#   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 constructs Hamiltonians of the Richardson Gaudin type.
"""
from itertools import chain, product
import numpy
from openfermion.ops.representations import (PolynomialTensor,
                                             get_tensors_from_integrals)
from openfermion.ops.representations import DOCIHamiltonian
from openfermion.ops import QubitOperator


class RichardsonGaudin(DOCIHamiltonian):
    r"""Richardson Gaudin model.

    Class for storing and constructing Richardson Gaudin hamiltonians
    combining an equi-distant potential ladder like potential per
    qubit with a uniform coupling between any pair of
    qubits with coupling strength g, which can be either attractive
    (g<0) or repulsive (g>0).

    The operators represented by this class has the form:

    .. math::

        H = \sum_{p=0} (p + 1) N_p + g/2 \sum_{p < q} P_p^\dagger P_q,

    where

    .. math::

        \begin{align}
        N_p &= (1 - \sigma^Z_p)/2, \\
        P_p &= a_{p,\beta} a_{p,\alpha} = S^{-} = \sigma^X + i \sigma^Y, \\
        g &= constant coupling term
        \end{align}

    Note;
        The diagonal of the Hamiltonian is composed of the values in
        range((n_qubits+1)*n_qubits//2+1).
    """

    def __init__(self, g, n_qubits):
        r"""Richardson Gaudin model on a given number of qubits.

        Args:
            g (float): Coupling strength
            n_qubits (int): Number of qubits
        """
        hc = numpy.zeros((n_qubits,))
        hr1 = numpy.zeros((n_qubits, n_qubits))
        hr2 = numpy.zeros((n_qubits, n_qubits))
        for p in range(n_qubits):
            hc[p] = 2 * (p + 1)
            for q in range(n_qubits):
                if p != q:
                    hr1[p, q] = g
        super().__init__(0, hc, hr1, hr2)

    @DOCIHamiltonian.constant.setter
    def constant(self, value):
        raise TypeError('Raw edits of the constant of a RichardsonGaudin model'
                        'is not allowed. Either adjust the g parameter '
                        'or cast to another PolynomialTensor class.')

    @DOCIHamiltonian.n_body_tensors.setter
    def n_body_tensors(self, value):
        raise TypeError(
            'Raw edits of the n_body_tensors of a RichardsonGaudin model'
            'is not allowed. Either adjust the g parameter '
            'or cast to another PolynomialTensor class.')

    def get_antisymmetrized_tensors(self):
        r"""Antisymmetrized Tensors
        Directly returns antisymmetrized tensors, which, when used
        to construct an FermionOperator via an InteractionOperator
        produce a FermionOperator that acts like this RichardsonGaudin
        Hamiltonian on the paired (seniority zero) subspace.
        Compared to the FermionOperator that can be obtained via the
        n_body_tensors property from the DOCIHamiltonian class
        the FermionOperator from the tensors returned by this function
        do not contain same spin coupling terms. These terms
        act trivially on the paired subspace and this the two Hamiltonian
        agree on any senioirty zero state.
        Returns:
            tuple: Tuple of one and two body tensors.
        """
        g = self.hr1[0, 1]
        spatial_orbs = self.hc.shape[0]
        h1 = numpy.diag(numpy.arange(spatial_orbs) + 1)
        h1 = numpy.kron(h1, numpy.eye(2))
        h2 = numpy.zeros((2 * spatial_orbs,) * 4)
        for p, q in product(range(spatial_orbs), repeat=2):
            if p != q:
                h2[2 * p, 2 * p + 1, 2 * q + 1, 2 * q] = g / 2
                h2[2 * p + 1, 2 * p, 2 * q, 2 * q + 1] = g / 2

        h2 = h2 - numpy.einsum('ijlk', h2)

        return h1, h2

#   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 constructs Hamiltonians of the Richardson Gaudin type.
"""
from itertools import chain, product
import numpy
from openfermion.ops.representations import (PolynomialTensor,
                                             get_tensors_from_integrals)
from openfermion.ops.representations import DOCIHamiltonian
from openfermion.ops import QubitOperator


class RichardsonGaudin(DOCIHamiltonian):
    r"""Richardson Gaudin model.

    Class for storing and constructing Richardson Gaudin hamiltonians
    combining an equi-distant potential ladder like potential per
    qubit with a uniform coupling between any pair of
    qubits with coupling strength g, which can be either attractive
    (g<0) or repulsive (g>0).

