2)
bsz = A.phys_dim()**A.nsites
beta[1] = bsz # == sqrt(prod(A.shape))
compress_kws = {'max_bond': max_bond, 'method': 'svd'}
for j in range(1, K + 1):
Vt = A.apply(V, compress=True, **compress_kws)
Vt.add_MPO(-beta[j] * Vm1, inplace=True, compress=True, **compress_kws)
alpha[j] = (V.H @ Vt).real
Vt.add_MPO(-alpha[j] * V, inplace=True, compress=True, **compress_kws)
beta[j + 1] = (Vt.H @ Vt)**0.5
# check for convergence
if abs(beta[j + 1]) < beta_tol:
yield alpha[1:j + 1], beta[2:j + 2], beta[1]**2 / bsz
break
Vm1 = V.copy()
V = Vt / beta[j + 1]
if j >= k_min:
yield (np.copy(alpha[1:j + 1]), np.copy(beta[2:j + 2]),
np.copy(beta[1])**2 / bsz)
def construct_lanczos_tridiag_PTPTLazyMPS(A,
K,
v0=None,
initial_bond_dim=None,
beta_tol=1e-6,
max_bond=None,
v0_opts=None,
k_min=10,
seed=False):
"""
"""
if initial_bond_dim is None:
initial_bond_dim = 16
if max_bond is None:
max_bond = 16
if v0 is None:
if seed:
# needs to be truly random so MPI processes don't overlap
qu.seed_rand(random.SystemRandom().randint(0, 2**32 - 1))
V = A.rand_state(bond_dim=initial_bond_dim)
else: # normalize
V = v0 / (v0.H @ v0)**0.5
Vm1 = EEMPS_zeros_like(V)
alpha = np.zeros(K + 1)
beta = np.zeros(K + 2)
beta[1] = A.phys_dim()**((len(A.sysa) + len(A.sysb)) / 2)
compress_kws = {'max_bond': max_bond, 'method': 'svd'}
for j in range(1, K + 1):
Vt = A.apply(V)
Vt -= beta[j] * Vm1
Vt.compress_all(**compress_kws)
alpha[j] = (V.H @ Vt).real
Vt -= alpha[j] * V
beta[j + 1] = ((Vt.H @ Vt)**0.5).real
Vt.compress_all(**compress_kws)
# check for convergence
if abs(beta[j + 1]) < beta_tol:
yield alpha[1:j + 1], beta[2:j + 2], beta[1]**2
break
Vm1 = V.copy()
V = Vt / beta[j + 1]
if j >= k_min:
yield (np.copy(alpha[1:j + 1]), np.copy(beta[2:j + 2]),
np.copy(beta[1])**2)
def test_multisubsystem(self):
qu.seed_rand(42)
dims = [2, 2, 2]
IIX = qu.ikron(qu.rand_herm(2), dims, 2)
dcmp = qu.pauli_decomp(IIX, mode='c')
for p, x in dcmp.items():
if x == 0j:
assert (p[0] != 'I') or (p[1] != 'I')
else:
assert p[0] == p[1] == 'I'
K = qu.rand_iso(3 * 4, 4).reshape(3, 4, 4)
KIIXK = qu.kraus_op(IIX, K, dims=dims, where=[0, 2])
dcmp = qu.pauli_decomp(KIIXK, mode='c')
for p, x in dcmp.items():
if x == 0j:
assert p[1] != 'I'
else:
assert p[1] == 'I'