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import jax.numpy as jnp
from jax import jit
from varipeps.peps import PEPS_Tensor
from varipeps.contractions import apply_contraction
from typing import Sequence, List, Tuple, Literal
Corner_Literal = Literal["top-left", "top-right", "bottom-left", "bottom-right"]
@partial(jit, static_argnums=(5, 6))
def _three_site_triangle_workhorse(
top_left: jnp.ndarray,
top_right: jnp.ndarray,
bottom_left: jnp.ndarray,
bottom_right: jnp.ndarray,
gates: Tuple[jnp.ndarray, ...],
traced: Corner_Literal,
real_result: bool = False,
) -> List[jnp.ndarray]:
if traced == "top-left":
one_physical_sites = jnp.tensordot(top_left, top_right, ((3, 4, 5), (2, 3, 4)))
two_physical_sites = jnp.tensordot(
bottom_right, bottom_left, ((5, 6, 7), (2, 3, 4))
)
transpose_order = (0, 4, 2, 1, 5, 3)
elif traced == "top-right":
one_physical_sites = jnp.tensordot(
top_right, bottom_right, ((3, 4, 5), (2, 3, 4))
)
two_physical_sites = jnp.tensordot(
bottom_left, top_left, ((5, 6, 7), (2, 3, 4))
)
transpose_order = (4, 2, 0, 5, 3, 1)
elif traced == "bottom-left":
one_physical_sites = jnp.tensordot(
bottom_left, top_left, ((3, 4, 5), (2, 3, 4))
)
two_physical_sites = jnp.tensordot(
top_right, bottom_right, ((5, 6, 7), (2, 3, 4))
)
transpose_order = (0, 2, 4, 1, 3, 5)
elif traced == "bottom-right":
one_physical_sites = jnp.tensordot(
bottom_right, bottom_left, ((3, 4, 5), (2, 3, 4))
)
two_physical_sites = jnp.tensordot(top_left, top_right, ((5, 6, 7), (2, 3, 4)))
transpose_order = (2, 4, 0, 3, 5, 1)
else:
raise ValueError('Invalid argument for parameter "traced".')
density_matrix = jnp.tensordot(
one_physical_sites, two_physical_sites, ((0, 1, 2, 5, 6, 7), (7, 8, 9, 2, 3, 4))
)
density_matrix = density_matrix.transpose(transpose_order)
density_matrix = density_matrix.reshape(
density_matrix.shape[0] * density_matrix.shape[1] * density_matrix.shape[2],
density_matrix.shape[3] * density_matrix.shape[4] * density_matrix.shape[5],
)
norm = jnp.trace(density_matrix)
if real_result:
return [
jnp.real(jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm)
for g in gates
]
else:
return [
jnp.tensordot(density_matrix, g, ((0, 1), (0, 1))) / norm for g in gates
]
def calc_three_sites_triangle_without_top_left_multiple_gates(
peps_tensors: Sequence[jnp.ndarray],
peps_tensor_objs: Sequence[PEPS_Tensor],
gates: Sequence[jnp.ndarray],
) -> List[jnp.ndarray]:
"""
Calculate the three site expectation values for three as triangle ordered
PEPS tensor and their environment without the top-left tensor.
The order of the PEPS sequence have to be
[top-left, top-right, bottom-left, bottom-right].
The gate is applied in the order [top-right, bottom-left, bottom-right].
Args:
peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
The PEPS tensor arrays. Have to be the same objects as the tensor
attribute of the `peps_tensor_obj` argument.
peps_tensor_objs (:term:`sequence` of :obj:`~varipeps.peps.PEPS_Tensor`):
PEPS tensor objects.
gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
Sequence with the gates which should be applied to the PEPS tensors.
Gates are expected to be a matrix with first axis corresponding to
the Hilbert space and the second axis corresponding to the dual room.
Returns:
:obj:`list` of :obj:`jax.numpy.ndarray`:
List with the calculated expectation values of each gate.
