Kerr parametric oscillators (KPOs) implemented in the circuit QED
architecture can operate as qubits. Their applications to quantum annealing and
universal quantum computation have been studied intensely. For these
applications, the readout of the state of KPOs is of practical importance. We
develop a scheme of state tomography for KPOs with reflection measurement.
Although it is known that the reflection coefficient depends on the state of
the KPO, it is unclear whether tomography of a qubit encoded into a KPO can be
performed in a practical way mitigating decoherence during the measurement, and
how accurate it is. We show that the reflection coefficient has a one-to-one
correspondence with a diagonal element of the density matrix of the qubit when
a probe frequency is properly chosen and an additional single-photon-drive is
introduced. Thus, our scheme offers a novel way to readout the qubit along an
axis of the Bloch sphere, and therefore the reflection measurement and
single-qubit gates can constitute state tomography