def tensor_contract(qobj, *pairs):
"""Contracts a qobj along one or more index pairs.
Note that this uses dense representations and thus
should *not* be used for very large Qobjs.
Parameters
----------
pairs : tuple
One or more tuples ``(i, j)`` indicating that the
``i`` and ``j`` dimensions of the original qobj
should be contracted.
Returns
-------
cqobj : Qobj
The original Qobj with all named index pairs contracted
away.
"""
# Record and label the original dims.
dims = qobj.dims
dims_idxs = enumerate_flat(dims)
tensor_dims = dims_to_tensor_shape(dims)
# Convert to dense first, since sparse won't support the reshaping we need.
qtens = qobj.data.toarray()
# Reshape by the flattened dims.
qtens = qtens.reshape(tensor_dims)
# Contract out the indices from the flattened object.
# Note that we need to feed pairs through dims_idxs_to_tensor_idxs
# to ensure that we are contracting the right indices.
qtens = _tensor_contract_dense(qtens,
*dims_idxs_to_tensor_idxs(dims, pairs))
# Remove the contracted indexes from dims so we know how to
# reshape back.
# This concerns dims, and not the tensor indices, so we need
# to make sure to use the original dims indices and not the ones
# generated by dims_to_* functions.
contracted_idxs = deep_remove(dims_idxs, *flatten(list(map(list, pairs))))
contracted_dims = unflatten(flatten(dims), contracted_idxs)
# We don't need to check for tensor idxs versus dims idxs here,
# as column- versus row-stacking will never move an index for the
# vectorized operator spaces all the way from the left to the right.
l_mtx_dims, r_mtx_dims = map(np.product, map(flatten, contracted_dims))
# Reshape back into a 2D matrix.
qmtx = qtens.reshape((l_mtx_dims, r_mtx_dims))
# Return back as a qobj.
return Qobj(qmtx, dims=contracted_dims, superrep=qobj.superrep)
def tensor_contract(qobj, *pairs):
"""Contracts a qobj along one or more index pairs.
Note that this uses dense representations and thus
should *not* be used for very large Qobjs.
Parameters
----------
pairs : tuple
One or more tuples ``(i, j)`` indicating that the
``i`` and ``j`` dimensions of the original qobj
should be contracted.
Returns
-------
cqobj : Qobj
The original Qobj with all named index pairs contracted
away.
"""
# Record and label the original dims.
dims = qobj.dims
dims_idxs = enumerate_flat(dims)
tensor_dims = dims_to_tensor_shape(dims)
# Convert to dense first, since sparse won't support the reshaping we need.
qtens = qobj.data.toarray()
# Reshape by the flattened dims.
qtens = qtens.reshape(tensor_dims)
# Contract out the indices from the flattened object.
# Note that we need to feed pairs through dims_idxs_to_tensor_idxs
# to ensure that we are contracting the right indices.
qtens = _tensor_contract_dense(qtens, *dims_idxs_to_tensor_idxs(dims, pairs))
# Remove the contracted indexes from dims so we know how to
# reshape back.
# This concerns dims, and not the tensor indices, so we need
# to make sure to use the original dims indices and not the ones
# generated by dims_to_* functions.
contracted_idxs = deep_remove(dims_idxs, *flatten(list(map(list, pairs))))
contracted_dims = unflatten(flatten(dims), contracted_idxs)
# We don't need to check for tensor idxs versus dims idxs here,
# as column- versus row-stacking will never move an index for the
# vectorized operator spaces all the way from the left to the right.
l_mtx_dims, r_mtx_dims = map(np.product, map(flatten, contracted_dims))
# Reshape back into a 2D matrix.
qmtx = qtens.reshape((l_mtx_dims, r_mtx_dims))
# Return back as a qobj.
return Qobj(qmtx, dims=contracted_dims, superrep=qobj.superrep)
def test_dims_to_tensor_shape():