"""
traced_density_matrix_top_left = apply_contraction(
"ctmrg_top_left", [peps_tensors[0]], [peps_tensor_objs[0]], []
)
density_matrix_top_right = apply_contraction(
"density_matrix_four_sites_top_right",
[peps_tensors[1]],
[peps_tensor_objs[1]],
[],
)
density_matrix_bottom_left = apply_contraction(
"density_matrix_four_sites_bottom_left",
[peps_tensors[2]],
[peps_tensor_objs[2]],
[],
)
density_matrix_bottom_right = apply_contraction(
"density_matrix_four_sites_bottom_right",
[peps_tensors[3]],
[peps_tensor_objs[3]],
[],
)
real_result = all(jnp.allclose(g, g.T.conj()) for g in gates)
return _three_site_triangle_workhorse(
traced_density_matrix_top_left,
density_matrix_top_right,
density_matrix_bottom_left,
density_matrix_bottom_right,
tuple(gates),
"top-left",
real_result,
)
def calc_three_sites_triangle_without_top_left_single_gate(
peps_tensors: Sequence[jnp.ndarray],
peps_tensor_objs: Sequence[PEPS_Tensor],
gate: jnp.ndarray,
) -> jnp.ndarray:
"""
Calculate the two site expectation value for three as triangle ordered
PEPS tensor and their environment without the top-left tensor.
The order of the PEPS sequence have to be
[top-left, top-right, bottom-left, bottom-right].
The gate is applied in the order [top-right, bottom-left, bottom-right].
This function just wraps
:obj:`~varipeps.expectation.three_sites.calc_three_sites_triangle_without_top_left_multiple_gates`.
Args:
peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
The PEPS tensor arrays. Have to be the same objects as the tensor
attribute of the `peps_tensor_obj` argument.
peps_tensor_objs (:term:`sequence` of :obj:`~varipeps.peps.PEPS_Tensor`):
PEPS tensor objects.
gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
Gate which should be applied to the PEPS tensors.
The gate is expected to be a matrix with first axis corresponding to
the Hilbert space and the second axis corresponding to the dual room.
Returns:
:obj:`jax.numpy.ndarray`:
Calculated expectation value of the gate.
"""
return calc_three_sites_triangle_without_top_left_multiple_gates(
peps_tensors, peps_tensor_objs, (gate,)
)[0]
def calc_three_sites_triangle_without_top_right_multiple_gates(
peps_tensors: Sequence[jnp.ndarray],
peps_tensor_objs: Sequence[PEPS_Tensor],
gates: Sequence[jnp.ndarray],
) -> List[jnp.ndarray]:
"""
Calculate the three site expectation values for three as triangle ordered
PEPS tensor and their environment without the top-right tensor.
The order of the PEPS sequence have to be
[top-left, top-right, bottom-left, bottom-right].
The gate is applied in the order [top-left, bottom-left, bottom-right].
Args:
peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
The PEPS tensor arrays. Have to be the same objects as the tensor
attribute of the `peps_tensor_obj` argument.
peps_tensor_objs (:term:`sequence` of :obj:`~varipeps.peps.PEPS_Tensor`):
PEPS tensor objects.
gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
Sequence with the gates which should be applied to the PEPS tensors.
Gates are expected to be a matrix with first axis corresponding to
the Hilbert space and the second axis corresponding to the dual room.
Returns:
:obj:`list` of :obj:`jax.numpy.ndarray`:
List with the calculated expectation values of each gate.
"""
density_matrix_top_left = apply_contraction(
"density_matrix_four_sites_top_left",
[peps_tensors[0]],
[peps_tensor_objs[0]],
[],
)
traced_density_matrix_top_right = apply_contraction(
"ctmrg_top_right",
[peps_tensors[1]],
[peps_tensor_objs[1]],
[],
)
density_matrix_bottom_left = apply_contraction(
"density_matrix_four_sites_bottom_left",
[peps_tensors[2]],
[peps_tensor_objs[2]],
[],
)
density_matrix_bottom_right = apply_contraction(
"density_matrix_four_sites_bottom_right",
[peps_tensors[3]],
[peps_tensor_objs[3]],
[],
)
real_result = all(jnp.allclose(g, g.T.conj()) for g in gates)
return _three_site_triangle_workhorse(
density_matrix_top_left,
traced_density_matrix_top_right,
density_matrix_bottom_left,
density_matrix_bottom_right,
tuple(gates),
"top-right",
real_result,
)
def calc_three_sites_triangle_without_top_right_single_gate(
peps_tensors: Sequence[jnp.ndarray],
peps_tensor_objs: Sequence[PEPS_Tensor],
gate: jnp.ndarray,
) -> jnp.ndarray:
"""
Calculate the two site expectation value for three as triangle ordered
PEPS tensor and their environment without the top-right tensor.
