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Gates Base API Reference

This page documents the base classes available in the skq.gates module.

Base Gate

The BaseGate class serves as the foundation for all quantum gates in SKQ.

skq.gates.base.BaseGate

Bases: Operator

Base class for quantum gates of any computational basis. The gate must be a 2D unitary matrix. :param input_array: Input array to create the gate. Will be converted to a NumPy array.

Source code in src/skq/gates/base.py 
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class BaseGate(Operator):
    """
    Base class for quantum gates of any computational basis.
    The gate must be a 2D unitary matrix.
    :param input_array: Input array to create the gate. Will be converted to a NumPy array.
    """

    def __new__(cls, input_array) -> "BaseGate":
        obj = super().__new__(cls, input_array)
        assert obj.is_unitary(), "Gate must be unitary."
        return obj

    def is_unitary(self) -> bool:
        """Check if the gate is unitary (U*U^dagger = I)"""
        identity = np.eye(self.shape[0])
        return np.allclose(self @ self.conjugate_transpose(), identity)

    def kernel_density(self, other: "BaseGate") -> complex:
        """
        Calculate the quantum kernel using density matrices.
        The kernel is defined as Tr(U * V).
        :param other: Gate object to compute the kernel with.
        :return kernel: Complex number representing the kernel density.
        """
        assert isinstance(other, BaseGate), "Other object must be an instance of BaseUnitary (i.e. a Unitary matrix)."
        assert self.num_levels() == other.num_levels(), "Gates must have the same number of rows for the kernel density."
        return np.trace(self @ other)

    def hilbert_schmidt_inner_product(self, other: "BaseGate") -> complex:
        """
        Calculate the Hilbert-Schmidt inner product with another gate.
        The inner product is Tr(U^dagger * V).
        :param other: Gate object to compute the inner product with.
        :return inner_product: Complex number representing the inner product.
        """
        assert isinstance(other, BaseGate), "Other object must be an instance of BaseUnitary (i.e. a Unitary matrix)."
        assert self.num_levels() == other.num_levels(), "Gates must have the same number of rows for the Hilbert-Schmidt inner product."
        return np.trace(self.conjugate_transpose() @ other)

    def convert_endianness(self) -> "BaseGate":
        """Convert a gate matrix from big-endian to little-endian and vice versa."""
        num_qubits = self.num_qubits
        perm = np.argsort([int(bin(i)[2:].zfill(num_qubits)[::-1], 2) for i in range(2**num_qubits)])
        return self[np.ix_(perm, perm)]

convert_endianness()

Convert a gate matrix from big-endian to little-endian and vice versa.

Source code in src/skq/gates/base.py 
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def convert_endianness(self) -> "BaseGate":
    """Convert a gate matrix from big-endian to little-endian and vice versa."""
    num_qubits = self.num_qubits
    perm = np.argsort([int(bin(i)[2:].zfill(num_qubits)[::-1], 2) for i in range(2**num_qubits)])
    return self[np.ix_(perm, perm)]

hilbert_schmidt_inner_product(other)

Calculate the Hilbert-Schmidt inner product with another gate. The inner product is Tr(U^dagger * V). :param other: Gate object to compute the inner product with. :return inner_product: Complex number representing the inner product.

Source code in src/skq/gates/base.py 
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def hilbert_schmidt_inner_product(self, other: "BaseGate") -> complex:
    """
    Calculate the Hilbert-Schmidt inner product with another gate.
    The inner product is Tr(U^dagger * V).
    :param other: Gate object to compute the inner product with.
    :return inner_product: Complex number representing the inner product.
    """
    assert isinstance(other, BaseGate), "Other object must be an instance of BaseUnitary (i.e. a Unitary matrix)."
    assert self.num_levels() == other.num_levels(), "Gates must have the same number of rows for the Hilbert-Schmidt inner product."
    return np.trace(self.conjugate_transpose() @ other)

is_unitary()

Check if the gate is unitary (U*U^dagger = I)

Source code in src/skq/gates/base.py 
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def is_unitary(self) -> bool:
    """Check if the gate is unitary (U*U^dagger = I)"""
    identity = np.eye(self.shape[0])
    return np.allclose(self @ self.conjugate_transpose(), identity)

kernel_density(other)

Calculate the quantum kernel using density matrices. The kernel is defined as Tr(U * V). :param other: Gate object to compute the kernel with. :return kernel: Complex number representing the kernel density.

Source code in src/skq/gates/base.py 
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def kernel_density(self, other: "BaseGate") -> complex:
    """
    Calculate the quantum kernel using density matrices.
    The kernel is defined as Tr(U * V).
    :param other: Gate object to compute the kernel with.
    :return kernel: Complex number representing the kernel density.
    """
    assert isinstance(other, BaseGate), "Other object must be an instance of BaseUnitary (i.e. a Unitary matrix)."
    assert self.num_levels() == other.num_levels(), "Gates must have the same number of rows for the kernel density."
    return np.trace(self @ other)