# antinature/qiskit_integration/systems.py

from typing import Any, Dict, List, Optional, Tuple, Union

import numpy as np

# Import qiskit if available
try:
    from qiskit import QuantumCircuit
    from qiskit.circuit import Parameter
    from qiskit_nature.second_q.drivers import PySCFDriver
    from qiskit_nature.second_q.hamiltonians import ElectronicEnergy
    from qiskit_nature.second_q.mappers import (
        BravyiKitaevMapper,
        JordanWignerMapper,
        ParityMapper,
    )
    from qiskit_nature.second_q.operators import FermionicOp
    from qiskit_nature.second_q.problems import ElectronicStructureProblem

    # QubitOperator type is available when Qiskit is imported
    HAS_QISKIT = True
except ImportError:
    HAS_QISKIT = False


class AntinatureQuantumSystems:
    """
    Implements various antinature systems for quantum computation.

    This class provides methods to create Hamiltonians and quantum
    circuits for various antinature systems including positronium,
    anti-hydrogen, positronium molecule, and anti-helium.
    """

    def __init__(self, mapper_type: str = 'jordan_wigner'):
        """
        Initialize the antinature quantum systems.

        Parameters:
        -----------
        mapper_type : str
            Type of fermion-to-qubit mapping to use:
            'jordan_wigner', 'parity', 'bravyi_kitaev'
        """
        if not HAS_QISKIT:
            raise ImportError("Qiskit Nature is required for this functionality")

        self.mapper_type = mapper_type

        # Set the mapper based on type
        if mapper_type == 'jordan_wigner':
            self.mapper = JordanWignerMapper()
        elif mapper_type == 'parity':
            self.mapper = ParityMapper()
        elif mapper_type == 'bravyi_kitaev':
            self.mapper = BravyiKitaevMapper()
        else:
            raise ValueError(f"Unknown mapper type: {mapper_type}")

    def positronium(self) -> Tuple[Any, QuantumCircuit]:
        """
        Create a Hamiltonian and quantum circuit for positronium.

        Positronium is an electron-positron bound system, which can
        be modeled as a quantum system with specialized interactions.

        Returns:
        --------
        Tuple[Any, QuantumCircuit]
            Qubit operator representing the Hamiltonian, and quantum circuit
        """
        # Create simplified 2-qubit representation of positronium
        # In positronium, we have one electron and one positron

        # Create one-body terms
        one_body = np.zeros((2, 2))
        # Kinetic energy terms (diagonal)
        one_body[0, 0] = 0.5  # Electron kinetic energy
        one_body[1, 1] = 0.5  # Positron kinetic energy

        # Create two-body terms (electron-positron interaction)
        two_body = np.zeros((2, 2, 2, 2))
        # Electron-positron attraction (opposite charges attract)
        # The interaction is stronger when modeling positronium correctly
        two_body[0, 0, 1, 1] = -1.0  # e-p attraction
        two_body[1, 1, 0, 0] = -1.0  # p-e attraction (same due to symmetry)

        # Create electronic energy operator
        energy_op = ElectronicEnergy.from_raw_integrals(one_body, two_body)

        # Convert to fermionic operator first, then map to qubit operator
        fermionic_op = energy_op.second_q_op()
        qubit_op = self.mapper.map(fermionic_op)

        # Create specialized positronium circuit
        circuit = self._create_positronium_circuit()

        return qubit_op, circuit

    def _create_positronium_circuit(self) -> QuantumCircuit:
        """Create a specialized circuit for positronium."""
        # This creates a 2-qubit circuit for positronium
        circuit = QuantumCircuit(2)

        # Initialize with electron and positron in superposition
        circuit.h(0)  # Electron
        circuit.h(1)  # Positron

        # Add entanglement layer (electron-positron correlation)
        circuit.cx(0, 1)

        # Add parameterized rotations for variational optimization
        circuit.rx(Parameter('θ0'), 0)
        circuit.ry(Parameter('θ1'), 0)
        circuit.rx(Parameter('θ2'), 1)
        circuit.ry(Parameter('θ3'), 1)

        # Add entanglement layer with parameterized phase
        circuit.cx(0, 1)
        circuit.rz(Parameter('θ4'), 1)
        circuit.cx(0, 1)

        return circuit

    def anti_hydrogen(self) -> Tuple[Any, QuantumCircuit]:
        """
        Create a Hamiltonian and quantum circuit for anti-hydrogen.

        Anti-hydrogen consists of an antiproton and a positron and can
        be modeled as a quantum system similar to hydrogen but with
        opposite charges.