The order of the PEPS sequence have to be
[top-left, top-right, bottom-left, bottom-right].
The gate is applied in the order [top-left, bottom-left, bottom-right].
This function just wraps
:obj:`~varipeps.expectation.three_sites.calc_three_sites_triangle_without_top_right_multiple_gates`.
Args:
peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
The PEPS tensor arrays. Have to be the same objects as the tensor
attribute of the `peps_tensor_obj` argument.
peps_tensor_objs (:term:`sequence` of :obj:`~varipeps.peps.PEPS_Tensor`):
PEPS tensor objects.
gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
Gate which should be applied to the PEPS tensors.
The gate is expected to be a matrix with first axis corresponding to
the Hilbert space and the second axis corresponding to the dual room.
Returns:
:obj:`jax.numpy.ndarray`:
Calculated expectation value of the gate.
"""
return calc_three_sites_triangle_without_top_right_multiple_gates(
peps_tensors, peps_tensor_objs, (gate,)
)[0]
def calc_three_sites_triangle_without_bottom_left_multiple_gates(
peps_tensors: Sequence[jnp.ndarray],
peps_tensor_objs: Sequence[PEPS_Tensor],
gates: Sequence[jnp.ndarray],
) -> List[jnp.ndarray]:
"""
Calculate the three site expectation values for three as triangle ordered
PEPS tensor and their environment without the bottom-left tensor.
The order of the PEPS sequence have to be
[top-left, top-right, bottom-left, bottom-right].
The gate is applied in the order [top-left, top-right, bottom-right].
Args:
peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
The PEPS tensor arrays. Have to be the same objects as the tensor
attribute of the `peps_tensor_obj` argument.
peps_tensor_objs (:term:`sequence` of :obj:`~varipeps.peps.PEPS_Tensor`):
PEPS tensor objects.
gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
Sequence with the gates which should be applied to the PEPS tensors.
Gates are expected to be a matrix with first axis corresponding to
the Hilbert space and the second axis corresponding to the dual room.
Returns:
:obj:`list` of :obj:`jax.numpy.ndarray`:
List with the calculated expectation values of each gate.
"""
density_matrix_top_left = apply_contraction(
"density_matrix_four_sites_top_left",
[peps_tensors[0]],
[peps_tensor_objs[0]],
[],
)
density_matrix_top_right = apply_contraction(
"density_matrix_four_sites_top_right",
[peps_tensors[1]],
[peps_tensor_objs[1]],
[],
)
traced_density_matrix_bottom_left = apply_contraction(
"ctmrg_bottom_left",
[peps_tensors[2]],
[peps_tensor_objs[2]],
[],
)
density_matrix_bottom_right = apply_contraction(
"density_matrix_four_sites_bottom_right",
[peps_tensors[3]],
[peps_tensor_objs[3]],
[],
)
real_result = all(jnp.allclose(g, g.T.conj()) for g in gates)
return _three_site_triangle_workhorse(
density_matrix_top_left,
density_matrix_top_right,
traced_density_matrix_bottom_left,
density_matrix_bottom_right,
tuple(gates),
"bottom-left",
real_result,
)
def calc_three_sites_triangle_without_bottom_left_single_gate(
peps_tensors: Sequence[jnp.ndarray],
peps_tensor_objs: Sequence[PEPS_Tensor],
gate: jnp.ndarray,
) -> jnp.ndarray:
"""
Calculate the two site expectation value for three as triangle ordered
PEPS tensor and their environment without the bottom-left tensor.
The order of the PEPS sequence have to be
[top-left, top-right, bottom-left, bottom-right].
The gate is applied in the order [top-left, top-right, bottom-right].
This function just wraps
:obj:`~varipeps.expectation.three_sites.calc_three_sites_triangle_without_bottom_left_multiple_gates`.