    The operators represented by this class has the form:

    .. math::

        H = \sum_{p=0} (p + 1) N_p + g/2 \sum_{p < q} P_p^\dagger P_q,

    where

    .. math::

        \begin{align}
        N_p &= (1 - \sigma^Z_p)/2, \\
        P_p &= a_{p,\beta} a_{p,\alpha} = S^{-} = \sigma^X + i \sigma^Y, \\
        g &= constant coupling term
        \end{align}

    Note;
        The diagonal of the Hamiltonian is composed of the values in
        range((n_qubits+1)*n_qubits//2+1).
    """

    def __init__(self, g, n_qubits):
        r"""Richardson Gaudin model on a given number of qubits.

        Args:
            g (float): Coupling strength
            n_qubits (int): Number of qubits
        """
        hc = numpy.zeros((n_qubits,))
        hr1 = numpy.zeros((n_qubits, n_qubits))
        hr2 = numpy.zeros((n_qubits, n_qubits))
        for p in range(n_qubits):
            hc[p] = 2 * (p + 1)
            for q in range(n_qubits):
                if p != q:
                    hr1[p, q] = g
        super().__init__(0, hc, hr1, hr2)

    @DOCIHamiltonian.constant.setter
    def constant(self, value):
        raise TypeError('Raw edits of the constant of a RichardsonGaudin model'
                        'is not allowed. Either adjust the g parameter '
                        'or cast to another PolynomialTensor class.')

    @DOCIHamiltonian.n_body_tensors.setter
    def n_body_tensors(self, value):
        raise TypeError(
            'Raw edits of the n_body_tensors of a RichardsonGaudin model'
            'is not allowed. Either adjust the g parameter '
            'or cast to another PolynomialTensor class.')

    def get_antisymmetrized_tensors(self):
        r"""Antisymmetrized Tensors
        Directly returns antisymmetrized tensors, which, when used
        to construct an FermionOperator via an InteractionOperator
        produce a FermionOperator that acts like this RichardsonGaudin
        Hamiltonian on the paired (seniority zero) subspace.
        Compared to the FermionOperator that can be obtained via the
        n_body_tensors property from the DOCIHamiltonian class
        the FermionOperator from the tensors returned by this function
        do not contain same spin coupling terms. These terms
        act trivially on the paired subspace and this the two Hamiltonian
        agree on any senioirty zero state.
        Returns:
            tuple: Tuple of one and two body tensors.
        """
        g = self.hr1[0, 1]
        spatial_orbs = self.hc.shape[0]
        h1 = numpy.diag(numpy.arange(spatial_orbs) + 1)
        h1 = numpy.kron(h1, numpy.eye(2))
        h2 = numpy.zeros((2 * spatial_orbs,) * 4)
        for p, q in product(range(spatial_orbs), repeat=2):
            if p != q:
                h2[2 * p, 2 * p + 1, 2 * q + 1, 2 * q] = g / 2
                h2[2 * p + 1, 2 * p, 2 * q, 2 * q + 1] = g / 2

        h2 = h2 - numpy.einsum('ijlk', h2)

        return h1, h2

#   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 constructs Hamiltonians of the Richardson Gaudin type. Richardson Gaudin model.      Class for storing and constructing Richardson Gaudin hamiltonians     combining an equi-distant potential ladder like potential per     qubit with a uniform coupling between any pair of     qubits with coupling strength g, which can be either attractive     (g<0) or repulsive (g>0).      The operators represented by this class has the form:      .. math::          H = \sum_{p=0} (p + 1) N_p + g/2 \sum_{p < q} P_p^\dagger P_q,      where      .. math::          \begin{align}         N_p &= (1 - \sigma^Z_p)/2, \\         P_p &= a_{p,\beta} a_{p,\alpha} = S^{-} = \sigma^X + i \sigma^Y, \\         g &= constant coupling term         \end{align}      Note;         The diagonal of the Hamiltonian is composed of the values in         range((n_qubits+1)*n_qubits//2+1). Richardson Gaudin model on a given number of qubits.          Args:             g (float): Coupling strength             n_qubits (int): Number of qubits Antisymmetrized Tensors         Directly returns antisymmetrized tensors, which, when used         to construct an FermionOperator via an InteractionOperator         produce a FermionOperator that acts like this RichardsonGaudin         Hamiltonian on the paired (seniority zero) subspace.         Compared to the FermionOperator that can be obtained via the         n_body_tensors property from the DOCIHamiltonian class         the FermionOperator from the tensors returned by this function         do not contain same spin coupling terms. These terms         act trivially on the paired subspace and this the two Hamiltonian         agree on any senioirty zero state.         Returns:             tuple: Tuple of one and two body tensors.