        Returns:
        --------
        Tuple[Any, QuantumCircuit]
            Qubit operator representing the Hamiltonian, and quantum circuit
        """
        # In anti-hydrogen, we have a positron (positively charged) and
        # an antiproton (negatively charged, opposite of hydrogen)

        # Create one-body terms for simplified 3-orbital model
        n_orbitals = 3
        one_body = np.zeros((n_orbitals, n_orbitals))

        # Kinetic energy and orbital energy terms
        one_body[0, 0] = 0.5  # Ground state orbital
        one_body[1, 1] = 0.6  # First excited orbital
        one_body[2, 2] = 0.7  # Second excited orbital

        # Off-diagonal terms for orbital transitions
        one_body[0, 1] = 0.1
        one_body[1, 0] = 0.1
        one_body[1, 2] = 0.05
        one_body[2, 1] = 0.05

        # Create two-body terms (positron-antiproton attraction)
        two_body = np.zeros((n_orbitals, n_orbitals, n_orbitals, n_orbitals))

        # Attractive interaction between positron and antiproton
        # This is the dominant term in the anti-hydrogen Hamiltonian
        for i in range(n_orbitals):
            for j in range(n_orbitals):
                # Simplified Coulomb interaction
                two_body[i, i, j, j] = -1.0 if i != j else 0.0

        # Create electronic energy operator
        energy_op = ElectronicEnergy.from_raw_integrals(one_body, two_body)

        # Convert to fermionic operator first, then map to qubit operator
        fermionic_op = energy_op.second_q_op()
        qubit_op = self.mapper.map(fermionic_op)

        # Create specialized anti-hydrogen circuit
        circuit = self._create_anti_hydrogen_circuit(n_orbitals)

        return qubit_op, circuit

    def _create_anti_hydrogen_circuit(self, n_orbitals: int) -> QuantumCircuit:
        """Create a specialized circuit for anti-hydrogen."""
        # This creates a circuit with n_orbitals qubits
        circuit = QuantumCircuit(n_orbitals)

        # Initialize with positron occupying the ground state
        circuit.x(0)

        # Add superposition layers to represent orbital mixing
        for i in range(n_orbitals):
            circuit.h(i)

        # Add parameterized rotations for each orbital
        for i in range(n_orbitals):
            circuit.rx(Parameter(f'rx_{i}'), i)
            circuit.ry(Parameter(f'ry_{i}'), i)
            circuit.rz(Parameter(f'rz_{i}'), i)

        # Add entanglement representing orbital interactions
        for i in range(n_orbitals - 1):
            circuit.cx(i, i + 1)
            circuit.rz(Parameter(f'rz_{i}_{i+1}'), i + 1)
            circuit.cx(i, i + 1)

        # Connect last orbital to first (circular)
        if n_orbitals > 2:
            circuit.cx(n_orbitals - 1, 0)
            circuit.rz(Parameter(f'rz_loop'), 0)
            circuit.cx(n_orbitals - 1, 0)

        return circuit

    def positronium_molecule(self) -> Tuple[Any, QuantumCircuit]:
        """
        Create a Hamiltonian and quantum circuit for positronium molecule.

        Positronium molecule (Ps₂) consists of two positronium atoms
        bound together (2 electrons and 2 positrons).

        Returns:
        --------
        Tuple[Any, QuantumCircuit]
            Qubit operator representing the Hamiltonian, and quantum circuit
        """
        # In positronium molecule, we have 2 electrons and 2 positrons
        # We use a 4-orbital model (one for each particle)
        n_orbitals = 4

        # Create one-body terms
        one_body = np.zeros((n_orbitals, n_orbitals))

        # Kinetic energy and orbital energy terms
        # First two orbitals for electrons, second two for positrons
        for i in range(n_orbitals):
            one_body[i, i] = 0.5  # Kinetic energy term

        # Create two-body terms (electron-positron interactions)
        two_body = np.zeros((n_orbitals, n_orbitals, n_orbitals, n_orbitals))

        # Define indices
        e1, e2 = 0, 1  # Electrons
        p1, p2 = 2, 3  # Positrons

        # Electron-positron attractions (negative energy contribution)
        # First positronium atom: e1-p1
        two_body[e1, e1, p1, p1] = -1.0
        two_body[p1, p1, e1, e1] = -1.0

        # Second positronium atom: e2-p2
        two_body[e2, e2, p2, p2] = -1.0
        two_body[p2, p2, e2, e2] = -1.0

        # Cross attractions (weaker, but important for molecule formation)
        # e1-p2 attraction
        two_body[e1, e1, p2, p2] = -0.5
        two_body[p2, p2, e1, e1] = -0.5