Args:
peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
The PEPS tensor arrays. Have to be the same objects as the tensor
attribute of the `peps_tensor_obj` argument.
peps_tensor_objs (:term:`sequence` of :obj:`~varipeps.peps.PEPS_Tensor`):
PEPS tensor objects.
gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
Gate which should be applied to the PEPS tensors.
The gate is expected to be a matrix with first axis corresponding to
the Hilbert space and the second axis corresponding to the dual room.
Returns:
:obj:`jax.numpy.ndarray`:
Calculated expectation value of the gate.
"""
return calc_three_sites_triangle_without_bottom_left_multiple_gates(
peps_tensors, peps_tensor_objs, (gate,)
)[0]
def calc_three_sites_triangle_without_bottom_right_multiple_gates(
peps_tensors: Sequence[jnp.ndarray],
peps_tensor_objs: Sequence[PEPS_Tensor],
gates: Sequence[jnp.ndarray],
) -> List[jnp.ndarray]:
"""
Calculate the three site expectation values for three as triangle ordered
PEPS tensor and their environment without the bottom-right tensor.
The order of the PEPS sequence have to be
[top-left, top-right, bottom-left, bottom-left].
The gate is applied in the order [top-left, top-right, bottom-left].
Args:
peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
The PEPS tensor arrays. Have to be the same objects as the tensor
attribute of the `peps_tensor_obj` argument.
peps_tensor_objs (:term:`sequence` of :obj:`~varipeps.peps.PEPS_Tensor`):
PEPS tensor objects.
gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
Sequence with the gates which should be applied to the PEPS tensors.
Gates are expected to be a matrix with first axis corresponding to
the Hilbert space and the second axis corresponding to the dual room.
Returns:
:obj:`list` of :obj:`jax.numpy.ndarray`:
List with the calculated expectation values of each gate.
"""
density_matrix_top_left = apply_contraction(
"density_matrix_four_sites_top_left",
[peps_tensors[0]],
[peps_tensor_objs[0]],
[],
)
density_matrix_top_right = apply_contraction(
"density_matrix_four_sites_top_right",
[peps_tensors[1]],
[peps_tensor_objs[1]],
[],
)
density_matrix_bottom_left = apply_contraction(
"density_matrix_four_sites_bottom_left",
[peps_tensors[2]],
[peps_tensor_objs[2]],
[],
)
traced_density_matrix_bottom_right = apply_contraction(
"ctmrg_bottom_right",
[peps_tensors[3]],
[peps_tensor_objs[3]],
[],
)
real_result = all(jnp.allclose(g, g.T.conj()) for g in gates)
return _three_site_triangle_workhorse(
density_matrix_top_left,
density_matrix_top_right,
density_matrix_bottom_left,
traced_density_matrix_bottom_right,
tuple(gates),
"bottom-right",
real_result,
)
def calc_three_sites_triangle_without_bottom_right_single_gate(
peps_tensors: Sequence[jnp.ndarray],
peps_tensor_objs: Sequence[PEPS_Tensor],
gate: jnp.ndarray,
) -> jnp.ndarray:
"""
Calculate the two site expectation value for three as triangle ordered
PEPS tensor and their environment without the bottom-left tensor.
The order of the PEPS sequence have to be
[top-left, top-right, bottom-left, bottom-right].
The gate is applied in the order [top-left, top-right, bottom-left].
This function just wraps
:obj:`~varipeps.expectation.three_sites.calc_three_sites_triangle_without_bottom_right_multiple_gates`.
Args:
peps_tensors (:term:`sequence` of :obj:`jax.numpy.ndarray`):
The PEPS tensor arrays. Have to be the same objects as the tensor
attribute of the `peps_tensor_obj` argument.
peps_tensor_objs (:term:`sequence` of :obj:`~varipeps.peps.PEPS_Tensor`):
PEPS tensor objects.
gates (:term:`sequence` of :obj:`jax.numpy.ndarray`):
Gate which should be applied to the PEPS tensors.
The gate is expected to be a matrix with first axis corresponding to
the Hilbert space and the second axis corresponding to the dual room.
Returns:
:obj:`jax.numpy.ndarray`:
Calculated expectation value of the gate.
"""
return calc_three_sites_triangle_without_bottom_right_multiple_gates(
peps_tensors, peps_tensor_objs, (gate,)
)[0]
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