# Source code for pennylane.ops.qubit.parametric_ops_multi_qubit

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# pylint: disable=too-many-arguments
"""
This submodule contains the discrete-variable quantum operations that are the
core parameterized gates.
"""
# pylint:disable=abstract-method,arguments-differ,protected-access,invalid-overridden-method
import functools
from operator import matmul
from typing import Optional, Union

import numpy as np

import pennylane as qml
from pennylane.math import expand_matrix
from pennylane.operation import AnyWires, FlatPytree, Operation
from pennylane.typing import TensorLike
from pennylane.utils import pauli_eigs
from pennylane.wires import Wires, WiresLike

from .non_parametric_ops import Hadamard, PauliX, PauliY, PauliZ
from .parametric_ops_single_qubit import RX, RY, RZ, PhaseShift, _can_replace, stack_last

[docs]class MultiRZ(Operation): r""" Arbitrary multi Z rotation. .. math:: MultiRZ(\theta) = \exp\left(-i \frac{\theta}{2} Z^{\otimes n}\right) **Details:** * Number of wires: Any * Number of parameters: 1 * Number of dimensions per parameter: (0,) * Gradient recipe: :math:\frac{d}{d\theta}f(MultiRZ(\theta)) = \frac{1}{2}\left[f(MultiRZ(\theta +\pi/2)) - f(MultiRZ(\theta-\pi/2))\right] where :math:f is an expectation value depending on :math:MultiRZ(\theta). .. note:: If the MultiRZ gate is not supported on the targeted device, PennyLane will decompose the gate using :class:~.RZ and :class:~.CNOT gates. Args: theta (tensor_like or float): rotation angle :math:\theta wires (Sequence[int] or int): the wires the operation acts on id (str or None): String representing the operation (optional) """ num_wires = AnyWires num_params = 1 """int: Number of trainable parameters that the operator depends on.""" ndim_params = (0,) """tuple[int]: Number of dimensions per trainable parameter that the operator depends on.""" grad_method = "A" parameter_frequencies = [(1,)] def _flatten(self) -> FlatPytree: return self.data, (self.wires, tuple()) def __init__(self, theta: TensorLike, wires: WiresLike, id: Optional[str] = None): wires = Wires(wires) self.hyperparameters["num_wires"] = len(wires) super().__init__(theta, wires=wires, id=id)
[docs] @staticmethod def compute_matrix( theta: TensorLike, num_wires: int ) -> TensorLike: # pylint: disable=arguments-differ r"""Representation of the operator as a canonical matrix in the computational basis (static method). The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order. .. seealso:: :meth:~.MultiRZ.matrix Args: theta (tensor_like or float): rotation angle num_wires (int): number of wires the rotation acts on Returns: tensor_like: canonical matrix **Example** >>> qml.MultiRZ.compute_matrix(torch.tensor(0.1), 2) tensor([[0.9988-0.0500j, 0.0000+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j], [0.0000+0.0000j, 0.9988+0.0500j, 0.0000+0.0000j, 0.0000+0.0000j], [0.0000+0.0000j, 0.0000+0.0000j, 0.9988+0.0500j, 0.0000+0.0000j], [0.0000+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j, 0.9988-0.0500j]]) """ eigs = qml.math.convert_like(pauli_eigs(num_wires), theta) if qml.math.get_interface(theta) == "tensorflow": theta = qml.math.cast_like(theta, 1j) eigs = qml.math.cast_like(eigs, 1j) if qml.math.ndim(theta) == 0: return qml.math.diag(qml.math.exp(-0.5j * theta * eigs)) diags = qml.math.exp(qml.math.outer(-0.5j * theta, eigs)) return diags[:, :, np.newaxis] * qml.math.cast_like( qml.math.eye(2**num_wires, like=diags), diags )
[docs] def generator(self) -> "qml.Hamiltonian": return qml.Hamiltonian([-0.5], [functools.reduce(matmul, [PauliZ(w) for w in self.wires])])
[docs] @staticmethod def compute_eigvals( theta: TensorLike, num_wires: int ) -> TensorLike: # pylint: disable=arguments-differ r"""Eigenvalues of the operator in the computational basis (static method). If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger}, the operator can be reconstructed as .. math:: O = U \Sigma U^{\dagger}, where :math:\Sigma is the diagonal matrix containing the eigenvalues. Otherwise, no particular order for the eigenvalues is guaranteed. .. seealso:: :meth:~.MultiRZ.eigvals Args: theta (tensor_like or float): rotation angle num_wires (int): number of wires the rotation acts on Returns: tensor_like: eigenvalues **Example** >>> qml.MultiRZ.compute_eigvals(torch.tensor(0.5), 3) tensor([0.9689-0.2474j, 0.9689+0.2474j, 0.9689+0.2474j, 0.9689-0.2474j, 0.9689+0.2474j, 0.9689-0.2474j, 0.9689-0.2474j, 0.9689+0.2474j]) """ eigs = qml.math.convert_like(pauli_eigs(num_wires), theta) if qml.math.get_interface(theta) == "tensorflow": theta = qml.math.cast_like(theta, 1j) eigs = qml.math.cast_like(eigs, 1j) if qml.math.ndim(theta) == 0: return qml.math.exp(-0.5j * theta * eigs) return qml.math.exp(qml.math.outer(-0.5j * theta, eigs))
[docs] @staticmethod def compute_decomposition( # pylint: disable=arguments-differ,unused-argument theta: TensorLike, wires: WiresLike, **kwargs ) -> list["qml.operation.Operator"]: r"""Representation of the operator as a product of other operators (static method). : .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:~.MultiRZ.decomposition. Args: theta (float): rotation angle :math:\theta wires (Iterable, Wires): the wires the operation acts on Returns: list[Operator]: decomposition into lower level operations **Example:** >>> qml.MultiRZ.compute_decomposition(1.2, wires=(0,1)) [CNOT(wires=[1, 0]), RZ(1.2, wires=[0]), CNOT(wires=[1, 0])] """ ops = [qml.CNOT(wires=(w0, w1)) for w0, w1 in zip(wires[~0:0:-1], wires[~1::-1])] ops.append(RZ(theta, wires=wires[0])) ops += [qml.CNOT(wires=(w0, w1)) for w0, w1 in zip(wires[1:], wires[:~0])] return ops
[docs] def adjoint(self) -> "MultiRZ": return MultiRZ(-self.parameters[0], wires=self.wires)
[docs] def pow(self, z: Union[int, float]) -> list["qml.operation.Operator"]: return [MultiRZ(self.data[0] * z, wires=self.wires)]
[docs] def simplify(self) -> "MultiRZ": theta = self.data[0] % (4 * np.pi) if _can_replace(theta, 0): return qml.Identity(wires=self.wires[0]) return MultiRZ(theta, wires=self.wires)
[docs]class PauliRot(Operation): r""" Arbitrary Pauli word rotation. .. math:: RP(\theta, P) = \exp\left(-i \frac{\theta}{2} P\right) **Details:** * Number of wires: Any * Number of parameters: 1 * Number of dimensions per parameter: (0,) * Gradient recipe: :math:\frac{d}{d\theta}f(RP(\theta)) = \frac{1}{2}\left[f(RP(\theta +\pi/2)) - f(RP(\theta-\pi/2))\right] where :math:f is an expectation value depending on :math:RP(\theta). .. note:: If the PauliRot gate is not supported on the targeted device, PennyLane will decompose the gate using :class:~.RX, :class:~.Hadamard, :class:~.RZ and :class:~.CNOT gates. Args: theta (float): rotation angle :math:\theta pauli_word (string): the Pauli word defining the rotation wires (Sequence[int] or int): the wire the operation acts on id (str or None): String representing the operation (optional) **Example** >>> dev = qml.device('default.qubit', wires=1) >>> @qml.qnode(dev) ... def example_circuit(): ... qml.PauliRot(0.5, 'X', wires=0) ... return qml.expval(qml.Z(0)) >>> print(example_circuit()) 0.8775825618903724 """ num_wires = AnyWires num_params = 1 """int: Number of trainable parameters that the operator depends on.""" ndim_params = (0,) """tuple[int]: Number of dimensions per trainable parameter that the operator depends on.""" do_check_domain = False grad_method = "A" parameter_frequencies = [(1,)] _ALLOWED_CHARACTERS = "IXYZ" _PAULI_CONJUGATION_MATRICES = { "X": Hadamard.compute_matrix(), "Y": RX.compute_matrix(np.pi / 2), "Z": np.array([[1, 0], [0, 1]]), } @classmethod def _primitive_bind_call(cls, theta, pauli_word, wires=None, id=None): return super()._primitive_bind_call(theta, pauli_word=pauli_word, wires=wires, id=id) def __init__( self, theta: TensorLike, pauli_word: str, wires: WiresLike, id: Optional[str] = None, ): super().