Source code for pennylane.templates.tensornetworks.mera
# 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.
"""
Contains the MERA template.
"""
# pylint: disable-msg=too-many-branches,too-many-arguments,protected-access
import warnings
from typing import Callable
import numpy as np
import pennylane as qml
from pennylane.operation import Operation, AnyWires
def compute_indices(wires, n_block_wires):
"""Generate a list containing the wires for each block.
Args:
wires (Iterable): wires that the template acts on
n_block_wires (int): number of wires per block
Returns:
layers (array): array of wire labels for each block
"""
n_wires = len(wires)
if n_block_wires % 2 != 0:
raise ValueError(f"n_block_wires must be an even integer; got {n_block_wires}")
if n_block_wires < 2:
raise ValueError(
f"number of wires in each block must be larger than or equal to 2; got n_block_wires = {n_block_wires}"
)
if n_block_wires > n_wires:
raise ValueError(
f"n_block_wires must be smaller than or equal to the number of wires; "
f"got n_block_wires = {n_block_wires} and number of wires = {n_wires}"
)
if not np.log2(n_wires / n_block_wires).is_integer(): # pylint:disable=no-member
warnings.warn(
f"The number of wires should be n_block_wires times 2^n; got n_wires/n_block_wires = {n_wires/n_block_wires}"
)
# number of layers in MERA
n_layers = np.floor(np.log2(n_wires / n_block_wires)).astype(int) * 2 + 1
wires_list = []
wires_list.append(list(wires[0:n_block_wires]))
highest_index = n_block_wires
# compute block indices for all layers
for i in range(n_layers - 1):
# number of blocks in previous layer
n_elements_pre = 2 ** ((i + 1) // 2)
if i % 2 == 0:
# layer with new wires
new_list = []
list_len = len(wires_list)
for j in range(list_len - n_elements_pre, list_len):
new_wires = [
wires[k] for k in range(highest_index, highest_index + n_block_wires // 2)
]
highest_index += n_block_wires // 2
new_list.append(wires_list[j][0 : n_block_wires // 2] + new_wires)
new_wires = [
wires[k] for k in range(highest_index, highest_index + n_block_wires // 2)
]
highest_index += n_block_wires // 2
new_list.append(new_wires + wires_list[j][n_block_wires // 2 : :])
wires_list = wires_list + new_list
else:
# layer only using previous wires
list_len = len(wires_list)
new_list = []
for j in range(list_len - n_elements_pre, list_len - 1):
new_list.append(
wires_list[j][n_block_wires // 2 : :]
+ wires_list[j + 1][0 : n_block_wires // 2]
)
new_list.append(
wires_list[j + 1][n_block_wires // 2 : :]
+ wires_list[list_len - n_elements_pre][0 : n_block_wires // 2]
)
wires_list = wires_list + new_list
return tuple(tuple(l) for l in wires_list[::-1])
[docs]class MERA(Operation):
"""The MERA template broadcasts an input circuit across many wires following the
architecture of a multi-scale entanglement renormalization ansatz tensor network.
This architecture can be found in `arXiv:quant-ph/0610099 <https://arxiv.org/abs/quant-ph/0610099>`_
and closely resembles `quantum convolutional neural networks <https://arxiv.org/abs/1810.03787>`_.
The argument ``block`` is a user-defined quantum circuit. Each ``block`` may depend on a different set of parameters.
These are passed as a list by the ``template_weights`` argument.
For more details, see *Usage Details* below.
Args:
wires (Iterable): wires that the template acts on
n_block_wires (int): number of wires per block
block (Callable): quantum circuit that defines a block
n_params_block (int): the number of parameters in a block
template_weights (Sequence): list containing the weights for all blocks
.. details::
:title: Usage Details
In general, the block takes D parameters and **must** have the following signature:
.. code-block:: python
unitary(parameter1, parameter2, ... parameterD, wires)
For a block with multiple parameters, ``n_params_block`` is equal to the number of parameters in ``block``.
For a block with a single parameter, ``n_params_block`` is equal to the length of the parameter array.
To avoid using ragged arrays, all block parameters should have the same dimension.
The length of the ``template_weights`` argument should match the number of blocks.
The expected number of blocks can be obtained from ``qml.MERA.get_n_blocks(wires, n_block_wires)``.
This example demonstrates the use of ``MERA`` for a simple block.
