def test_kron(backend, dtype, pivots):
""" Checks that Tensor.kron() works.
"""
pivotA, pivotB = pivots
shapeA = (2, 3, 4)
shapeB = (1, 2)
shapeC = (2, 3, 4, 1, 2)
A, _ = testing_utils.safe_randn(shapeA, backend, dtype)
if A is not None:
B, _ = testing_utils.safe_randn(shapeB, backend, dtype)
if pivotA is None and pivotB is None:
C = tensornetwork.kron(A, B)
matrixA = tensornetwork.pivot(A, pivot_axis=-1)
matrixB = tensornetwork.pivot(B, pivot_axis=-1)
elif pivotA is None:
C = tensornetwork.kron(A, B, pivot_axisB=pivotB)
matrixA = tensornetwork.pivot(A, pivot_axis=-1)
matrixB = tensornetwork.pivot(B, pivot_axis=pivotB)
elif pivotB is None:
C = tensornetwork.kron(A, B, pivot_axisA=pivotA)
matrixA = tensornetwork.pivot(A, pivot_axis=pivotA)
matrixB = tensornetwork.pivot(B, pivot_axis=-1)
else:
C = tensornetwork.kron(A,
B,
pivot_axisA=pivotA,
pivot_axisB=pivotB)
matrixA = tensornetwork.pivot(A, pivot_axis=pivotA)
matrixB = tensornetwork.pivot(B, pivot_axis=pivotB)
Ctest = C.backend.einsum("ij,kl->ikjl", matrixA.array, matrixB.array)
Ctest = C.backend.reshape(Ctest, shapeC)
np.testing.assert_allclose(C.array, Ctest)
def test_kron_raises(backend):
with tn.DefaultBackend(backend):
A = tn.Node(np.ones((2, 2, 2)))
B = tn.Node(np.ones((2, 2, 2)))
with pytest.raises(
ValueError,
match="All operator tensors must have an even order."):
tn.kron([A, B])
def H_XX(backend: Optional[BackendType] = None,
dtype: Optional[DtypeType] = None) -> tn.Tensor:
"""
Args:
backend: The backend.
dtype : dtype of data.
Returns:
H : The Hamiltonian, a tn.Tensor shape (2, 2, 2, 2).
"""
X = sigX(backend=backend, dtype=dtype)
Y = sigY(backend=backend, dtype=dtype)
return tn.kron(X, X) + tn.kron(Y, Y).real
def test_operator_kron(backend):
with tn.DefaultBackend(backend):
X = np.array([[0, 1], [1, 0]], dtype=np.float32)
Z = np.array([[1, 0], [0, -1]], dtype=np.float32)
expected = np.kron(X, Z).reshape(2, 2, 2, 2)
result = tn.kron([tn.Node(X), tn.Node(Z)])
np.testing.assert_allclose(result.tensor, expected)
def H_XXZ(delta: float = 1,
ud: float = 2.,
scale: float = 1.,
backend: Optional[BackendType] = None,
dtype: Optional[DtypeType] = None) -> tn.Tensor:
"""
H = (-1/(8scale))*[ud*[UD + DU] + delta*ZZ]
Args:
delta, ud, scale: Couplings.
backend: The backend.
dtype : dtype of data.
Returns:
H : The Hamiltonian, a tn.Tensor shape (2, 2, 2, 2).
"""
U = sigU(backend=backend, dtype=dtype)
D = sigD(backend=backend, dtype=dtype)
Z = sigZ(backend=backend, dtype=dtype)
UD = ud * (tn.kron(U, D) + tn.kron(D, U))
return -(UD + delta * tn.kron(Z, Z)) / (8 * scale)
def H_ising(h: float,
J: float = 1.,
backend: Optional[BackendType] = None,
dtype: Optional[DtypeType] = None) -> tn.Tensor:
"""
The famous and beloved transverse-field Ising model,
H = J * XX + h * ZI
Args:
h : Transverse field.
J : Coupling strength, default 1.
backend: The backend.
dtype : dtype of data.
Returns:
H : The Hamiltonian, a tn.Tensor shape (2, 2, 2, 2).
"""
X = sigX(backend=backend, dtype=dtype)
Z = sigZ(backend=backend, dtype=dtype)
Id = tn.eye(2, backend=backend, dtype=dtype)
return J * tn.kron(X, X) + 0.5 * h * (tn.kron(Z, Id) + tn.kron(Id, Z))