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tensor.py
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tensor.py
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# This file is part of QuTiP: Quantum Toolbox in Python.
#
# Copyright (c) 2011 and later, Paul D. Nation and Robert J. Johansson.
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
# of its contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
# PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
# HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################
"""
Module for the creation of composite quantum objects via the tensor product.
"""
import numpy as np
import scipy.sparse as sp
from qutip.qobj import Qobj
from qutip.permute import reshuffle
import qutip.settings
def tensor(*args):
"""Calculates the tensor product of input operators.
Parameters
----------
args : array_like
``list`` or ``array`` of quantum objects for tensor product.
Returns
-------
obj : qobj
A composite quantum object.
Examples
--------
>>> tensor([sigmax(), sigmax()])
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]]
"""
if not args:
raise TypeError("Requires at least one input argument")
if len(args) == 1 and isinstance(args[0], (list, np.ndarray)):
# this is the case when tensor is called on the form:
# tensor([q1, q2, q3, ...])
qlist = args[0]
elif len(args) == 1 and isinstance(args[0], Qobj):
# tensor is called with a single Qobj as an argument, do nothing
return args[0]
else:
# this is the case when tensor is called on the form:
# tensor(q1, q2, q3, ...)
qlist = args
if not all([isinstance(q, Qobj) for q in qlist]):
# raise error if one of the inputs is not a quantum object
raise TypeError("One of inputs is not a quantum object")
out = Qobj()
if qlist[0].issuper:
out.superrep = qlist[0].superrep
if not all([q.superrep == out.superrep for q in qlist]):
raise TypeError("In tensor products of superroperators, all must" +
"have the same representation")
out.isherm = True
for n, q in enumerate(qlist):
if n == 0:
out.data = q.data
out.dims = q.dims
else:
out.data = sp.kron(out.data, q.data, format='csr')
out.dims = [out.dims[0] + q.dims[0], out.dims[1] + q.dims[1]]
out.isherm = out.isherm and q.isherm
if not out.isherm:
out._isherm = None
return out.tidyup() if qutip.settings.auto_tidyup else out
def super_tensor(*args):
"""Calculates the tensor product of input superoperators, by tensoring
together the underlying Hilbert spaces on which each vectorized operator
acts.
Parameters
----------
args : array_like
``list`` or ``array`` of quantum objects with ``type="super"``.
Returns
-------
obj : qobj
A composite quantum object.
"""
if isinstance(args[0], list):
args = args[0]
if not all(arg.type == "super" and arg.superrep == "super"
for arg in args):
raise TypeError(
"super_tensor is only implemented for "
"superrep='super'."
)
# Reshuffle the superoperators.
shuffled_ops = list(map(reshuffle, args))
# Tensor the result.
shuffled_tensor = tensor(shuffled_ops)
# Unshuffle and return.
out = reshuffle(shuffled_tensor)
out.superrep = args[0].superrep
return out