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Source code for qiskit_finance.circuit.library.probability_distributions.uniform

# This code is part of a Qiskit project.
#
# (C) Copyright IBM 2017, 2023.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""The uniform probability distribution circuit."""

from qiskit.circuit import QuantumCircuit


class UniformDistribution(QuantumCircuit):
    r"""A circuit to encode a discretized uniform distribution in qubit amplitudes.

    This simply corresponds to applying Hadamard gates on all qubits.

    The probability density function of the discretized uniform distribution on
    :math:`N` values is

    .. math::

        \mathbb{P}(X = x) = \frac{1}{N}.

    This circuit considers :math:`N = 2^n`, where :math:`n =` ``num_qubits`` and prepares the state

    .. math::

        \mathcal{P}_X |0\rangle^{\otimes n} = \frac{1}{\sqrt{2^n}} \sum_{x=0}^{2^n - 1} |x\rangle

    Examples:
        >>> from qiskit_finance.circuit.library.probability_distributions import UniformDistribution
        >>> circuit = UniformDistribution(3)
        >>> circuit.decompose().draw()
             ┌───┐
        q_0: ┤ H ├
             ├───┤
        q_1: ┤ H ├
             ├───┤
        q_2: ┤ H ├
             └───┘

    """

    def __init__(self, num_qubits: int, name: str = "P(X)") -> None:
        """
        Args:
            num_qubits: The number of qubits in the circuit, the distribution is uniform over
                ``2 ** num_qubits`` values.
            name: The name of the circuit.
        """
        inner = QuantumCircuit(num_qubits, name=name)
        inner.h(inner.qubits)

        super().__init__(num_qubits, name=name)
        self.append(inner.to_gate(), inner.qubits)