  Quantum computers with Kerr-nonlinear parametric oscillators (KPOs) have
recently been proposed by the author and others. Quantum computation using KPOs
is based on quantum adiabatic bifurcations of the KPOs, which lead to quantum
superpositions of coherent states, such as Schrodinger cat states. Therefore,
these quantum computers are referred to as "quantum bifurcation machines
(QbMs)." QbMs can be used for qauntum adiabatic optimization and universal
quantum computation. Superconducting circuits with Josephson junctions,
Josephson parametric oscillators (JPOs) in particular, are promising for
physical implementation of KPOs. Thus, KPOs and QbMs offer not only a new path
toward the realization of quantum bits (qubits) and quantum computers, but also
a new application of JPOs. Here we theoretically explain the physics of KPOs
and QbMs, comparing them with their dissipative counterparts. Their physical
implementations with superconducting circuits are also presented.
