Source code for pennylane.utils
# Copyright 2018-2021 Xanadu Quantum Technologies Inc.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
This module contains utilities and auxiliary functions which are shared
across the PennyLane submodules.
"""
# pylint: disable=protected-access,too-many-branches
from collections.abc import Iterable
import functools
import inspect
import numbers
import warnings
import numpy as np
import pennylane as qml
[docs]def sparse_hamiltonian(H, wires=None):
r"""Warning: This method is deprecated. Use :meth:~.Hamiltonian.sparse_matrix` instead.
Computes the sparse matrix representation a Hamiltonian in the computational basis.
Args:
H (~.Hamiltonian): Hamiltonian operator for which the matrix representation should be
computed
wires (Iterable): Wire labels that indicate the order of wires according to which the matrix
is constructed. If not profided, ``H.wires`` is used.
Returns:
csr_matrix: a sparse matrix in scipy Compressed Sparse Row (CSR) format with dimension
:math:`(2^n, 2^n)`, where :math:`n` is the number of wires
**Example:**
This function can be used by passing a `qml.Hamiltonian` object as:
>>> coeffs = [1, -0.45]
>>> obs = [qml.PauliZ(0) @ qml.PauliZ(1), qml.PauliY(0) @ qml.PauliZ(1)]
>>> H = qml.Hamiltonian(coeffs, obs)
>>> H_sparse = sparse_hamiltonian(H)
>>> H_sparse
<4x4 sparse matrix of type '<class 'numpy.complex128'>'
with 2 stored elements in COOrdinate format>
The resulting sparse matrix can be either used directly or transformed into a numpy array:
>>> H_sparse.toarray()
array([[ 1.+0.j , 0.+0.j , 0.+0.45j, 0.+0.j ],
[ 0.+0.j , -1.+0.j , 0.+0.j , 0.-0.45j],
[ 0.-0.45j, 0.+0.j , -1.+0.j , 0.+0.j ],
[ 0.+0.j , 0.+0.45j, 0.+0.j , 1.+0.j ]])
"""
warnings.warn(
"The method sparse_hamiltonian is deprecated. Please use the method "
"sparse_matrix of the Hamiltonian operator instead.",
UserWarning,
)
if not isinstance(H, qml.Hamiltonian):
raise TypeError("Passed Hamiltonian must be of type `qml.Hamiltonian`")
if wires is None: # not sure if this if-else is still necessary
wires = H.wires
else:
wires = qml.wires.Wires(wires)
return H.sparse_matrix(wire_order=wires)
def _flatten(x):
"""Iterate recursively through an arbitrarily nested structure in depth-first order.
See also :func:`_unflatten`.
Args:
x (array, Iterable, Any): each element of an array or an Iterable may itself be any of these types
Yields:
Any: elements of x in depth-first order
"""
if isinstance(x, np.ndarray):
yield from _flatten(x.flat) # should we allow object arrays? or just "yield from x.flat"?
elif isinstance(x, qml.wires.Wires):
# Reursive calls to flatten `Wires` will cause infinite recursion (`Wires` atoms are `Wires`).
# Since Wires are always flat, just yield.
for item in x:
yield item
elif isinstance(x, Iterable) and not isinstance(x, (str, bytes)):
for item in x:
yield from _flatten(item)
else:
yield x
def _unflatten(flat, model):
"""Restores an arbitrary nested structure to a flattened iterable.
See also :func:`_flatten`.
Args:
flat (array): 1D array of items
model (array, Iterable, Number): model nested structure
Raises:
TypeError: if ``model`` contains an object of unsupported type
Returns:
Union[array, list, Any], array: first elements of flat arranged into the nested
structure of model, unused elements of flat
"""
if isinstance(model, (numbers.Number, str)):
return flat[0], flat[1:]
if isinstance(model, np.ndarray):
idx = model.size
res = np.array(flat)[:idx].reshape(model.shape)
return res, flat[idx:]
if isinstance(model, Iterable):
res = []
for x in model:
val, flat = _unflatten(flat, x)
res.append(val)
return res, flat
raise TypeError(f"Unsupported type in the model: {type(model)}")
[docs]def unflatten(flat, model):
"""Wrapper for :func:`_unflatten`.
Args:
flat (array): 1D array of items
model (array, Iterable, Number): model nested structure
Raises:
ValueError: if ``flat`` has more elements than ``model``
"""
# pylint:disable=len-as-condition
res, tail = _unflatten(np.asarray(flat), model)
if len(tail) != 0:
raise ValueError("Flattened iterable has more elements than the model.")
return res
def _inv_dict(d):
"""Reverse a dictionary mapping.
Returns multimap where the keys are the former values,
and values are sets of the former keys.
Args:
d (dict[a->b]): mapping to reverse
Returns:
dict[b->set[a]]: reversed mapping
"""
ret = {}
for k, v in d.items():
ret.setdefault(v, set()).add(k)
return ret
def _get_default_args(func):
"""Get the default arguments of a function.
Args:
func (callable): a function
Returns:
dict[str, tuple]: mapping from argument name to (positional idx, default value)
"""
signature = inspect.signature(func)
return {
k: (idx, v.default)
for idx, (k, v) in enumerate(signature.parameters.items())
if v.default is not inspect.Parameter.empty
}
[docs]@functools.lru_cache()
def pauli_eigs(n):
r"""Eigenvalues for :math:`A^{\otimes n}`, where :math:`A` is
Pauli operator, or shares its eigenvalues.
As an example if n==2, then the eigenvalues of a tensor product consisting
of two matrices sharing the eigenvalues with Pauli matrices is returned.
Args:
n (int): the number of qubits the matrix acts on
Returns:
list: the eigenvalues of the specified observable
"""
if n == 1:
return np.array([1, -1])
return np.concatenate([pauli_eigs(n - 1), -pauli_eigs(n - 1)])
[docs]def expand_vector(vector, original_wires, expanded_wires):
r"""Expand a vector to more wires.
Args:
vector (array): :math:`2^n` vector where n = len(original_wires).
original_wires (Sequence[int]): original wires of vector
expanded_wires (Union[Sequence[int], int]): expanded wires of vector, can be shuffled
If a single int m is given, corresponds to list(range(m))
Returns:
array: :math:`2^m` vector where m = len(expanded_wires).
"""
if isinstance(expanded_wires, numbers.Integral):
expanded_wires = list(range(expanded_wires))
N = len(original_wires)
M = len(expanded_wires)
D = M - N
if not set(expanded_wires).issuperset(original_wires):
raise ValueError("Invalid target subsystems provided in 'original_wires' argument.")
if qml.math.shape(vector) != (2**N,):
raise ValueError("Vector parameter must be of length 2**len(original_wires)")
dims = [2] * N
tensor = qml.math.reshape(vector, dims)
if D > 0:
extra_dims = [2] * D
ones = qml.math.ones(2**D).reshape(extra_dims)
expanded_tensor = qml.math.tensordot(tensor, ones, axes=0)
else:
expanded_tensor = tensor
wire_indices = []
for wire in original_wires:
wire_indices.append(expanded_wires.index(wire))
wire_indices = np.array(wire_indices)
# Order tensor factors according to wires
original_indices = np.array(range(N))
expanded_tensor = qml.math.moveaxis(
expanded_tensor, tuple(original_indices), tuple(wire_indices)
)
return qml.math.reshape(expanded_tensor, 2**M)
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