Hamming Code

General nomenclature

Suppose you have a message |m> that is long n bits and you want to encode it in a noise resistant message |M>.

To do so you have to create a quantum circuit that is big enough to be able to hold |M> and additional ancillas (ancillas are required only for the syndrome).

How to use the gates

The function HammingEncode() returns a hamming encoding capable of encoding n Qbits

def HammingEncode(n, kind="both", name="Hamming encoder"):
    """Returns a hamming encoding gate of order N.
    To see the number of input qubits required for this circuit you can call 
    the function HammingSize()

    Args:
        n (int): The number of Qbits of you non-encoded message
        kind (str, optional): Set to "bit" for correcting bit flip errors,
        "phase" for correcting phase flip errors, "both" corrects both errors. 
        Defaults to "both".

    Returns:
        Gates: Hamming encode
    """

If you want decode the Hamming code you just have to add the HammingDecode gate to your circuit. If you don't want to read the output and you just want to correct an error assign read=False, that way the bits don't get switched for a easier readability.

def HammingDecode(n, kind="both", read=True, name="Hamming decoder"):
    """
    Args:
        n (int): The number of Qbits of you non-encoded message
        kind (str): The kind argument must be one of 'bit', 'phase' or 'both'. Defaults to 'both'.
        read (bool): If True returns the output on the first qbits, otherwise it doesn't switch the output. Defaults to True.
        name (str): The name written on the gate. Defaults to "Hamming decoder".

    Returns:
        gate: Hamming decode
    """

How big are these gates?

Every gate returned by these two functions has the size attribute, which tells how big the gate is