.. code-block:: python
import pennylane as qml
import numpy as np
def block(weights, wires):
qml.CNOT(wires=[wires[0],wires[1]])
qml.RY(weights[0], wires=wires[0])
qml.RY(weights[1], wires=wires[1])
n_wires = 4
n_block_wires = 2
n_params_block = 2
n_blocks = qml.MERA.get_n_blocks(range(n_wires),n_block_wires)
template_weights = [[0.1,-0.3]]*n_blocks
dev= qml.device('default.qubit',wires=range(n_wires))
@qml.qnode(dev)
def circuit(template_weights):
qml.MERA(range(n_wires),n_block_wires,block, n_params_block, template_weights)
return qml.expval(qml.Z(1))
It may be necessary to reorder the wires to see the MERA architecture clearly:
>>> print(qml.draw(circuit, expansion_strategy='device', wire_order=[2,0,1,3])(template_weights))
2: ───────────────╭●──RY(0.10)──╭X──RY(-0.30)───────────────┤
0: ─╭X──RY(-0.30)─│─────────────╰●──RY(0.10)──╭●──RY(0.10)──┤
1: ─╰●──RY(0.10)──│─────────────╭X──RY(-0.30)─╰X──RY(-0.30)─┤ <Z>
3: ───────────────╰X──RY(-0.30)─╰●──RY(0.10)────────────────┤
"""
num_wires = AnyWires
grad_method = None
@property
def num_params(self):
return 1
@classmethod
def _unflatten(cls, data, metadata):
new_op = cls.__new__(cls)
new_op._hyperparameters = dict(metadata[1])
Operation.__init__(new_op, data, wires=metadata[0])
return new_op
def __init__(
self,
wires,
n_block_wires,
block: Callable,
n_params_block,
template_weights=None,
id=None,
):
ind_gates = compute_indices(wires, n_block_wires)
n_wires = len(wires)
shape = qml.math.shape(template_weights) # (n_params_block, n_blocks)
n_blocks = int(2 ** (np.floor(np.log2(n_wires / n_block_wires)) + 2) - 3)
if shape == ():
template_weights = np.random.rand(n_params_block, n_blocks)
else:
if shape[0] != n_blocks:
raise ValueError(
f"Weights tensor must have first dimension of length {n_blocks}; got {shape[0]}"
)
if shape[-1] != n_params_block:
raise ValueError(
f"Weights tensor must have last dimension of length {n_params_block}; got {shape[-1]}"
)
self._hyperparameters = {"ind_gates": ind_gates, "block": block}
super().__init__(template_weights, wires=wires, id=id)
[docs] @staticmethod
def compute_decomposition(
weights, wires, block, ind_gates
): # pylint: disable=arguments-differ,unused-argument
r"""Representation of the operator as a product of other operators.
.. math:: O = O_1 O_2 \dots O_n.
.. seealso:: :meth:`~.MERA.decomposition`.
Args:
weights (list[tensor_like]): list containing the weights for all blocks
wires (Iterable): wires that the template acts on
block (Callable): quantum circuit that defines a block
ind_gates (array): array of wire indices
Returns:
list[.Operator]: decomposition of the operator
"""
op_list = []
block_gen = qml.tape.make_qscript(block)
if block.__code__.co_argcount > 2:
for idx, w in enumerate(ind_gates):
op_list += block_gen(*weights[idx], wires=w)
elif block.__code__.co_argcount == 2:
for idx, w in enumerate(ind_gates):
op_list += block_gen(weights[idx], wires=w)
else:
for w in ind_gates:
op_list += block_gen(wires=w)
return [qml.apply(op) for op in op_list] if qml.QueuingManager.recording() else op_list
[docs] @staticmethod
def get_n_blocks(wires, n_block_wires):
"""Returns the expected number of blocks for a set of wires and number of wires per block.
Args:
wires (Sequence): number of wires the template acts on
n_block_wires (int): number of wires per block
Returns:
n_blocks (int): number of blocks; expected length of the template_weights argument
"""
n_wires = len(wires)
if not np.log2(n_wires / n_block_wires).is_integer(): # pylint:disable=no-member
warnings.warn(
f"The number of wires should be n_block_wires times 2^n; got n_wires/n_block_wires = {n_wires/n_block_wires}"
)
if n_block_wires > n_wires:
raise ValueError(
f"n_block_wires must be smaller than or equal to the number of wires; got n_block_wires = {n_block_wires} and number of wires = {n_wires}"
)
n_blocks = 2 ** (np.floor(np.log2(n_wires / n_block_wires)) + 2) - 3
return int(n_blocks)
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