def test_local_overlap(N):
import matplotlib.pyplot as plt
plt.style.use('ggplot')
L = 5
width = 3
fig, ax = plt.subplots(1, 5, sharex=True, sharey=True, figsize=(L*width, width+0.8))
for k in range(0, L):
real_overlaps = []
approx_overlaps = []
print(k)
for _ in range(N):
y = fMPS().random(L, 2, 3).left_canonicalise()
x = y.copy().left_canonicalise(1)
As = [list(range(i, i+1+k)) for i in range(L-k)]
approx_overlaps.append(x.approx_overlap(y, As))
real_overlaps.append(np.abs(x.overlap(y)**2))
ax[k].set_xlabel(f'{k+1}-local approximate overlaps')
ax[k].scatter(approx_overlaps, real_overlaps, marker='+')
ax[0].set_ylabel('true overlap')
fig.suptitle('$k$-local approx overlap: $\\frac{1}{N-k}\sum_{i=1}^{N-k} tr(\\rho^1_{i...i+k}\\rho^2_{i...i+k})$. Overlap between L=5, D=3 mps, and same mps truncated to D=1.')
fig.tight_layout()
fig.subplots_adjust(top=0.8)
plt.savefig('overlaps.pdf')
def test_OTOCs_eye(self):
"""OTOC zero for W=eye"""
Sx1, Sy1, Sz1 = N_body_spins(0.5, 1, 5)
Sx2, Sy2, Sz2 = N_body_spins(0.5, 2, 5)
Sx3, Sy3, Sz3 = N_body_spins(0.5, 3, 5)
Sx4, Sy4, Sz4 = N_body_spins(0.5, 4, 5)
Sx5, Sy5, Sz5 = N_body_spins(0.5, 5, 5)
mps = fMPS().random(5, 2, None).left_canonicalise()
W = mps.L * [MPO_TFI(0, 0.25, 0.5, 0.5)]
H = Sz1@Sz2+Sz2@Sz3+Sz3@Sz4+Sz4@Sz5+\
Sx1+Sx2+Sx3+Sx4+Sx5+\
Sz1+Sz2+Sz3+Sz4+Sz5
ops = eye(2**5), eye(2**5)
ops_ = ((eye(2), 0), (eye(2), 0))
T = linspace(0, 1, 3)
F = Trajectory(mps, H=H, W=W)
ed_evs = F.ed_OTOC(T, ops)
mps_evs = F.mps_OTOC(T, ops_)
plt.plot(mps_evs)
plt.show()
self.assertTrue(allclose(ed_evs, 0))
self.assertTrue(allclose(mps_evs, 0))
def setUp(self):
"""setUp"""
self.N = N = 4 # Number of MPSs to test
# min and max params for randint
L_min, L_max = 7, 8
d_min, d_max = 2, 3
D, D_sq = 3, 9
# N random MPSs
self.pure_cases = [
fTFD().random(randint(L_min, L_max),
randint(d_min, d_max),
D=D,
pure=True) for _ in range(N)
]
self.mixed_cases = [
fTFD().random(randint(L_min, L_max),
randint(d_min, d_max),
D=D_sq,
pure=False) for _ in range(N)
]
psi_0_2 = load('../../tests/fixtures/mat2x2.npy')
self.tfd_0_2 = fTFD().from_fMPS(fMPS().left_from_state(psi_0_2))
def test_OTOCs_ed(self):
"""test mps otocs against ed"""
Sx1, Sy1, Sz1 = N_body_spins(0.5, 1, 5)
Sx2, Sy2, Sz2 = N_body_spins(0.5, 2, 5)
Sx3, Sy3, Sz3 = N_body_spins(0.5, 3, 5)
Sx4, Sy4, Sz4 = N_body_spins(0.5, 4, 5)
Sx5, Sy5, Sz5 = N_body_spins(0.5, 5, 5)
mps = fMPS().random(5, 2, None).left_canonicalise()
W = mps.L * [MPO_TFI(0, 0.25, 0.5, 0.5)]
H = Sz1@Sz2+Sz2@Sz3+Sz3@Sz4+Sz4@Sz5+\
Sx1+Sx2+Sx3+Sx4+Sx5+\
Sz1+Sz2+Sz3+Sz4+Sz5
ops = Sz2, Sz5
ops_ = ((Sz, 1), (Sz, 4))
T = linspace(0, 1, 3)
F = Trajectory(mps, H=H, W=W, fullH=True)
ed_evs = F.ed_OTOC(T, ops)
mps_evs = F.mps_OTOC(T, ops_)
plt.plot(mps_evs)
plt.plot(ed_evs)
plt.show()
self.assertTrue(allclose(ed_evs, 0))
self.assertTrue(allclose(mps_evs, 0))
def setUp(self):
"""setUp"""