# Dims for a superoperator:
# L(L(C⁰ × C¹, C² × C³), L(C³ × C⁴, C⁵ × C⁶)),
# where L(X, Y) is a linear operator from X to Y (dims [Y, X]).
in_dims = [[2, 3], [0, 1]]
out_dims = [[3, 4], [5, 6]]
dims = [out_dims, in_dims]
# To make the expected shape, we want the left and right spaces to each
# be flipped, then the whole thing flattened.
shape = (5, 6, 3, 4, 0, 1, 2, 3)
assert_equal(dims_to_tensor_shape(dims), shape)
def test_dims_to_tensor_shape():
# Dims for a superoperator:
# L(L(C⁰ × C¹, C² × C³), L(C³ × C⁴, C⁵ × C⁶)),
# where L(X, Y) is a linear operator from X to Y (dims [Y, X]).
in_dims = [[2, 3], [0, 1]]
out_dims = [[3, 4], [5, 6]]
dims = [out_dims, in_dims]
# To make the expected shape, we want the left and right spaces to each
# be flipped, then the whole thing flattened.
shape = (5, 6, 3, 4, 0, 1, 2, 3)
assert_equal(
dims_to_tensor_shape(dims),
shape
)
def tensor_swap(q_oper, *pairs):
"""Transposes one or more pairs of indices of a Qobj.
Note that this uses dense representations and thus
should *not* be used for very large Qobjs.
Parameters
----------
pairs : tuple
One or more tuples ``(i, j)`` indicating that the
``i`` and ``j`` dimensions of the original qobj
should be swapped.
Returns
-------
sqobj : Qobj
The original Qobj with all named index pairs swapped with each other
"""
dims = q_oper.dims
tensor_pairs = dims_idxs_to_tensor_idxs(dims, pairs)
data = q_oper.data.toarray()
# Reshape into tensor indices
data = data.reshape(dims_to_tensor_shape(dims))
# Now permute the dims list so we know how to get back.
flat_dims = flatten(dims)
perm = list(range(len(flat_dims)))
for i, j in pairs:
flat_dims[i], flat_dims[j] = flat_dims[j], flat_dims[i]
for i, j in tensor_pairs:
perm[i], perm[j] = perm[j], perm[i]
dims = unflatten(flat_dims, enumerate_flat(dims))
# Next, permute the actual indices of the dense tensor.
data = data.transpose(perm)
# Reshape back, using the left and right of dims.
data = data.reshape(list(map(np.prod, dims)))
return Qobj(inpt=data, dims=dims, superrep=q_oper.superrep)
def tensor_swap(q_oper, *pairs):
"""Transposes one or more pairs of indices of a Qobj.
Note that this uses dense representations and thus
should *not* be used for very large Qobjs.
Parameters
----------
pairs : tuple
One or more tuples ``(i, j)`` indicating that the
``i`` and ``j`` dimensions of the original qobj
should be swapped.
Returns
-------
sqobj : Qobj
The original Qobj with all named index pairs swapped with each other
"""
dims = q_oper.dims
tensor_pairs = dims_idxs_to_tensor_idxs(dims, pairs)
data = q_oper.data.toarray()
# Reshape into tensor indices
data = data.reshape(dims_to_tensor_shape(dims))
# Now permute the dims list so we know how to get back.
flat_dims = flatten(dims)
perm = list(range(len(flat_dims)))
for i, j in pairs:
flat_dims[i], flat_dims[j] = flat_dims[j], flat_dims[i]
for i, j in tensor_pairs:
perm[i], perm[j] = perm[j], perm[i]
dims = unflatten(flat_dims, enumerate_flat(dims))
# Next, permute the actual indices of the dense tensor.
data = data.transpose(perm)
# Reshape back, using the left and right of dims.
data = data.reshape(list(map(np.prod, dims)))
return Qobj(inpt=data, dims=dims, superrep=q_oper.superrep)
def test_dims_to_tensor_shape(self, indices):
assert dims_to_tensor_shape(indices.base) == indices.shape