__init__(theta, wires=wires, id=id) self.hyperparameters["pauli_word"] = pauli_word if not PauliRot._check_pauli_word(pauli_word): raise ValueError( f'The given Pauli word "{pauli_word}" contains characters that are not allowed. ' "Allowed characters are I, X, Y and Z" ) num_wires = 1 if isinstance(wires, int) else len(wires) if not len(pauli_word) == num_wires: raise ValueError( f"The given Pauli word has length {len(pauli_word)}, length " f"{num_wires} was expected for wires {wires}" ) def __repr__(self) -> str: return f"PauliRot({self.data[0]}, {self.hyperparameters['pauli_word']}, wires={self.wires.tolist()})"
[docs] def label( self, decimals: Optional[int] = None, base_label: Optional[str] = None, cache: Optional[dict] = None, ) -> str: r"""A customizable string representation of the operator. Args: decimals=None (int): If None, no parameters are included. Else, specifies how to round the parameters. base_label=None (str): overwrite the non-parameter component of the label cache=None (dict): dictionary that caries information between label calls in the same drawing Returns: str: label to use in drawings **Example:** >>> op = qml.PauliRot(0.1, "XYY", wires=(0,1,2)) >>> op.label() 'RXYY' >>> op.label(decimals=2) 'RXYY\n(0.10)' >>> op.label(base_label="PauliRot") 'PauliRot\n(0.10)' """ pauli_word = self.hyperparameters["pauli_word"] op_label = base_label or ("R" + pauli_word) # TODO[dwierichs]: Implement a proper label for parameter-broadcasted operators if decimals is not None and self.batch_size is None: param_string = f"\n({qml.math.asarray(self.parameters[0]):.{decimals}f})" op_label += param_string return op_label
@staticmethod def _check_pauli_word(pauli_word) -> bool: """Check that the given Pauli word has correct structure. Args: pauli_word (str): Pauli word to be checked Returns: bool: Whether the Pauli word has correct structure. """ return all(pauli in PauliRot._ALLOWED_CHARACTERS for pauli in set(pauli_word))
[docs] @staticmethod def compute_matrix( theta: TensorLike, pauli_word: str ) -> TensorLike: # pylint: disable=arguments-differ r"""Representation of the operator as a canonical matrix in the computational basis (static method). The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order. .. seealso:: :meth:~.PauliRot.matrix Args: theta (tensor_like or float): rotation angle pauli_word (str): string representation of Pauli word Returns: tensor_like: canonical matrix **Example** >>> qml.PauliRot.compute_matrix(0.5, 'X') [[9.6891e-01+4.9796e-18j 2.7357e-17-2.4740e-01j] [2.7357e-17-2.4740e-01j 9.6891e-01+4.9796e-18j]] """ if not PauliRot._check_pauli_word(pauli_word): raise ValueError( f'The given Pauli word "{pauli_word}" contains characters that are not allowed. ' "Allowed characters are I, X, Y and Z" ) interface = qml.math.get_interface(theta) if interface == "tensorflow": theta = qml.math.cast_like(theta, 1j) # Simplest case is if the Pauli is the identity matrix if set(pauli_word) == {"I"}: return qml.GlobalPhase.compute_matrix(0.5 * theta, n_wires=len(pauli_word)) # We first generate the matrix excluding the identity parts and expand it afterwards. # To this end, we have to store on which wires the non-identity parts act non_identity_wires, non_identity_gates = zip( *[(wire, gate) for wire, gate in enumerate(pauli_word) if gate != "I"] ) multi_Z_rot_matrix = MultiRZ.compute_matrix(theta, len(non_identity_gates)) # now we conjugate with Hadamard and RX to create the Pauli string conjugation_matrix = functools.reduce( qml.math.kron, [PauliRot._PAULI_CONJUGATION_MATRICES[gate] for gate in non_identity_gates], ) if interface == "tensorflow": conjugation_matrix = qml.math.cast_like(conjugation_matrix, 1j) # Note: we use einsum with reverse arguments here because it is not multi-dispatched # and the tensordot containing multi_Z_rot_matrix should decide about the interface return expand_matrix( qml.math.einsum( "...jk,ij->...ik", qml.math.tensordot(multi_Z_rot_matrix, conjugation_matrix, axes=[[-1], [0]]), qml.math.conj(conjugation_matrix), ), non_identity_wires, list(range(len(pauli_word))), )
[docs] def generator(self) -> "qml.Hamiltonian": pauli_word = self.hyperparameters["pauli_word"] wire_map = {w: i for i, w in enumerate(self.wires)} return qml.Hamiltonian( [-0.5], [qml.pauli.string_to_pauli_word(pauli_word, wire_map=wire_map)] )
[docs] @staticmethod def compute_eigvals( theta: TensorLike, pauli_word: str ) -> TensorLike: # pylint: disable=arguments-differ r"""Eigenvalues of the operator in the computational basis (static method). If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger}, the operator can be reconstructed as .. math:: O = U \Sigma U^{\dagger}, where :math:\Sigma is the diagonal matrix containing the eigenvalues. Otherwise, no particular order for the eigenvalues is guaranteed. .. seealso:: :meth:~.PauliRot.eigvals Returns: tensor_like: eigenvalues **Example** >>> qml.PauliRot.compute_eigvals(torch.tensor(0.5), "X") tensor([0.9689-0.2474j, 0.9689+0.2474j]) """ if qml.math.get_interface(theta) == "tensorflow": theta = qml.math.cast_like(theta, 1j) # Identity must be treated specially because its eigenvalues are all the same if set(pauli_word) == {"I"}: return qml.GlobalPhase.compute_eigvals(0.5 * theta, n_wires=len(pauli_word)) return MultiRZ.compute_eigvals(theta, len(pauli_word))
[docs] @staticmethod def compute_decomposition( theta: TensorLike, wires: WiresLike, pauli_word: str ) -> list["qml.operation.Operator"]: r"""Representation of the operator as a product of other operators (static method). : .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:~.PauliRot.decomposition. Args: theta (float): rotation angle :math:\theta wires (Iterable, Wires): the wires the operation acts on pauli_word (string): the Pauli word defining the rotation Returns: list[Operator]: decomposition into lower level operations **Example:** >>> qml.PauliRot.compute_decomposition(1.2, "XY", wires=(0,1)) [Hadamard(wires=[0]), RX(1.5707963267948966, wires=[1]), MultiRZ(1.2, wires=[0, 1]), Hadamard(wires=[0]), RX(-1.5707963267948966, wires=[1])] """ if isinstance(wires, int): # Catch cases when the wire is passed as a single int. wires = [wires] # Check for identity and do nothing if set(pauli_word) == {"I"}: return [qml.GlobalPhase(phi=theta / 2)] active_wires, active_gates = zip( *[(wire, gate) for wire, gate in zip(wires, pauli_word) if gate != "I"] ) ops = [] for wire, gate in zip(active_wires, active_gates): if gate == "X": ops.append(Hadamard(wires=[wire])) elif gate == "Y": ops.append(RX(np.pi / 2, wires=[wire])) ops.append(MultiRZ(theta, wires=list(active_wires))) for wire, gate in zip(active_wires, active_gates): if gate == "X": ops.append(Hadamard(wires=[wire])) elif gate == "Y": ops.append(RX(-np.pi / 2, wires=[wire])) return ops
