Revision d38084d993f6b218862f3aa0693aacc2e3b4b1b3 authored by TUNA Caglayan on 29 April 2021, 08:44:25 UTC, committed by TUNA Caglayan on 12 May 2021, 12:26:22 UTC
1 parent e54a8ff
entropy.py
import tensorly as tl
from .. import backend as T
from ..cp_tensor import CPTensor, cp_normalize
from ..tt_tensor import tt_to_tensor
# Author: Taylor Lee Patti <taylorpatti@g.harvard.edu>
def vonneumann_entropy(tensor):
"""Returns the von Neumann entropy of a density matrix (2-mode, square) tensor (matrix).
Parameters
----------
tensor : (matrix)
Data structure
Returns
-------
von_neumann_entropy : order-0 tensor
"""
try:
eig_vals = T.eigh(tensor)[0]
except:
#All density matrices are Hermitian, here real. Hermitianize matrix if rounding/transformation
#errors have occured.
tensor = (tensor + tl.transpose(tensor))/2
eig_vals = T.eigh(tensor)[0]
eps = tl.eps(eig_vals.dtype)
eig_vals = eig_vals[eig_vals > eps]
return -T.sum(T.log2(eig_vals) * eig_vals)
def tt_vonneumann_entropy(tensor):
"""Returns the von Neumann entropy of a density matrix (square matrix) in TT tensor form.
Parameters
----------
tensor : (TT tensor)
Data structure
Returns
-------
tt_von_neumann_entropy : order-0 tensor
"""
square_dim = int(tl.sqrt(tl.prod(tl.tensor(tensor.shape))))
tensor = tl.reshape(tt_to_tensor(tensor), (square_dim, square_dim))
return vonneumann_entropy(tensor)
def cp_vonneumann_entropy(tensor):
"""Returns the von Neumann entropy of a density matrix (square matrix) in CP tensor.
Parameters
----------
tensor : (CP tensor)
Data structure
Returns
-------
cp_von_neumann_entropy : order-0 tensor
"""
eig_vals = cp_normalize(tensor).weights
eps = tl.eps(eig_vals.dtype)
eig_vals = eig_vals[eig_vals > eps]
return -T.sum(T.log2(eig_vals) * eig_vals)
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