  A superconducting quantum interference device (SQUID) comprising 0- and
$\pi$-Josephson junctions (JJs), called $\pi$-SQUID, is studied by the
resistively shunted junction model. The $\pi$-SQUID shows half-integer
Shapiro-steps (SS) under microwave irradiation at the voltage $V$ =
$(\hbar/2e)\Omega (n/2)$, with angular frequency $\Omega$ and half-integer
$n$/2 in addition to integer $n$. We show that the $\pi$-SQUID can be a
$\pi$-qubit with spontaneous loop currents by which the half-integer SS are
induced. Making the 0- and $\pi$-JJs equivalent is a key for the half-integer
SS and realizing the $\pi$-qubit.