[docs] def adjoint(self): return PauliRot(-self.parameters[0], self.hyperparameters["pauli_word"], wires=self.wires)
[docs] def pow(self, z): return [PauliRot(self.data[0] * z, self.hyperparameters["pauli_word"], wires=self.wires)]
[docs]class PCPhase(Operation): r"""PCPhase(phi, dim, wires) A projector-controlled phase gate. This gate applies a complex phase :math:e^{i\phi} to the first :math:dim basis vectors of the input state while applying a complex phase :math:e^{-i \phi} to the remaining basis vectors. For example, consider the 2-qubit case where :math:dim = 3: .. math:: \Pi(\phi) = \begin{bmatrix} e^{i\phi} & 0 & 0 & 0 \\ 0 & e^{i\phi} & 0 & 0 \\ 0 & 0 & e^{i\phi} & 0 \\ 0 & 0 & 0 & e^{-i\phi} \end{bmatrix}. **Details:** * Number of wires: Any (the operation can act on any number of wires) * Number of parameters: 1 * Number of dimensions per parameter: (0,) Args: phi (float): rotation angle :math:\phi dim (int): the dimension of the subspace wires (Iterable[int, str], Wires): the wires the operation acts on id (str or None): String representing the operation (optional) **Example:** We can define a circuit using :class:~.PCPhase as follows: >>> dev = qml.device('default.qubit', wires=2) >>> @qml.qnode(dev) >>> def example_circuit(): ... qml.PCPhase(0.27, dim = 2, wires=range(2)) ... return qml.state() The resulting operation applies a complex phase :math:e^{0.27i} to the first :math:dim = 2 basis vectors and :math:e^{-0.27i} to the remaining basis vectors. >>> print(np.round(qml.matrix(example_circuit)(),2)) [[0.96+0.27j 0. +0.j 0. +0.j 0. +0.j ] [0. +0.j 0.96+0.27j 0. +0.j 0. +0.j ] [0. +0.j 0. +0.j 0.96-0.27j 0. +0.j ] [0. +0.j 0. +0.j 0. +0.j 0.96-0.27j]] We can also choose a different :math:dim value to apply the phase shift to a different set of basis vectors as follows: >>> pc_op = qml.PCPhase(1.23, dim=3, wires=[1, 2]) >>> print(np.round(qml.matrix(pc_op),2)) [[0.33+0.94j 0. +0.j 0. +0.j 0. +0.j ] [0. +0.j 0.33+0.94j 0. +0.j 0. +0.j ] [0. +0.j 0. +0.j 0.33+0.94j 0. +0.j ] [0. +0.j 0. +0.j 0. +0.j 0.33-0.94j]] """ num_wires = AnyWires num_params = 1 """int: Number of trainable parameters that the operator depends on.""" ndim_params = (0,) """tuple[int]: Number of dimensions per trainable parameter that the operator depends on.""" basis = "Z" grad_method = "A" parameter_frequencies = [(2,)]
[docs] def generator(self) -> "qml.Hermitian": dim, shape = self.hyperparameters["dimension"] mat = np.diag([1 if index < dim else -1 for index in range(shape)]) return qml.Hermitian(mat, wires=self.wires)
def _flatten(self) -> FlatPytree: hyperparameter = (("dim", self.hyperparameters["dimension"][0]),) return tuple(self.data), (self.wires, hyperparameter) def __init__(self, phi: TensorLike, dim: int, wires: WiresLike, id: Optional[str] = None): wires = wires if isinstance(wires, Wires) else Wires(wires) if not (isinstance(dim, int) and (dim <= 2 ** len(wires))): raise ValueError( f"The projected dimension {dim} must be an integer that is less than or equal to " f"the max size of the matrix {2 ** len(wires)}. Try adding more wires." ) super().__init__(phi, wires=wires, id=id) self.hyperparameters["dimension"] = (dim, 2 ** len(wires))
[docs] @staticmethod def compute_matrix(phi: TensorLike, dimension: tuple[int, int]) -> TensorLike: """Get the matrix representation of Pi-controlled phase unitary.""" d, t = dimension if qml.math.get_interface(phi) == "tensorflow": p = qml.math.exp(1j * qml.math.cast_like(phi, 1j)) minus_p = qml.math.exp(-1j * qml.math.cast_like(phi, 1j)) zeros = qml.math.zeros_like(p) columns = [] for i in range(t): columns.append( [p if j == i else zeros for j in range(t)] if i < d else [minus_p if j == i else zeros for j in range(t)] ) r = qml.math.stack(columns, like="tensorflow", axis=-2) return r arg = 1j * phi prefactors = qml.math.array([1 if index < d else -1 for index in range(t)], like=phi) if qml.math.ndim(arg) == 0: return qml.math.diag(qml.math.exp(arg * prefactors)) diags = qml.math.exp(qml.math.outer(arg, prefactors)) return qml.math.stack([qml.math.diag(d) for d in diags])
[docs] @staticmethod def compute_eigvals(*params: TensorLike, **hyperparams) -> TensorLike: """Get the eigvals for the Pi-controlled phase unitary.""" phi = params[0] d, t = hyperparams["dimension"] if qml.math.get_interface(phi) == "tensorflow": phase = qml.math.exp(1j * qml.math.cast_like(phi, 1j)) minus_phase = qml.math.exp(-1j * qml.math.cast_like(phi, 1j)) return stack_last([phase if index < d else minus_phase for index in range(t)]) arg = 1j * phi prefactors = qml.math.array([1 if index < d else -1 for index in range(t)], like=phi) if qml.math.ndim(phi) == 0: product = arg * prefactors else: product = qml.math.outer(arg, prefactors) return qml.math.exp(product)
[docs] @staticmethod def compute_decomposition( *params: TensorLike, wires: Optional[WiresLike] = None, **hyperparams ) -> list["qml.operation.Operator"]: r"""Representation of the operator as a product of other operators (static method). .. math:: O = O_1 O_2 \dots O_n. .. note:: Operations making up the decomposition should be queued within the compute_decomposition method. .. seealso:: :meth:~.Operator.decomposition. Args: *params (list): trainable parameters of the operator, as stored in the parameters attribute wires (Iterable[Any], Wires): wires that the operator acts on **hyperparams (dict): non-trainable hyper-parameters of the operator, as stored in the hyperparameters attribute Returns: list[Operator]: decomposition of the operator """ phi = params[0] k, n = hyperparams["dimension"] def _get_op_from_binary_rep(binary_rep, theta, wires): if len(binary_rep) == 1: op = ( PhaseShift(theta, wires[0]) if int(binary_rep) else PauliX(wires[0]) @ PhaseShift(theta, wires[0]) @ PauliX(wires[0]) ) else: base_op = ( PhaseShift(theta, wires[-1]) if int(binary_rep[-1]) else PauliX(wires[-1]) @ PhaseShift(theta, wires[-1]) @ PauliX(wires[-1]) ) op = qml.ctrl( base_op, control=wires[:-1], control_values=[int(i) for i in binary_rep[:-1]] ) return op n_log2 = int(np.log2(n)) positive_binary_reps = [bin(_k)[2:].zfill(n_log2) for _k in range(k)] negative_binary_reps = [bin(_k)[2:].zfill(n_log2) for _k in range(k, n)] positive_ops = [ _get_op_from_binary_rep(br, phi, wires=wires) for br in positive_binary_reps ] negative_ops = [ _get_op_from_binary_rep(br, -1 * phi, wires=wires) for br in negative_binary_reps ] return positive_ops + negative_ops
[docs] def adjoint(self) -> "PCPhase": """Computes the adjoint of the operator.""" phi = self.parameters[0] dim, _ = self.hyperparameters["dimension"] return PCPhase(-1 * phi, dim=dim, wires=self.wires)
[docs] def pow(self, z: Union[int, float]) -> list["qml.operation.Operator"]: """Computes the operator raised to z.""" phi = self.parameters[0] dim, _ = self.hyperparameters["dimension"] return [PCPhase(phi * z, dim=dim, wires=self.wires)]
