File size: 3,853 Bytes
6288873 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 | from functools import partial
import jax.numpy as jnp
from jax import jit
from varipeps.peps import PEPS_Tensor
from varipeps.contractions import apply_contraction_jitted
from typing import Sequence, List, Tuple, Literal
Corner_Literal = Literal["top-left", "top-right", "bottom-left", "bottom-right"]
@partial(jit, static_argnums=(5,))
def _four_sites_quadrat_workhorse(
top_left: jnp.ndarray,
top_right: jnp.ndarray,
bottom_left: jnp.ndarray,
bottom_right: jnp.ndarray,
gates: Tuple[jnp.ndarray, ...],
real_result: bool = False,
) -> List[jnp.ndarray]:
density_matrix = jnp.tensordot(top_left, top_right, ((5, 6, 7), (2, 3, 4)))
density_matrix = jnp.tensordot(density_matrix, bottom_left, ((2, 3, 4), (5, 6, 7)))
density_matrix = jnp.tensordot(
density_matrix, bottom_right, ((4, 5, 6, 9, 10, 11), (2, 3, 4, 5, 6, 7))
)
density_matrix = density_matrix.transpose(0, 2, 4, 6, 1, 3, 5, 7)
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]
* density_matrix.shape[6]
* density_matrix.shape[7],
)
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_four_sites_quadrat_multiple_gates(
peps_tensors: Sequence[jnp.ndarray],
peps_tensor_objs: Sequence[PEPS_Tensor],
gates: Sequence[jnp.ndarray],
) -> List[jnp.ndarray]:
"""
Calculate the four site expectation values for three as quadrat ordered
PEPS tensor and their environment.
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, 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_jitted(
"density_matrix_four_sites_top_left",
[peps_tensors[0]],
[peps_tensor_objs[0]],
[],
)
density_matrix_top_right = apply_contraction_jitted(
"density_matrix_four_sites_top_right",
[peps_tensors[1]],
[peps_tensor_objs[1]],
[],
)
density_matrix_bottom_left = apply_contraction_jitted(
"density_matrix_four_sites_bottom_left",
[peps_tensors[2]],
[peps_tensor_objs[2]],
[],
)
density_matrix_bottom_right = apply_contraction_jitted(
"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 _four_sites_quadrat_workhorse(
density_matrix_top_left,
density_matrix_top_right,
density_matrix_bottom_left,
density_matrix_bottom_right,
tuple(gates),
real_result,
)
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