        # e2-p1 attraction
        two_body[e2, e2, p1, p1] = -0.5
        two_body[p1, p1, e2, e2] = -0.5

        # Electron-electron repulsion (positive energy contribution)
        two_body[e1, e1, e2, e2] = 0.4
        two_body[e2, e2, e1, e1] = 0.4

        # Positron-positron repulsion (positive energy contribution)
        two_body[p1, p1, p2, p2] = 0.4
        two_body[p2, p2, p1, p1] = 0.4

        # Create electronic energy operator
        energy_op = ElectronicEnergy.from_raw_integrals(one_body, two_body)

        # Convert to fermionic operator first, then map to qubit operator
        fermionic_op = energy_op.second_q_op()
        qubit_op = self.mapper.map(fermionic_op)

        # Create specialized positronium molecule circuit
        circuit = self._create_positronium_molecule_circuit()

        return qubit_op, circuit

    def _create_positronium_molecule_circuit(self) -> QuantumCircuit:
        """Create a specialized circuit for positronium molecule."""
        # This creates a 4-qubit circuit for positronium molecule
        # qubits 0,1: electrons
        # qubits 2,3: positrons
        circuit = QuantumCircuit(4)

        # Initialize with all particles in superposition
        for i in range(4):
            circuit.h(i)

        # Add parameterized rotations for each particle
        for i in range(4):
            circuit.rx(Parameter(f'rx_{i}'), i)
            circuit.ry(Parameter(f'ry_{i}'), i)

        # Add entanglement for intra-atom correlations
        # First positronium: e1-p1
        circuit.cx(0, 2)
        circuit.rz(Parameter('ep1'), 2)
        circuit.cx(0, 2)

        # Second positronium: e2-p2
        circuit.cx(1, 3)
        circuit.rz(Parameter('ep2'), 3)
        circuit.cx(1, 3)

        # Add entanglement for inter-atom correlations
        # Electron-electron
        circuit.cx(0, 1)
        circuit.rz(Parameter('ee'), 1)
        circuit.cx(0, 1)

        # Positron-positron
        circuit.cx(2, 3)
        circuit.rz(Parameter('pp'), 3)
        circuit.cx(2, 3)

        # Cross correlations
        # e1-p2
        circuit.cx(0, 3)
        circuit.rz(Parameter('ep12'), 3)
        circuit.cx(0, 3)

        # e2-p1
        circuit.cx(1, 2)
        circuit.rz(Parameter('ep21'), 2)
        circuit.cx(1, 2)

        return circuit

    def anti_helium(self) -> Tuple[Any, QuantumCircuit]:
        """
        Create a Hamiltonian and quantum circuit for anti-helium.

        Anti-helium consists of an anti-nucleus with 2 antiprotons
        and 2 positrons orbiting it.

        Returns:
        --------
        Tuple[Any, QuantumCircuit]
            Qubit operator representing the Hamiltonian, and quantum circuit
        """
        # In anti-helium, we have 2 positrons orbiting an anti-nucleus
        # with 2 antiprotons and 2 antineutrons
        # We use a 6-orbital model
        n_orbitals = 6

        # Create one-body terms
        one_body = np.zeros((n_orbitals, n_orbitals))

        # Kinetic energy and orbital energy terms
        for i in range(n_orbitals):
            one_body[i, i] = 0.5  # Kinetic energy

        # Create two-body terms (interactions)
        two_body = np.zeros((n_orbitals, n_orbitals, n_orbitals, n_orbitals))

        # Define indices for clarity
        p1_orbs = [0, 1]  # Positron 1 orbitals
        p2_orbs = [2, 3]  # Positron 2 orbitals
        nucleus = [4, 5]  # Anti-nucleus representation

        # Positron-nucleus attractions (very strong)
        for p_orb in p1_orbs + p2_orbs:
            for n_orb in nucleus:
                two_body[p_orb, p_orb, n_orb, n_orb] = (
                    -2.0
                )  # Strong attraction (2 antiprotons)
                two_body[n_orb, n_orb, p_orb, p_orb] = -2.0

        # Positron-positron repulsions
        for p1_orb in p1_orbs:
            for p2_orb in p2_orbs:
                two_body[p1_orb, p1_orb, p2_orb, p2_orb] = 1.0  # Repulsion
                two_body[p2_orb, p2_orb, p1_orb, p1_orb] = 1.0