[docs] def simplify(self) -> "PCPhase": """Simplifies the operator if possible.""" phi = self.parameters[0] % (2 * np.pi) dim, _ = self.hyperparameters["dimension"] if _can_replace(phi, 0): return qml.Identity(wires=self.wires[0]) return PCPhase(phi, dim=dim, wires=self.wires)
[docs] def label( self, decimals: Optional[int] = None, base_label: Optional[str] = None, cache: Optional[dict] = None, ) -> str: """The label of the operator when displayed in a circuit.""" return super().label(decimals=decimals, base_label=base_label or "∏_ϕ", cache=cache)
[docs]class IsingXX(Operation): r""" Ising XX coupling gate .. math:: XX(\phi) = \exp\left(-i \frac{\phi}{2} (X \otimes X)\right) = \begin{bmatrix} = \cos(\phi / 2) & 0 & 0 & -i \sin(\phi / 2) \\ 0 & \cos(\phi / 2) & -i \sin(\phi / 2) & 0 \\ 0 & -i \sin(\phi / 2) & \cos(\phi / 2) & 0 \\ -i \sin(\phi / 2) & 0 & 0 & \cos(\phi / 2) \end{bmatrix}. .. note:: Special cases of using the :math:XX operator include: * :math:XX(0) = I; * :math:XX(\pi) = i (X \otimes X). **Details:** * Number of wires: 2 * Number of parameters: 1 * Number of dimensions per parameter: (0,) * Gradient recipe: :math:\frac{d}{d\phi}f(XX(\phi)) = \frac{1}{2}\left[f(XX(\phi +\pi/2)) - f(XX(\phi-\pi/2))\right] where :math:f is an expectation value depending on :math:XX(\phi). Args: phi (float): the phase angle wires (int): the subsystem the gate acts on id (str or None): String representing the operation (optional) """ num_wires = 2 num_params = 1 """int: Number of trainable parameters that the operator depends on.""" ndim_params = (0,) """tuple[int]: Number of dimensions per trainable parameter that the operator depends on.""" grad_method = "A" parameter_frequencies = [(1,)]
[docs] def generator(self) -> "qml.Hamiltonian": return qml.Hamiltonian([-0.5], [PauliX(wires=self.wires[0]) @ PauliX(wires=self.wires[1])])
def __init__(self, phi: TensorLike, wires: WiresLike, id: Optional[str] = None): super().__init__(phi, wires=wires, id=id)
[docs] @staticmethod def compute_matrix(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Representation of the operator as a canonical matrix in the computational basis (static method). The canonical matrix is the textbook matrix representation that does not consider wires. .. seealso:: :meth:~.IsingXX.matrix Args: phi (tensor_like or float): phase angle Returns: tensor_like: canonical matrix **Example** >>> qml.IsingXX.compute_matrix(torch.tensor(0.5)) tensor([[0.9689+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j, 0.0000-0.2474j], [0.0000+0.0000j, 0.9689+0.0000j, 0.0000-0.2474j, 0.0000+0.0000j], [0.0000+0.0000j, 0.0000-0.2474j, 0.9689+0.0000j, 0.0000+0.0000j], [0.0000-0.2474j, 0.0000+0.0000j, 0.0000+0.0000j, 0.9689+0.0000j]], dtype=torch.complex128) """ c = qml.math.cos(phi / 2) s = qml.math.sin(phi / 2) eye = qml.math.eye(4, like=phi) rev_eye = qml.math.convert_like(np.eye(4)[::-1].copy(), phi) if qml.math.get_interface(phi) == "tensorflow": c = qml.math.cast_like(c, 1j) s = qml.math.cast_like(s, 1j) eye = qml.math.cast_like(eye, 1j) rev_eye = qml.math.cast_like(rev_eye, 1j) # The following avoids casting an imaginary quantity to reals when backpropagating js = -1j * s if qml.math.ndim(phi) == 0: return c * eye + js * rev_eye return qml.math.tensordot(c, eye, axes=0) + qml.math.tensordot(js, rev_eye, axes=0)
[docs] @staticmethod def compute_decomposition(phi: TensorLike, wires: WiresLike) -> list["qml.operation.Operator"]: r"""Representation of the operator as a product of other operators (static method). : .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:~.IsingXX.decomposition. Args: phi (float): the phase angle wires (Iterable, Wires): the subsystem the gate acts on Returns: list[Operator]: decomposition into lower level operations **Example:** >>> qml.IsingXX.compute_decomposition(1.23, wires=(0,1)) [CNOT(wires=[0, 1]), RX(1.23, wires=[0]), CNOT(wires=[0, 1]] """ decomp_ops = [ qml.CNOT(wires=wires), RX(phi, wires=[wires[0]]), qml.CNOT(wires=wires), ] return decomp_ops
[docs] def adjoint(self) -> "IsingXX": (phi,) = self.parameters return IsingXX(-phi, wires=self.wires)
[docs] def pow(self, z: Union[int, float]) -> list["qml.operation.Operator"]: return [IsingXX(self.data[0] * z, wires=self.wires)]
[docs] def simplify(self) -> "IsingXX": phi = self.data[0] % (4 * np.pi) if _can_replace(phi, 0): return qml.Identity(wires=self.wires[0]) return IsingXX(phi, wires=self.wires)
[docs]class IsingYY(Operation): r""" Ising YY coupling gate .. math:: \mathtt{YY}(\phi) = \exp\left(-i \frac{\phi}{2} (Y \otimes Y)\right) = \begin{bmatrix} \cos(\phi / 2) & 0 & 0 & i \sin(\phi / 2) \\ 0 & \cos(\phi / 2) & -i \sin(\phi / 2) & 0 \\ 0 & -i \sin(\phi / 2) & \cos(\phi / 2) & 0 \\ i \sin(\phi / 2) & 0 & 0 & \cos(\phi / 2) \end{bmatrix}. .. note:: Special cases of using the :math:YY operator include: * :math:YY(0) = I; * :math:YY(\pi) = i (Y \otimes Y). **Details:** * Number of wires: 2 * Number of parameters: 1 * Number of dimensions per parameter: (0,) * Gradient recipe: :math:\frac{d}{d\phi}f(YY(\phi)) = \frac{1}{2}\left[f(YY(\phi +\pi/2)) - f(YY(\phi-\pi/2))\right] where :math:f is an expectation value depending on :math:YY(\phi). Args: phi (float): the phase angle wires (int): the subsystem the gate acts on id (str or None): String representing the operation (optional) """ num_wires = 2 num_params = 1 """int: Number of trainable parameters that the operator depends on.""" ndim_params = (0,) """tuple[int]: Number of dimensions per trainable parameter that the operator depends on.""" grad_method = "A" parameter_frequencies = [(1,)]
[docs] def generator(self) -> "qml.Hamiltonian": return qml.Hamiltonian([-0.5], [PauliY(wires=self.wires[0]) @ PauliY(wires=self.wires[1])])
def __init__(self, phi: TensorLike, wires: WiresLike, id: Optional[str] = None): super().__init__(phi, wires=wires, id=id)
[docs] @staticmethod def compute_decomposition(phi: TensorLike, wires: WiresLike) -> list["qml.operation.Operator"]: r"""Representation of the operator as a product of other operators (static method). : .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:~.IsingYY.decomposition. Args: phi (float): the phase angle wires (Iterable, Wires): the subsystem the gate acts on Returns: list[Operator]: decomposition into lower level operations **Example:** >>> qml.IsingYY.compute_decomposition(1.23, wires=(0,1)) [CY(wires=[0, 1]), RY(1.23, wires=[0]), CY(wires=[0, 1])] """ return [ qml.CY(wires=wires), RY(phi, wires=[wires[0]]), qml.CY(wires=wires), ]
[docs] @staticmethod def compute_matrix(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Representation of the operator as a canonical matrix in the computational basis (static method). The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order. .. seealso:: :meth:~.IsingYY.matrix Args: phi (tensor_like or float): phase angle Returns: tensor_like: canonical matrix **Example** >>> qml.IsingYY.compute_matrix(torch.tensor(0.5)) tensor([[0.9689+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j, 0.0000+0.2474j], [0.0000+0.0000j, 0.9689+0.0000j, 0.0000-0.2474j, 0.0000+0.0000j], [0.0000+0.0000j, 0.0000-0.2474j, 0.9689+0.0000j, 0.0000+0.0000j], [0.0000+0.2474j, 0.0000+0.0000j, 0.0000+0.0000j, 0.9689+0.0000j]]) """ c = qml.math.cos(phi / 2) s = qml.math.sin(phi / 2) if qml.math.get_interface(phi) == "tensorflow": c = qml.math.cast_like(c, 1j) s = qml.math.cast_like(s, 1j) js = 1j * s r_term = qml.math.cast_like( qml.math.array( [ [0.0, 0.0, 0.0, 1.0], [0.0, 0.0, -1.0, 0.0], [0.0, -1.0, 0.0, 0.0], [1.0, 0.0, 0.0, 0.0], ], like=js, ), 1j, ) if qml.math.ndim(phi) == 0: return c * qml.math.cast_like(qml.math.eye(4, like=c), c) + js * r_term return qml.math.tensordot(c, np.eye(4), axes=0) + qml.math.tensordot(js, r_term, axes=0)