self.N = N = 5 # Number of MPSs to test
# min and max params for randint
L_min, L_max = 7, 8
d_min, d_max = 2, 3
D_min, D_max = 9, 10
ut_min, ut_max = 3, 7
# N random MPSs
self.rand_cases = [fMPS().random(randint(L_min, L_max),
randint(d_min, d_max),
randint(D_min, D_max))
for _ in range(N)]
# N random MPSs, right canonicalised and truncated to random D
self.right_cases = [fMPS().random(
randint(L_min, L_max),
randint(d_min, d_max),
randint(D_min, D_max)).right_canonicalise(
randint(D_min, D_max))
for _ in range(N)]
self.right_ortho_cases = [fMPS().random(
randint(L_min, L_max),
randint(d_min, d_max),
randint(D_min, D_max)).right_orthogonalise()
for _ in range(N)]
# N random MPSs, left canonicalised and truncated to random D
self.left_cases = [fMPS().random(
randint(L_min, L_max),
randint(d_min, d_max),
randint(D_min, D_max)).left_canonicalise(
randint(D_min, D_max))
for _ in range(N)]
self.left_ortho_cases = [fMPS().random(
randint(L_min, L_max),
randint(d_min, d_max),
randint(D_min, D_max)).left_orthogonalise()
for _ in range(N)]
self.mixed_cases = [fMPS().random(
randint(L_min, L_max),
randint(d_min, d_max),
randint(D_min, D_max)).mixed_canonicalise(
randint(ut_min, ut_max),
randint(D_min, D_max))
for _ in range(N)]
# finite fixtures
fix_loc = 'fixtures/'
self.tens_0_2 = load(fix_loc+'mat2x2.npy')
self.tens_0_3 = load(fix_loc+'mat3x3.npy')
self.tens_0_4 = load(fix_loc+'mat4x4.npy')
self.tens_0_5 = load(fix_loc+'mat5x5.npy')
self.tens_0_6 = load(fix_loc+'mat6x6.npy')
self.tens_0_7 = load(fix_loc+'mat7x7.npy')
self.tens_0_8 = load(fix_loc+'mat8x8.npy')
self.tens_0_9 = load(fix_loc+'mat9x9.npy')
self.mps_0_2 = fMPS().left_from_state(self.tens_0_2)
self.psi_0_2 = self.mps_0_2.recombine().reshape(-1)
self.mps_0_3 = fMPS().left_from_state(self.tens_0_3)
self.psi_0_3 = self.mps_0_3.recombine().reshape(-1)
self.mps_0_4 = fMPS().left_from_state(self.tens_0_4)
self.psi_0_4 = self.mps_0_4.recombine().reshape(-1)
self.mps_0_5 = fMPS().left_from_state(self.tens_0_5)
self.psi_0_5 = self.mps_0_5.recombine().reshape(-1)
self.mps_0_6 = fMPS().left_from_state(self.tens_0_6)
self.psi_0_6 = self.mps_0_6.recombine().reshape(-1)
self.mps_0_7 = fMPS().left_from_state(self.tens_0_7)
self.psi_0_7 = self.mps_0_7.recombine().reshape(-1)
self.mps_0_8 = fMPS().left_from_state(self.tens_0_8)
self.psi_0_8 = self.mps_0_8.recombine().reshape(-1)
self.mps_0_9 = fMPS().left_from_state(self.tens_0_9)
self.psi_0_9 = self.mps_0_9.recombine().reshape(-1)
self.fixtures = [self.mps_0_2, self.mps_0_3, self.mps_0_4,
self.mps_0_5, self.mps_0_6, self.mps_0_7,
self.mps_0_8, self.mps_0_9]
self.all_cases = self.rand_cases+self.right_cases+self.left_cases+self.mixed_cases+self.fixtures
def test_serialize_deserialize_real(self):
mps = self.mps_0_4
mps_ = fMPS().deserialize(mps.serialize(True), mps.L, mps.d, mps.D, True)
self.assertTrue(mps==mps_)