        # Create electronic energy operator
        energy_op = ElectronicEnergy.from_raw_integrals(one_body, two_body)

        # Convert to fermionic operator first, then map to qubit operator
        fermionic_op = energy_op.second_q_op()
        qubit_op = self.mapper.map(fermionic_op)

        # Create specialized anti-helium circuit
        circuit = self._create_anti_helium_circuit()

        return qubit_op, circuit

    def _create_anti_helium_circuit(self) -> QuantumCircuit:
        """Create a specialized circuit for anti-helium."""
        # This creates a 6-qubit circuit for anti-helium
        circuit = QuantumCircuit(6)

        # Initialize with all particles in superposition
        for i in range(6):
            circuit.h(i)

        # Add parameterized rotations
        for i in range(6):
            circuit.rx(Parameter(f'rx_{i}'), i)
            circuit.ry(Parameter(f'ry_{i}'), i)
            circuit.rz(Parameter(f'rz_{i}'), i)

        # Add entanglement for positron-nucleus interactions
        # First positron (orbitals 0,1) with nucleus (orbitals 4,5)
        for i in range(2):
            for j in range(4, 6):
                circuit.cx(i, j)
                circuit.rz(Parameter(f'p1n_{i}_{j}'), j)
                circuit.cx(i, j)

        # Second positron (orbitals 2,3) with nucleus (orbitals 4,5)
        for i in range(2, 4):
            for j in range(4, 6):
                circuit.cx(i, j)
                circuit.rz(Parameter(f'p2n_{i}_{j}'), j)
                circuit.cx(i, j)

        # Add entanglement for positron-positron interactions
        # Orbitals of positron 1 with positron 2
        for i in range(2):
            for j in range(2, 4):
                circuit.cx(i, j)
                circuit.rz(Parameter(f'pp_{i}_{j}'), j)
                circuit.cx(i, j)

        return circuit

    def custom_antinature_system(
        self, one_body: np.ndarray, two_body: np.ndarray
    ) -> Tuple[Any, QuantumCircuit]:
        """
        Create a Hamiltonian and circuit for a custom antinature system.

        This allows users to define their own one-body and two-body
        integrals for custom antinature systems.

        Parameters:
        -----------
        one_body : np.ndarray
            One-body integral terms (kinetic energy, external fields)
        two_body : np.ndarray
            Two-body integral terms (particle-particle interactions)

        Returns:
        --------
        Tuple[Any, QuantumCircuit]
            Qubit operator representing the Hamiltonian, and quantum circuit
        """
        # Validate input shapes
        n_orbitals = one_body.shape[0]
        if one_body.shape != (n_orbitals, n_orbitals):
            raise ValueError(
                f"one_body shape expected {(n_orbitals, n_orbitals)}, got {one_body.shape}"
            )

        if two_body.shape != (n_orbitals, n_orbitals, n_orbitals, n_orbitals):
            raise ValueError(
                f"two_body shape expected {(n_orbitals, n_orbitals, n_orbitals, n_orbitals)}, got {two_body.shape}"
            )

        # Create electronic energy operator
        energy_op = ElectronicEnergy.from_raw_integrals(one_body, two_body)

        # Convert to fermionic operator first, then map to qubit operator
        fermionic_op = energy_op.second_q_op()
        qubit_op = self.mapper.map(fermionic_op)

        # Create a generic hardware-efficient circuit
        circuit = self._create_hardware_efficient_circuit(n_orbitals)

        return qubit_op, circuit

    def _create_hardware_efficient_circuit(self, n_qubits: int) -> QuantumCircuit:
        """Create a hardware-efficient circuit for a given number of qubits."""
        circuit = QuantumCircuit(n_qubits)

        # Initialize in superposition
        for i in range(n_qubits):
            circuit.h(i)

        # Layer of parameterized rotations
        for i in range(n_qubits):
            circuit.rx(Parameter(f'rx_{i}'), i)
            circuit.ry(Parameter(f'ry_{i}'), i)
            circuit.rz(Parameter(f'rz_{i}'), i)

        # Entanglement layer
        for i in range(n_qubits - 1):
            circuit.cx(i, i + 1)

        # Connect first and last qubit (circular)
        if n_qubits > 2:
            circuit.cx(n_qubits - 1, 0)

        # Second layer of parameterized rotations
        for i in range(n_qubits):
            circuit.rx(Parameter(f'rx2_{i}'), i)
            circuit.ry(Parameter(f'ry2_{i}'), i)
            circuit.rz(Parameter(f'rz2_{i}'), i)

        return circuit