[docs] def adjoint(self) -> "IsingYY": (phi,) = self.parameters return IsingYY(-phi, wires=self.wires)
[docs] def pow(self, z: Union[int, float]) -> list["qml.operation.Operator"]: return [IsingYY(self.data[0] * z, wires=self.wires)]
[docs] def simplify(self) -> "IsingYY": phi = self.data[0] % (4 * np.pi) if _can_replace(phi, 0): return qml.Identity(wires=self.wires[0]) return IsingYY(phi, wires=self.wires)
[docs]class IsingZZ(Operation): r""" Ising ZZ coupling gate .. math:: ZZ(\phi) = \exp\left(-i \frac{\phi}{2} (Z \otimes Z)\right) = \begin{bmatrix} e^{-i \phi / 2} & 0 & 0 & 0 \\ 0 & e^{i \phi / 2} & 0 & 0 \\ 0 & 0 & e^{i \phi / 2} & 0 \\ 0 & 0 & 0 & e^{-i \phi / 2} \end{bmatrix}. .. note:: Special cases of using the :math:ZZ operator include: * :math:ZZ(0) = I; * :math:ZZ(\pi) = - (Z \otimes Z); * :math:ZZ(2\pi) = - I; **Details:** * Number of wires: 2 * Number of parameters: 1 * Number of dimensions per parameter: (0,) * Gradient recipe: :math:\frac{d}{d\phi}f(ZZ(\phi)) = \frac{1}{2}\left[f(ZZ(\phi +\pi/2)) - f(ZZ(\phi-\pi/2))\right] where :math:f is an expectation value depending on :math:ZZ(\theta). Args: phi (float): the phase angle wires (int): the subsystem the gate acts on id (str or None): String representing the operation (optional) """ num_wires = 2 num_params = 1 """int: Number of trainable parameters that the operator depends on.""" ndim_params = (0,) """tuple[int]: Number of dimensions per trainable parameter that the operator depends on.""" grad_method = "A" parameter_frequencies = [(1,)]
[docs] def generator(self) -> "qml.Hamiltonian": return qml.Hamiltonian([-0.5], [PauliZ(wires=self.wires[0]) @ PauliZ(wires=self.wires[1])])
def __init__(self, phi: TensorLike, wires: WiresLike, id: Optional[str] = None): super().__init__(phi, wires=wires, id=id)
[docs] @staticmethod def compute_decomposition(phi: TensorLike, wires: WiresLike): r"""Representation of the operator as a product of other operators (static method). : .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:~.IsingZZ.decomposition. Args: phi (float): the phase angle wires (Iterable, Wires): the subsystem the gate acts on Returns: list[Operator]: decomposition into lower level operations **Example:** >>> qml.IsingZZ.compute_decomposition(1.23, wires=[0, 1]) [CNOT(wires=[0, 1]), RZ(1.23, wires=[1]), CNOT(wires=[0, 1])] """ return [ qml.CNOT(wires=wires), RZ(phi, wires=[wires[1]]), qml.CNOT(wires=wires), ]
[docs] @staticmethod def compute_matrix(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Representation of the operator as a canonical matrix in the computational basis (static method). The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order. .. seealso:: :meth:~.IsingZZ.matrix Args: phi (tensor_like or float): phase angle Returns: tensor_like: canonical matrix **Example** >>> qml.IsingZZ.compute_matrix(torch.tensor(0.5)) tensor([[0.9689-0.2474j, 0.0000+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j], [0.0000+0.0000j, 0.9689+0.2474j, 0.0000+0.0000j, 0.0000+0.0000j], [0.0000+0.0000j, 0.0000+0.0000j, 0.9689+0.2474j, 0.0000+0.0000j], [0.0000+0.0000j, 0.0000+0.0000j, 0.0000+0.0000j, 0.9689-0.2474j]]) """ if qml.math.get_interface(phi) == "tensorflow": p = qml.math.exp(-0.5j * qml.math.cast_like(phi, 1j)) if qml.math.ndim(p) == 0: return qml.math.diag([p, qml.math.conj(p), qml.math.conj(p), p]) diags = stack_last([p, qml.math.conj(p), qml.math.conj(p), p]) return diags[:, :, np.newaxis] * qml.math.cast_like(qml.math.eye(4, like=diags), diags) signs = qml.math.array([1, -1, -1, 1], like=phi) arg = -0.5j * phi if qml.math.ndim(arg) == 0: return qml.math.diag(qml.math.exp(arg * signs)) diags = qml.math.exp(qml.math.outer(arg, signs)) return diags[:, :, np.newaxis] * qml.math.cast_like(qml.math.eye(4, like=diags), diags)
[docs] @staticmethod def compute_eigvals(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Eigenvalues of the operator in the computational basis (static method). If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger}, the operator can be reconstructed as .. math:: O = U \Sigma U^{\dagger}, where :math:\Sigma is the diagonal matrix containing the eigenvalues. Otherwise, no particular order for the eigenvalues is guaranteed. .. seealso:: :meth:~.IsingZZ.eigvals Args: phi (tensor_like or float): phase angle Returns: tensor_like: eigenvalues **Example** >>> qml.IsingZZ.compute_eigvals(torch.tensor(0.5)) tensor([0.9689-0.2474j, 0.9689+0.2474j, 0.9689+0.2474j, 0.9689-0.2474j]) """ if qml.math.get_interface(phi) == "tensorflow": phase = qml.math.exp(-0.5j * qml.math.cast_like(phi, 1j)) return stack_last([phase, qml.math.conj(phase), qml.math.conj(phase), phase]) prefactors = qml.math.array([-0.5j, 0.5j, 0.5j, -0.5j], like=phi) if qml.math.ndim(phi) == 0: product = phi * prefactors else: product = qml.math.outer(phi, prefactors) return qml.math.exp(product)
[docs] def adjoint(self) -> "IsingZZ": (phi,) = self.parameters return IsingZZ(-phi, wires=self.wires)
[docs] def pow(self, z: Union[int, float]) -> list["qml.operation.Operator"]: return [IsingZZ(self.data[0] * z, wires=self.wires)]
[docs] def simplify(self) -> "IsingZZ": phi = self.data[0] % (4 * np.pi) if _can_replace(phi, 0): return qml.Identity(wires=self.wires[0]) return IsingZZ(phi, wires=self.wires)
[docs]class IsingXY(Operation): r""" Ising (XX + YY) coupling gate .. math:: \mathtt{XY}(\phi) = \exp\left(i \frac{\theta}{4} (X \otimes X + Y \otimes Y)\right) = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos(\phi / 2) & i \sin(\phi / 2) & 0 \\ 0 & i \sin(\phi / 2) & \cos(\phi / 2) & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}. .. note:: Special cases of using the :math:XY operator include: * :math:XY(0) = I; * :math:XY(\frac{\pi}{2}) = \sqrt{iSWAP}; * :math:XY(\pi) = iSWAP; **Details:** * Number of wires: 2 * Number of parameters: 1 * Number of dimensions per parameter: (0,) * Gradient recipe: The XY operator satisfies a four-term parameter-shift rule .. math:: \frac{d}{d \phi} f(XY(\phi)) = c_+ \left[ f(XY(\phi + a)) - f(XY(\phi - a)) \right] - c_- \left[ f(XY(\phi + b)) - f(XY(\phi - b)) \right] where :math:f is an expectation value depending on :math:XY(\phi), and - :math:a = \pi / 2 - :math:b = 3 \pi / 2 - :math:c_{\pm} = (\sqrt{2} \pm 1)/{4 \sqrt{2}} Args: phi (float): the phase angle wires (int): the subsystem the gate acts on id (str or None): String representing the operation (optional) """ num_wires = 2 num_params = 1 """int: Number of trainable parameters that the operator depends on.""" ndim_params = (0,) """tuple[int]: Number of dimensions per trainable parameter that the operator depends on.""" grad_method = "A" parameter_frequencies = [(0.5, 1.0)]
