def test_evolve_trotter_euclidean(num_sites, phys_dim, graph):
psi = tf.complex(
tf.random_normal([phys_dim] * num_sites, dtype=tf.float64),
tf.random_normal([phys_dim] * num_sites, dtype=tf.float64))
h = tf.complex(
tf.random_normal((phys_dim**2, phys_dim**2), dtype=tf.float64),
tf.random_normal((phys_dim**2, phys_dim**2), dtype=tf.float64))
h = 0.5 * (h + tf.linalg.adjoint(h))
h = tf.reshape(h, (phys_dim, phys_dim, phys_dim, phys_dim))
H = [h] * (num_sites - 1)
norm1 = wavefunctions.inner(psi, psi)
en1 = sum(wavefunctions.expval(psi, H[i], i) for i in range(num_sites - 1))
if graph:
psi, t = wavefunctions.evolve_trotter_defun(psi,
H,
0.1,
10,
euclidean=True)
else:
psi, t = wavefunctions.evolve_trotter(psi, H, 0.1, 10, euclidean=True)
norm2 = wavefunctions.inner(psi, psi)
en2 = sum(wavefunctions.expval(psi, H[i], i) for i in range(num_sites - 1))
np.testing.assert_allclose(t, 1.0)
np.testing.assert_almost_equal(norm2, 1.0)
assert en2.numpy() / norm2.numpy() < en1.numpy() / norm1.numpy()
def test_evolve_trotter(num_sites, phys_dim, graph):
psi = tf.complex(
tf.random.normal([phys_dim] * num_sites, dtype=tf.float64),
tf.random.normal([phys_dim] * num_sites, dtype=tf.float64))
h = tf.complex(
tf.random.normal((phys_dim**2, phys_dim**2), dtype=tf.float64),
tf.random.normal((phys_dim**2, phys_dim**2), dtype=tf.float64))
h = 0.5 * (h + tf.linalg.adjoint(h))
h = tf.reshape(h, (phys_dim, phys_dim, phys_dim, phys_dim))
H = [h] * (num_sites - 1)
norm1 = wavefunctions.inner(psi, psi)
en1 = sum(wavefunctions.expval(psi, H[i], i) for i in range(num_sites - 1))
if graph:
psi, t = wavefunctions.evolve_trotter_defun(psi, H, 0.001, 10)
else:
psi, t = wavefunctions.evolve_trotter(psi, H, 0.001, 10)
norm2 = wavefunctions.inner(psi, psi)
en2 = sum(wavefunctions.expval(psi, H[i], i) for i in range(num_sites - 1))
np.testing.assert_allclose(t, 0.01)
np.testing.assert_almost_equal(norm1 / norm2, 1.0)
np.testing.assert_almost_equal(en1 / en2, 1.0, decimal=2)
def test_apply_op(num_sites):
psi1 = np.zeros([2] * num_sites)
psi1_vec = psi1.reshape((2**num_sites, ))
psi1_vec[0] = 1.0
psi1 = tf.convert_to_tensor(psi1)
for j in range(num_sites):
psi2 = np.zeros([2] * num_sites)
psi2_vec = psi2.reshape((2**num_sites, ))
psi2_vec[2**j] = 1.0
psi2 = tf.convert_to_tensor(psi2)
opX = tf.convert_to_tensor(np.array([[0.0, 1.0], [1.0, 0.0]]))
psi2 = wavefunctions.apply_op(psi2, opX, num_sites - 1 - j)
res = wavefunctions.inner(psi1, psi2)
np.testing.assert_allclose(res, 1.0)
euclidean_evolution = False
print("----------------------------------------------------")
print("Evolving a random state by the Ising Hamiltonian.")
print("----------------------------------------------------")
print("System size:", N)
print("Trotter step size:", dt)
print("Euclidean?:", euclidean_evolution)
X = tf.convert_to_tensor([[0.0, 1.0], [1.0, 0.0]], dtype=dtype)
H = ising_hamiltonian(N, dtype)
psi = random_state(N, 2, dtype)
if build_graph:
f = wavefunctions.evolve_trotter_defun
else:
f = wavefunctions.evolve_trotter
print("----------------------------------------------------")
print("step\tnorm\t<X_0>")
print("----------------------------------------------------")
psi_t, t = f(psi,
H,
dt,
num_steps,
euclidean=euclidean_evolution,
callback=callback)
print("Final norm:", tf.norm(psi_t).numpy().real)
print("<psi | psi_t>:", wavefunctions.inner(psi, psi_t).numpy())
dt = 0.1
num_steps = 100
euclidean_evolution = False
print("----------------------------------------------------")
print("Evolving a random state by the Ising Hamiltonian.")
print("----------------------------------------------------")
print("System size:", N)
print("Trotter step size:", dt)
print("Euclidean?:", euclidean_evolution)
X = tf.convert_to_tensor([[0.0, 1.0], [1.0, 0.0]], dtype=dtype)
H = ising_hamiltonian(N, dtype)
psi = random_state(N, 2, dtype)
if build_graph:
f = wavefunctions.evolve_trotter_defun
else:
f = wavefunctions.evolve_trotter
print("----------------------------------------------------")
print("step\tnorm\t<X_0>")
print("----------------------------------------------------")
psi_t, t = f(
psi, H, dt, num_steps,
euclidean=euclidean_evolution,
callback=callback)
print("Final norm:", tf.norm(psi_t).numpy().real)
print("<psi | psi_t>:", wavefunctions.inner(psi, psi_t).numpy())