def _simplify_circuit_string(circuit_str):
    """
    Simplify a string representation of a circuit.

    The simplified string should evaluate to the same operation label tuple
    as the original.

    Parameters
    ----------
    circuit_str : string
        the string representation of a circuit to be simplified.
        (e.g. "Gx{}", "Gy^1Gx")

    Returns
    -------
    string
        the simplified string representation.
    """
    s = circuit_str.replace("{}", "")
    s = s.replace("^1G", "G")
    s = s.replace("^1(", "(")
    s = s.replace("^1{", "{")
    if s.endswith("^1"): s = s[:-2]
    return s if len(s) > 0 else "{}"