[docs] def generator(self) -> "qml.Hamiltonian": return qml.Hamiltonian( [0.25, 0.25], [ qml.X(wires=self.wires[0]) @ qml.X(wires=self.wires[1]), qml.Y(wires=self.wires[0]) @ qml.Y(wires=self.wires[1]), ], )
def __init__(self, phi: TensorLike, wires: WiresLike, id: Optional[str] = None): super().__init__(phi, wires=wires, id=id)
[docs] @staticmethod def compute_decomposition(phi: TensorLike, wires: WiresLike) -> list["qml.operation.Operator"]: r"""Representation of the operator as a product of other operators (static method). : .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:~.IsingXY.decomposition. Args: phi (float): the phase angle wires (Iterable, Wires): the subsystem the gate acts on Returns: list[Operator]: decomposition into lower level operations **Example:** >>> qml.IsingXY.compute_decomposition(1.23, wires=(0,1)) [Hadamard(wires=[0]), CY(wires=[0, 1]), RY(0.615, wires=[0]), RX(-0.615, wires=[1]), CY(wires=[0, 1]), Hadamard(wires=[0])] """ return [ Hadamard(wires=[wires[0]]), qml.CY(wires=wires), RY(phi / 2, wires=[wires[0]]), RX(-phi / 2, wires=[wires[1]]), qml.CY(wires=wires), Hadamard(wires=[wires[0]]), ]
[docs] @staticmethod def compute_matrix(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Representation of the operator as a canonical matrix in the computational basis (static method). The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order. .. seealso:: :meth:~.IsingXY.matrix Args: phi (tensor_like or float): phase angle Returns: tensor_like: canonical matrix **Example** >>> qml.IsingXY.compute_matrix(0.5) array([[1. +0.j , 0. +0.j , 0. +0.j , 0. +0.j ], [0. +0.j , 0.96891242+0.j , 0. +0.24740396j, 0. +0.j ], [0. +0.j , 0. +0.24740396j, 0.96891242+0.j , 0. +0.j ], [0. +0.j , 0. +0.j , 0. +0.j , 1. +0.j ]]) """ c = qml.math.cos(phi / 2) s = qml.math.sin(phi / 2) if qml.math.get_interface(phi) == "tensorflow": c = qml.math.cast_like(c, 1j) s = qml.math.cast_like(s, 1j) js = 1j * s off_diag = qml.math.cast_like( qml.math.array( [ [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0], [0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], ], like=js, ), 1j, ) if qml.math.ndim(phi) == 0: return qml.math.diag([1, c, c, 1]) + js * off_diag ones = qml.math.ones_like(c) diags = stack_last([ones, c, c, ones])[:, :, np.newaxis] return diags * np.eye(4) + qml.math.tensordot(js, off_diag, axes=0)
[docs] @staticmethod def compute_eigvals(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Eigenvalues of the operator in the computational basis (static method). If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger}, the operator can be reconstructed as .. math:: O = U \Sigma U^{\dagger}, where :math:\Sigma is the diagonal matrix containing the eigenvalues. Otherwise, no particular order for the eigenvalues is guaranteed. .. seealso:: :meth:~.IsingXY.eigvals Args: phi (tensor_like or float): phase angle Returns: tensor_like: eigenvalues **Example** >>> qml.IsingXY.compute_eigvals(0.5) array([0.96891242+0.24740396j, 0.96891242-0.24740396j, 1. +0.j , 1. +0.j ]) """ if qml.math.get_interface(phi) == "tensorflow": phi = qml.math.cast_like(phi, 1j) signs = np.array([1, -1, 0, 0]) if qml.math.ndim(phi) == 0: return qml.math.exp(0.5j * phi * signs) return qml.math.exp(qml.math.tensordot(0.5j * phi, signs, axes=0))
[docs] def adjoint(self) -> "IsingXY": (phi,) = self.parameters return IsingXY(-phi, wires=self.wires)
[docs] def pow(self, z: Union[int, float]) -> list["qml.operation.Operator"]: return [IsingXY(self.data[0] * z, wires=self.wires)]
[docs] def simplify(self) -> "IsingXY": phi = self.data[0] % (4 * np.pi) if _can_replace(phi, 0): return qml.Identity(wires=self.wires[0]) return IsingXY(phi, wires=self.wires)
[docs]class PSWAP(Operation): r"""Phase SWAP gate .. math:: PSWAP(\phi) = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & e^{i \phi} & 0 \\ 0 & e^{i \phi} & 0 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}. **Details:** * Number of wires: 2 * Number of parameters: 1 * Gradient recipe: .. math:: \frac{d}{d \phi} PSWAP(\phi) = \frac{1}{2} \left[ PSWAP(\phi + \pi / 2) - PSWAP(\phi - \pi / 2) \right] Args: phi (float): the phase angle wires (int): the subsystem the gate acts on id (str or None): String representing the operation (optional) """ num_wires = 2 num_params = 1 """int: Number of trainable parameters that the operator depends on.""" grad_method = "A" grad_recipe = ([[0.5, 1, np.pi / 2], [-0.5, 1, -np.pi / 2]],) def __init__(self, phi: TensorLike, wires: WiresLike, id: Optional[str] = None): super().__init__(phi, wires=wires, id=id)
[docs] @staticmethod def compute_decomposition(phi: TensorLike, wires: WiresLike) -> list["qml.operation.Operator"]: r"""Representation of the operator as a product of other operators (static method). : .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:~.PSWAP.decomposition. Args: phi (float): the phase angle wires (Iterable, Wires): the subsystem the gate acts on Returns: list[Operator]: decomposition into lower level operations **Example:** >>> qml.PSWAP.compute_decomposition(1.23, wires=(0,1)) [SWAP(wires=[0, 1]), CNOT(wires=[0, 1]), PhaseShift(1.23, wires=[1]), CNOT(wires=[0, 1])] """ return [ qml.SWAP(wires=wires), qml.CNOT(wires=wires), PhaseShift(phi, wires=[wires[1]]), qml.CNOT(wires=wires), ]
[docs] @staticmethod def compute_matrix(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Representation of the operator as a canonical matrix in the computational basis (static method). The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order. .. seealso:: :meth:~.PSWAP.matrix Args: phi (tensor_like or float): phase angle Returns: tensor_like: canonical matrix **Example** >>> qml.PSWAP.compute_matrix(0.5) array([[1. +0.j, 0. +0.j , 0. +0.j , 0. +0.j], [0. +0.j, 0. +0.j , 0.87758256+0.47942554j, 0. +0.j], [0. +0.j, 0.87758256+0.47942554j, 0. +0.j , 0. +0.j], [0. +0.j, 0. +0.j , 0. +0.j , 1. +0.j]]) """ if qml.math.get_interface(phi) == "tensorflow": phi = qml.math.cast_like(phi, 1j) e = qml.math.exp(1j * phi) return qml.math.stack( [ stack_last([1, 0, 0, 0]), stack_last([0, 0, e, 0]), stack_last([0, e, 0, 0]), stack_last([0, 0, 0, 1]), ], axis=-2, )
[docs] @staticmethod def compute_eigvals(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Eigenvalues of the operator in the computational basis (static method). If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger}, the operator can be reconstructed as .. math:: O = U \Sigma U^{\dagger}, where :math:\Sigma is the diagonal matrix containing the eigenvalues. Otherwise, no particular order for the eigenvalues is guaranteed. .. seealso:: :meth:~.PSWAP.eigvals Args: phi (tensor_like or float): phase angle Returns: tensor_like: eigenvalues **Example** >>> qml.PSWAP.compute_eigvals(0.5) array([ 1. +0.j , 1. +0.j, -0.87758256-0.47942554j, 0.87758256+0.47942554j]) """ if qml.math.get_interface(phi) == "tensorflow": phi = qml.math.cast_like(phi, 1j) return qml.math.stack([1, 1, -qml.math.exp(1j * phi), qml.math.exp(1j * phi)])
[docs] def adjoint(self) -> "PSWAP": (phi,) = self.parameters return PSWAP(-phi, wires=self.wires)
