Source code for pennylane.templates.subroutines.adder

# Copyright 2024 Xanadu Quantum Technologies Inc.

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"""
Contains the Adder template.
"""

import pennylane as qml
from pennylane.operation import Operation


[docs]class Adder(Operation): r"""Performs the in-place modular addition operation. This operator performs the modular addition by an integer :math:`k` modulo :math:`mod` in the computational basis: .. math:: \text{Adder}(k, mod) |x \rangle = | x+k \; \text{mod} \; mod \rangle. The implementation is based on the quantum Fourier transform method presented in `arXiv:2311.08555 <https://arxiv.org/abs/2311.08555>`_. .. note:: To obtain the correct result, :math:`x` must be smaller than :math:`mod`. .. seealso:: :class:`~.PhaseAdder` and :class:`~.OutAdder`. Args: k (int): the number that needs to be added x_wires (Sequence[int]): the wires the operation acts on. The number of wires must be enough for encoding `x` in the computational basis. The number of wires also limits the maximum value for `mod`. mod (int): the modulo for performing the addition. If not provided, it will be set to its maximum value, :math:`2^{\text{len(x_wires)}}`. work_wires (Sequence[int]): the auxiliary wires to use for the addition. The work wires are not needed if :math:`mod=2^{\text{len(x_wires)}}`, otherwise two work wires should be provided. Defaults to ``None``. **Example** This example computes the sum of two integers :math:`x=8` and :math:`k=5` modulo :math:`mod=15`. .. code-block:: x = 8 k = 5 mod = 15 x_wires =[0,1,2,3] work_wires=[4,5] dev = qml.device("default.qubit", shots=1) @qml.qnode(dev) def circuit(): qml.BasisEmbedding(x, wires=x_wires) qml.Adder(k, x_wires, mod, work_wires) return qml.sample(wires=x_wires) .. code-block:: pycon >>> print(circuit()) [1 1 0 1] The result, :math:`[1 1 0 1]`, is the binary representation of :math:`8 + 5 \; \text{modulo} \; 15 = 13`. .. details:: :title: Usage Details This template takes as input two different sets of wires. The first one is ``x_wires``, used to encode the integer :math:`x < \text{mod}` in the Fourier basis. To represent :math:`x`, ``x_wires`` must include at least :math:`\lceil \log_2(x) \rceil` wires. After the modular addition, the result can be as large as :math:`\text{mod} - 1`, requiring at least :math:`\lceil \log_2(\text{mod}) \rceil` wires. Since :math:`x < \text{mod}`, :math:`\lceil \log_2(\text{mod}) \rceil` is a sufficient length for ``x_wires`` to cover all possible inputs and outputs. The second set of wires is ``work_wires`` which consist of the auxiliary qubits used to perform the modular addition operation. - If :math:`mod = 2^{\text{len(x_wires)}}`, there will be no need for ``work_wires``, hence ``work_wires=None``. This is the case by default. - If :math:`mod \neq 2^{\text{len(x_wires)}}`, two ``work_wires`` have to be provided. Note that the ``Adder`` template allows us to perform modular addition in the computational basis. However if one just wants to perform standard addition (with no modulo), that would be equivalent to setting the modulo :math:`mod` to a large enough value to ensure that :math:`x+k < mod`. """ grad_method = None def __init__( self, k, x_wires, mod=None, work_wires=None, id=None ): # pylint: disable=too-many-arguments x_wires = qml.wires.Wires(x_wires) num_works_wires = 0 if work_wires is None else len(work_wires) if mod is None: mod = 2 ** len(x_wires) elif mod != 2 ** len(x_wires) and num_works_wires != 2: raise ValueError(f"If mod is not 2^{len(x_wires)}, two work wires should be provided") if not isinstance(k, int) or not isinstance(mod, int): raise ValueError("Both k and mod must be integers") if work_wires is not None: if any(wire in work_wires for wire in x_wires): raise ValueError("None of the wires in work_wires should be included in x_wires.") if mod > 2 ** len(x_wires): raise ValueError( "Adder must have enough x_wires to represent mod. The maximum mod " f"with len(x_wires)={len(x_wires)} is {2 ** len(x_wires)}, but received {mod}." ) all_wires = ( qml.wires.Wires(x_wires) + qml.wires.Wires(work_wires) if work_wires else qml.wires.Wires(x_wires) ) self.hyperparameters["k"] = k self.hyperparameters["mod"] = mod self.hyperparameters["work_wires"] = qml.wires.Wires(work_wires) self.hyperparameters["x_wires"] = x_wires super().__init__(wires=all_wires, id=id) @property def num_params(self): return 0 def _flatten(self): metadata = tuple((key, value) for key, value in self.hyperparameters.items()) return tuple(), metadata @classmethod def _unflatten(cls, data, metadata): hyperparams_dict = dict(metadata) return cls(**hyperparams_dict)
[docs] def map_wires(self, wire_map: dict): new_dict = { key: [wire_map.get(w, w) for w in self.hyperparameters[key]] for key in ["x_wires", "work_wires"] } return Adder( self.hyperparameters["k"], new_dict["x_wires"], self.hyperparameters["mod"], new_dict["work_wires"], )
[docs] def decomposition(self): # pylint: disable=arguments-differ return self.compute_decomposition(**self.hyperparameters)
@classmethod def _primitive_bind_call(cls, *args, **kwargs): return cls._primitive.bind(*args, **kwargs)
[docs] @staticmethod def compute_decomposition(k, x_wires, mod, work_wires): # pylint: disable=arguments-differ r"""Representation of the operator as a product of other operators. Args: k (int): the number that needs to be added x_wires (Sequence[int]): the wires the operation acts on. The number of wires must be enough for encoding `x` in the computational basis. The number of wires also limits the maximum value for `mod`. mod (int): the modulo for performing the addition. If not provided, it will be set to its maximum value, :math:`2^{\text{len(x_wires)}}`. work_wires (Sequence[int]): the auxiliary wires to use for the addition. The work wires are not needed if :math:`mod=2^{\text{len(x_wires)}}`, otherwise two work wires should be provided. Defaults to ``None``. Returns: list[.Operator]: Decomposition of the operator **Example** >>> qml.Adder.compute_decomposition(k=2, x_wires=[0,1,2], mod=8, work_wires=[3]) [QFT(wires=[0, 1, 2]), PhaseAdder(wires=[0, 1, 2]), Adjoint(QFT(wires=[0, 1, 2]))] """ op_list = [] if mod == 2 ** len(x_wires): qft_wires = x_wires work_wire = None else: qft_wires = work_wires[:1] + x_wires work_wire = work_wires[1:] op_list.append(qml.QFT(qft_wires)) op_list.append(qml.PhaseAdder(k, qft_wires, mod, work_wire)) op_list.append(qml.adjoint(qml.QFT)(qft_wires)) return op_list