Source code for pennylane.templates.subroutines.interferometer

# 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.
r"""
Contains the ``Interferometer`` template.
"""
from itertools import product
import pennylane as qml

# pylint: disable-msg=too-many-branches,too-many-arguments,protected-access
from pennylane.ops import Beamsplitter, Rotation
from pennylane.wires import Wires
from pennylane.operation import CVOperation, AnyWires


[docs]class Interferometer(CVOperation): r"""General linear interferometer, an array of beamsplitters and phase shifters. For :math:`M` wires, the general interferometer is specified by providing :math:`M(M-1)/2` transmittivity angles :math:`\theta` and the same number of phase angles :math:`\phi`, as well as :math:`M-1` additional rotation parameters :math:`\varphi`. By specifying the keyword argument ``mesh``, the scheme used to implement the interferometer may be adjusted: * ``mesh='rectangular'`` (default): uses the scheme described in `Clements et al. <https://dx.doi.org/10.1364/OPTICA.3.001460>`__, resulting in a *rectangular* array of :math:`M(M-1)/2` beamsplitters arranged in :math:`M` slices and ordered from left to right and top to bottom in each slice. The first beamsplitter acts on wires :math:`0` and :math:`1`: .. figure:: ../../_static/clements.png :align: center :width: 30% :target: javascript:void(0); * ``mesh='triangular'``: uses the scheme described in `Reck et al. <https://dx.doi.org/10.1103/PhysRevLett.73.58>`__, resulting in a *triangular* array of :math:`M(M-1)/2` beamsplitters arranged in :math:`2M-3` slices and ordered from left to right and top to bottom. The first and fourth beamsplitters act on wires :math:`M-1` and :math:`M`, the second on :math:`M-2` and :math:`M-1`, and the third on :math:`M-3` and :math:`M-2`, and so on. .. figure:: ../../_static/reck.png :align: center :width: 30% :target: javascript:void(0); In both schemes, the network of :class:`~pennylane.ops.Beamsplitter` operations is followed by :math:`M` local :class:`~pennylane.ops.Rotation` Operations. The rectangular decomposition is generally advantageous, as it has a lower circuit depth (:math:`M` vs :math:`2M-3`) and optical depth than the triangular decomposition, resulting in reduced optical loss. This is an example of a 4-mode interferometer with beamsplitters :math:`B` and rotations :math:`R`, using ``mesh='rectangular'``: .. figure:: ../../_static/layer_interferometer.png :align: center :width: 60% :target: javascript:void(0); .. note:: The decomposition as formulated in `Clements et al. <https://dx.doi.org/10.1364/OPTICA.3.001460>`__ uses a different convention for a beamsplitter :math:`T(\theta, \phi)` than PennyLane, namely: .. math:: T(\theta, \phi) = BS(\theta, 0) R(\phi) For the universality of the decomposition, the used convention is irrelevant, but for a given set of angles the resulting interferometers will be different. If an interferometer consistent with the convention from `Clements et al. <https://dx.doi.org/10.1364/OPTICA.3.001460>`__ is needed, the optional keyword argument ``beamsplitter='clements'`` can be specified. This will result in each :class:`~pennylane.ops.Beamsplitter` being preceded by a :class:`~pennylane.ops.Rotation` and thus increase the number of elementary operations in the circuit. Args: theta (tensor_like): size :math:`(M(M-1)/2,)` tensor of transmittivity angles :math:`\theta` phi (tensor_like): size :math:`(M(M-1)/2,)` tensor of phase angles :math:`\phi` varphi (tensor_like): size :math:`(M,)` tensor of rotation angles :math:`\varphi` wires (Iterable or Wires): Wires that the template acts on. Accepts an iterable of numbers or strings, or a Wires object. mesh (string): the type of mesh to use beamsplitter (str): if ``clements``, the beamsplitter convention from Clements et al. 2016 (https://dx.doi.org/10.1364/OPTICA.3.001460) is used; if ``pennylane``, the beamsplitter is implemented via PennyLane's ``Beamsplitter`` operation. Raises: ValueError: if inputs do not have the correct format Example: The template requires :math:`3` sets of parameters. The ``mesh`` and ``beamsplitter`` keyword arguments are optional and have ``'rectangular'`` and ``'pennylane'`` as default values. .. code-block:: python dev = qml.device('default.gaussian', wires=4) @qml.qnode(dev) def circuit(params): qml.Interferometer(*params, wires=range(4)) return qml.expval(qml.Identity(0)) shapes = [[6, ], [6, ], [4, ]] params = [] for shape in shapes: params.append(np.random.random(shape)) Using these random parameters, the resulting circuit is: >>> print(qml.draw(circuit, expansion_strategy="device")(params)) 0: ─╭BS(0.97,0.09)────────────────╭BS(0.89,0.33)──R(0.83)────────────────┤ <I> 1: ─╰BS(0.97,0.09)─╭BS(0.94,0.05)─╰BS(0.89,0.33)─╭BS(0.92,0.27)──R(0.36)─┤ 2: ─╭BS(0.78,0.20)─╰BS(0.94,0.05)─╭BS(0.60,0.39)─╰BS(0.92,0.27)──R(0.28)─┤ 3: ─╰BS(0.78,0.20)────────────────╰BS(0.60,0.39)──R(0.54)────────────────┤ Using different values for optional arguments: .. code-block:: python @qml.qnode(dev) def circuit(params): qml.Interferometer(*params, wires=range(4), mesh='triangular', beamsplitter='clements') return qml.expval(qml.Identity(0)) shapes = [[6, ], [6, ], [4, ]] params = [] for shape in shapes: params.append(np.random.random(shape)) print(qml.draw(circuit, expansion_strategy="device")(params)) .. code-block:: 0: ──R(0.71)───────────────────────────────╭BS(0.07,0.00)──R(0.36)────────────────────────────── 1: ──R(0.82)────────────────╭BS(0.80,0.00)─╰BS(0.07,0.00)──R(0.77)───────╭BS(0.77,0.00)──R(0.12) 2: ──R(0.01)─╭BS(0.14,0.00)─╰BS(0.80,0.00)──R(0.73)───────╭BS(0.99,0.00)─╰BS(0.77,0.00)──R(0.07) 3: ──────────╰BS(0.14,0.00)───────────────────────────────╰BS(0.99,0.00)──────────────────────── ──────────────────────────┤ <I> ──────────────────────────┤ ──╭BS(0.20,0.00)──R(0.86)─┤ ──╰BS(0.20,0.00)──R(0.62)─┤ """ num_wires = AnyWires grad_method = None def __init__( self, theta, phi, varphi, wires, mesh="rectangular", beamsplitter="pennylane", do_queue=True, id=None, ): wires = Wires(wires) n_wires = len(wires) shape_theta_phi = n_wires * (n_wires - 1) // 2 shape = qml.math.shape(theta) if shape != (shape_theta_phi,): raise ValueError(f"Theta must be of shape {(shape_theta_phi,)}; got {shape}.") shape = qml.math.shape(phi) if shape != (shape_theta_phi,): raise ValueError(f"Phi must be of shape {(shape_theta_phi,)}; got {shape}.") shape_varphi = qml.math.shape(varphi) if shape_varphi != (n_wires,): raise ValueError(f"Varphi must be of shape {(n_wires,)}; got {shape_varphi}.") self._hyperparameters = { "mesh": mesh, "beamsplitter": beamsplitter, } super().__init__(theta, phi, varphi, wires=wires, do_queue=do_queue, id=id)
[docs] @staticmethod def compute_decomposition( theta, phi, varphi, wires, mesh, beamsplitter ): # pylint: disable=arguments-differ r"""Representation of the operator as a product of other operators. .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:`~.Interferometer.decomposition`. Args: theta (tensor_like): size :math:`(M(M-1)/2,)` tensor of transmittivity angles phi (tensor_like): size :math:`(M(M-1)/2,)` tensor of phase angles varphi (tensor_like): size :math:`(M,)` tensor of rotation angles wires (Any or Iterable[Any]): wires that the operator acts on mesh (string): the type of mesh to use beamsplitter (str): beamsplitter convention Returns: list[.Operator]: decomposition of the operator """ wires = Wires(wires) M = len(wires) op_list = [] if M == 1: # the interferometer is a single rotation op_list.append(Rotation(varphi[0], wires=wires[0])) else: n = 0 # keep track of free parameters if mesh == "rectangular": # Apply the Clements beamsplitter array # The array depth is N for m, (k, (w1, w2)) in product(range(M), enumerate(zip(wires[:-1], wires[1:]))): # skip even or odd pairs depending on layer if (m + k) % 2 != 1: if beamsplitter == "clements": op_list.append(Rotation(phi[n], wires=Wires(w1))) op_list.append(Beamsplitter(theta[n], 0, wires=Wires([w1, w2]))) elif beamsplitter == "pennylane": op_list.append(Beamsplitter(theta[n], phi[n], wires=Wires([w1, w2]))) else: raise ValueError(f"did not recognize beamsplitter {beamsplitter}") n += 1 elif mesh == "triangular": # apply the Reck beamsplitter array # The array depth is 2*N-3 for m in range(2 * M - 3): for k in range(abs(m + 1 - (M - 1)), M - 1, 2): if beamsplitter == "clements": op_list.append(Rotation(phi[n], wires=wires[k])) op_list.append( Beamsplitter(theta[n], 0, wires=wires.subset([k, k + 1])) ) elif beamsplitter == "pennylane": op_list.append( Beamsplitter(theta[n], phi[n], wires=wires.subset([k, k + 1])) ) else: raise ValueError(f"did not recognize beamsplitter {beamsplitter} ") n += 1 else: raise ValueError(f"did not recognize mesh {mesh}") # apply the final local phase shifts to all modes for i in range(qml.math.shape(varphi)[0]): act_on = wires[i] op_list.append(Rotation(varphi[i], wires=act_on)) return op_list
[docs] @staticmethod def shape(n_wires): r"""Returns a list of shapes for the 3 parameter tensors. Args: n_wires (int): number of wires Returns: list[tuple[int]]: list of shapes """ shape_theta_phi = n_wires * (n_wires - 1) // 2 shapes = [(shape_theta_phi,)] * 2 + [(n_wires,)] return shapes