[docs] def simplify(self) -> "PSWAP": phi = self.data[0] % (2 * np.pi) if _can_replace(phi, 0): return qml.SWAP(wires=self.wires) return PSWAP(phi, wires=self.wires)
[docs]class CPhaseShift00(Operation): r""" A qubit controlled phase shift. .. math:: CR_{00}(\phi) = \begin{bmatrix} e^{i\phi} & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}. .. note:: The first wire provided corresponds to the **control qubit** and controls on the zero state :math:|0\rangle. **Details:** * Number of wires: 2 * Number of parameters: 1 * Number of dimensions per parameter: (0,) * Gradient recipe: .. math:: \frac{d}{d \phi} CR_{00}(\phi) = \frac{1}{2} \left[ CR_{00}(\phi + \pi / 2) - CR_{00}(\phi - \pi / 2) \right] Args: phi (float): rotation angle :math:\phi wires (Sequence[int]): the wire the operation acts on id (str or None): String representing the operation (optional) """ num_wires = 2 num_params = 1 """int: Number of trainable parameters that the operator depends on.""" ndim_params = (0,) """tuple[int]: Number of dimensions per trainable parameter that the operator depends on.""" grad_method = "A" parameter_frequencies = [(1,)]
[docs] def generator(self) -> "qml.Projector": return qml.Projector(np.array([0, 0]), wires=self.wires)
def __init__(self, phi: TensorLike, wires: WiresLike, id: Optional[str] = None): super().__init__(phi, wires=wires, id=id)
[docs] def label( self, decimals: Optional[int] = None, base_label: Optional[str] = None, cache: Optional[dict] = None, ) -> str: return super().label(decimals=decimals, base_label="Rϕ(00)", cache=cache)
[docs] @staticmethod def compute_matrix(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Representation of the operator as a canonical matrix in the computational basis (static method). The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order. .. seealso:: :meth:~.CPhaseShift00.matrix Args: phi (tensor_like or float): phase shift Returns: tensor_like: canonical matrix **Example** >>> qml.CPhaseShift00.compute_matrix(torch.tensor(0.5)) tensor([[0.8776+0.4794j, 0.0+0.0j, 0.0+0.0j, 0.0+0.0j], [0.0000+0.0000j, 1.0+0.0j, 0.0+0.0j, 0.0+0.0j], [0.0000+0.0000j, 0.0+0.0j, 1.0+0.0j, 0.0+0.0j], [0.0000+0.0000j, 0.0+0.0j, 0.0+0.0j, 1.0+0.0j]]) """ if qml.math.get_interface(phi) == "tensorflow": phi = qml.math.cast_like(phi, 1j) exp_part = qml.math.exp(1j * phi) if qml.math.ndim(phi) > 0: ones = qml.math.ones_like(exp_part) zeros = qml.math.zeros_like(exp_part) matrix = [ [exp_part, zeros, zeros, zeros], [zeros, ones, zeros, zeros], [zeros, zeros, ones, zeros], [zeros, zeros, zeros, ones], ] return qml.math.stack([stack_last(row) for row in matrix], axis=-2) return qml.math.diag([exp_part, 1, 1, 1])
[docs] @staticmethod def compute_eigvals(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Eigenvalues of the operator in the computational basis (static method). If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger}, the operator can be reconstructed as .. math:: O = U \Sigma U^{\dagger}, where :math:\Sigma is the diagonal matrix containing the eigenvalues. Otherwise, no particular order for the eigenvalues is guaranteed. .. seealso:: :meth:~.CPhaseShift00.eigvals Args: phi (tensor_like or float): phase shift Returns: tensor_like: eigenvalues **Example** >>> qml.CPhaseShift00.compute_eigvals(torch.tensor(0.5)) tensor([0.8776+0.4794j, 1.0000+0.0000j, 1.0000+0.0000j, 1.0000+0.0000j]) """ if qml.math.get_interface(phi) == "tensorflow": phi = qml.math.cast_like(phi, 1j) exp_part = qml.math.exp(1j * phi) ones = qml.math.ones_like(exp_part) return stack_last([exp_part, ones, ones, ones])
[docs] @staticmethod def compute_decomposition(phi: TensorLike, wires: WiresLike) -> list["qml.operation.Operator"]: r"""Representation of the operator as a product of other operators (static method). : .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:~.CPhaseShift00.decomposition. Args: phi (float): rotation angle :math:\phi wires (Iterable, Wires): wires that the operator acts on Returns: list[Operator]: decomposition into lower level operations **Example:** >>> qml.CPhaseShift00.compute_decomposition(1.234, wires=(0,1)) [X(0), X(1), PhaseShift(0.617, wires=[0]), PhaseShift(0.617, wires=[1]), CNOT(wires=[0, 1]), PhaseShift(-0.617, wires=[1]), CNOT(wires=[0, 1]), X(1), X(0)] """ decomp_ops = [ PauliX(wires[0]), PauliX(wires[1]), PhaseShift(phi / 2, wires=[wires[0]]), PhaseShift(phi / 2, wires=[wires[1]]), qml.CNOT(wires=wires), PhaseShift(-phi / 2, wires=[wires[1]]), qml.CNOT(wires=wires), PauliX(wires[1]), PauliX(wires[0]), ] return decomp_ops
[docs] def adjoint(self) -> "CPhaseShift00": return CPhaseShift00(-self.data[0], wires=self.wires)
[docs] def pow(self, z: Union[int, float]) -> "CPhaseShift00": return [CPhaseShift00(self.data[0] * z, wires=self.wires)]
@property def control_values(self) -> str: """str: The control values of the operation""" return "0" @property def control_wires(self) -> Wires: return self.wires[0:1]
[docs]class CPhaseShift01(Operation): r""" A qubit controlled phase shift. .. math:: CR_{01\phi}(\phi) = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & e^{i\phi} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}. .. note:: The first wire provided corresponds to the **control qubit** and controls on the zero state :math:|0\rangle. **Details:** * Number of wires: 2 * Number of parameters: 1 * Number of dimensions per parameter: (0,) * Gradient recipe: .. math:: \frac{d}{d \phi} CR_{01}(\phi) = \frac{1}{2} \left[ CR_{01}(\phi + \pi / 2) - CR_{01}(\phi - \pi / 2) \right] Args: phi (float): rotation angle :math:\phi wires (Sequence[int]): the wire the operation acts on id (str or None): String representing the operation (optional) """ num_wires = 2 num_params = 1 """int: Number of trainable parameters that the operator depends on.""" ndim_params = (0,) """tuple[int]: Number of dimensions per trainable parameter that the operator depends on.""" grad_method = "A" parameter_frequencies = [(1,)]
[docs] def generator(self) -> "qml.Projector": return qml.Projector(np.array([0, 1]), wires=self.wires)
def __init__(self, phi: TensorLike, wires: WiresLike, id: Optional[str] = None): super().__init__(phi, wires=wires, id=id)
[docs] def label( self, decimals: Optional[int] = None, base_label: Optional[str] = None, cache: Optional[dict] = None, ) -> str: return super().label(decimals=decimals, base_label="Rϕ(01)", cache=cache)
[docs] @staticmethod def compute_matrix(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Representation of the operator as a canonical matrix in the computational basis (static method). The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order. .. seealso:: :meth:~.CPhaseShift01.matrix Args: phi (tensor_like or float): phase shift Returns: tensor_like: canonical matrix **Example** >>> qml.CPhaseShift01.compute_matrix(torch.tensor(0.5)) tensor([[1.0+0.0j, 0.0000+0.0000j, 0.0+0.0j, 0.0+0.0j], [0.0+0.0j, 0.8776+0.4794j, 0.0+0.0j, 0.0+0.0j], [0.0+0.0j, 0.0000+0.0000j, 1.0+0.0j, 0.0+0.0j], [0.0+0.0j, 0.0000+0.0000j, 0.0+0.0j, 1.0+0.0j]]) """ if qml.math.get_interface(phi) == "tensorflow": phi = qml.math.cast_like(phi, 1j) exp_part = qml.math.exp(1j * phi) if qml.math.ndim(phi) > 0: ones = qml.math.ones_like(exp_part) zeros = qml.math.zeros_like(exp_part) matrix = [ [ones, zeros, zeros, zeros], [zeros, exp_part, zeros, zeros], [zeros, zeros, ones, zeros], [zeros, zeros, zeros, ones], ] return qml.math.stack([stack_last(row) for row in matrix], axis=-2) return qml.math.diag([1, exp_part, 1, 1])
