def oracle(circ):
    """
    Implements an oracle that flips the sign of states that contain P = 1.
    """
    circ.cu3(pi, pi, 0, net[0], net[1])
    circ.cu3(pi, pi, 0, net[0], net[1])
    return circ


def u_gate(circ):
    """
    Implements the U gate that flips states about the average amplitude.
    """
    # Implements the quantum circuit that converts ψ -> |000...0>
    circ.u3(-1*probToAngle(0.35), 0, 0, net[0])
    circ.u3(-1*probToAngle(0.76), 0, 0, net[1])
    circ.u3(-1*probToAngle(0.39), 0, 0, net[2])

    # Flipping the |000...0> state using a triple controlled Z gate condtioned on P, E and H,
    # and applied to the ancilla
    circ.x(net)
    circ.cu1(pi/4, net[0], net[3])
    circ.cx(net[0], net[1])
    circ.cu1(-pi/4, net[1], net[3])
    circ.cx(net[0], net[1])
    circ.cu1(pi/4, net[1], net[3])
    circ.cx(net[1], net[2])
    circ.cu1(-pi/4, net[2], net[3])
    circ.cx(net[0], net[2])
    circ.cu1(pi/4, net[2], net[3])
    circ.cx(net[1], net[2])
    circ.cu1(-pi/4, net[2], net[3])
    circ.cx(net[0], net[2])
    circ.cu1(pi/4, net[2], net[3])
    circ.x(net)

    # Implements the quantum circuit that converts |000...0> -> ψ
    circ.u3(probToAngle(0.35), 0, 0, net[0])
    circ.u3(probToAngle(0.76), 0, 0, net[1])
    circ.u3(probToAngle(0.39), 0, 0, net[2])

    return circ