[docs] @staticmethod def compute_eigvals(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Eigenvalues of the operator in the computational basis (static method). If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger}, the operator can be reconstructed as .. math:: O = U \Sigma U^{\dagger}, where :math:\Sigma is the diagonal matrix containing the eigenvalues. Otherwise, no particular order for the eigenvalues is guaranteed. .. seealso:: :meth:~.CPhaseShift01.eigvals Args: phi (tensor_like or float): phase shift Returns: tensor_like: eigenvalues **Example** >>> qml.CPhaseShift01.compute_eigvals(torch.tensor(0.5)) tensor([1.0000+0.0000j, 0.8776+0.4794j, 1.0000+0.0000j, 1.0000+0.0000j]) """ if qml.math.get_interface(phi) == "tensorflow": phi = qml.math.cast_like(phi, 1j) exp_part = qml.math.exp(1j * phi) ones = qml.math.ones_like(exp_part) return stack_last([ones, exp_part, ones, ones])
[docs] @staticmethod def compute_decomposition(phi: TensorLike, wires: WiresLike) -> list["qml.operation.Operator"]: r"""Representation of the operator as a product of other operators (static method). : .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:~.CPhaseShift01.decomposition. Args: phi (float): rotation angle :math:\phi wires (Iterable, Wires): wires that the operator acts on Returns: list[Operator]: decomposition into lower level operations **Example:** >>> qml.CPhaseShift01.compute_decomposition(1.234, wires=(0,1)) [X(0), PhaseShift(0.617, wires=[0]), PhaseShift(0.617, wires=[1]), CNOT(wires=[0, 1]), PhaseShift(-0.617, wires=[1]), CNOT(wires=[0, 1]), X(0)] """ decomp_ops = [ PauliX(wires[0]), PhaseShift(phi / 2, wires=[wires[0]]), PhaseShift(phi / 2, wires=[wires[1]]), qml.CNOT(wires=wires), PhaseShift(-phi / 2, wires=[wires[1]]), qml.CNOT(wires=wires), PauliX(wires[0]), ] return decomp_ops
[docs] def adjoint(self) -> "CPhaseShift01": return CPhaseShift01(-self.data[0], wires=self.wires)
[docs] def pow(self, z: Union[int, float]) -> "CPhaseShift01": return [CPhaseShift01(self.data[0] * z, wires=self.wires)]
@property def control_values(self) -> str: """str: The control values of the operation""" return "0" @property def control_wires(self) -> Wires: return self.wires[0:1]
[docs]class CPhaseShift10(Operation): r""" A qubit controlled phase shift. .. math:: CR_{10\phi}(\phi) = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{i\phi} & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}. .. note:: The first wire provided corresponds to the **control qubit**. **Details:** * Number of wires: 2 * Number of parameters: 1 * Number of dimensions per parameter: (0,) * Gradient recipe: .. math:: \frac{d}{d \phi} CR_{10}(\phi) = \frac{1}{2} \left[ CR_{10}(\phi + \pi / 2) - CR_{10}(\phi - \pi / 2) \right] Args: phi (float): rotation angle :math:\phi wires (Any, Wires): the wire the operation acts on id (str or None): String representing the operation (optional) """ num_wires = 2 num_params = 1 """int: Number of trainable parameters that the operator depends on.""" ndim_params = (0,) """tuple[int]: Number of dimensions per trainable parameter that the operator depends on.""" grad_method = "A" parameter_frequencies = [(1,)]
[docs] def generator(self) -> "qml.Projector": return qml.Projector(np.array([1, 0]), wires=self.wires)
def __init__(self, phi: TensorLike, wires: WiresLike, id: Optional[str] = None): super().__init__(phi, wires=wires, id=id)
[docs] def label( self, decimals: Optional[int] = None, base_label: Optional[str] = None, cache: Optional[dict] = None, ) -> str: return super().label(decimals=decimals, base_label="Rϕ(10)", cache=cache)
[docs] @staticmethod def compute_matrix(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Representation of the operator as a canonical matrix in the computational basis (static method). The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order. .. seealso:: :meth:~.CPhaseShift10.matrix Args: phi (tensor_like or float): phase shift Returns: tensor_like: canonical matrix **Example** >>> qml.CPhaseShift10.compute_matrix(torch.tensor(0.5)) tensor([[1.0+0.0j, 0.0+0.0j, 0.0000+0.0000j, 0.0+0.0j], [0.0+0.0j, 1.0+0.0j, 0.0000+0.0000j, 0.0+0.0j], [0.0+0.0j, 0.0+0.0j, 0.8776+0.4794j, 0.0+0.0j], [0.0+0.0j, 0.0+0.0j, 0.0000+0.0000j, 1.0+0.0j]]) """ if qml.math.get_interface(phi) == "tensorflow": phi = qml.math.cast_like(phi, 1j) exp_part = qml.math.exp(1j * phi) if qml.math.ndim(phi) > 0: ones = qml.math.ones_like(exp_part) zeros = qml.math.zeros_like(exp_part) matrix = [ [ones, zeros, zeros, zeros], [zeros, ones, zeros, zeros], [zeros, zeros, exp_part, zeros], [zeros, zeros, zeros, ones], ] return qml.math.stack([stack_last(row) for row in matrix], axis=-2) return qml.math.diag([1, 1, exp_part, 1])
[docs] @staticmethod def compute_eigvals(phi: TensorLike) -> TensorLike: # pylint: disable=arguments-differ r"""Eigenvalues of the operator in the computational basis (static method). If :attr:diagonalizing_gates are specified and implement a unitary :math:U^{\dagger}, the operator can be reconstructed as .. math:: O = U \Sigma U^{\dagger}, where :math:\Sigma is the diagonal matrix containing the eigenvalues. Otherwise, no particular order for the eigenvalues is guaranteed. .. seealso:: :meth:~.CPhaseShift10.eigvals Args: phi (tensor_like or float): phase shift Returns: tensor_like: eigenvalues **Example** >>> qml.CPhaseShift10.compute_eigvals(torch.tensor(0.5)) tensor([1.0000+0.0000j, 1.0000+0.0000j, 0.8776+0.4794j, 1.0000+0.0000j]) """ if qml.math.get_interface(phi) == "tensorflow": phi = qml.math.cast_like(phi, 1j) exp_part = qml.math.exp(1j * phi) ones = qml.math.ones_like(exp_part) return stack_last([ones, ones, exp_part, ones])
[docs] @staticmethod def compute_decomposition(phi: TensorLike, wires: WiresLike) -> list["qml.operation.Operator"]: r"""Representation of the operator as a product of other operators (static method). : .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:~.CPhaseShift10.decomposition. Args: phi (float): rotation angle :math:\phi wires (Iterable, Wires): wires that the operator acts on Returns: list[Operator]: decomposition into lower level operations **Example:** >>> qml.CPhaseShift10.compute_decomposition(1.234, wires=(0,1)) [X(1), PhaseShift(0.617, wires=[0]), PhaseShift(0.617, wires=[1]), CNOT(wires=[0, 1]), PhaseShift(-0.617, wires=[1]), CNOT(wires=[0, 1]), X(1)] """ decomp_ops = [ PauliX(wires[1]), PhaseShift(phi / 2, wires=[wires[0]]), PhaseShift(phi / 2, wires=[wires[1]]), qml.CNOT(wires=wires), PhaseShift(-phi / 2, wires=[wires[1]]), qml.CNOT(wires=wires), PauliX(wires[1]), ] return decomp_ops
[docs] def adjoint(self) -> "CPhaseShift10": return CPhaseShift10(-self.data[0], wires=self.wires)
[docs] def pow(self, z: Union[int, float]): return [CPhaseShift10(self.data[0] * z, wires=self.wires)]
@property def control_wires(self) -> Wires: return self.wires[0:1]

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