  Quantum tunneling is the phenomenon that makes superconducting circuits
"quantum". Recently, there has been a renewed interest in using quantum
tunneling in phase space of a Kerr parametric oscillator as a resource for
quantum information processing. Here, we report a direct observation of quantum
interference induced by such tunneling in a planar superconducting circuit
through Wigner tomography. We experimentally elucidate all essential properties
of this quantum interference, such as mapping from Fock states to cat states, a
temporal oscillation due to the pump detuning, as well as its characteristic
Rabi oscillations and Ramsey fringes. Finally, we perform gate operations as
manipulations of the observed quantum interference. Our findings lay the
groundwork for further studies on quantum properties of superconducting Kerr
parametric oscillators and their use in quantum information technologies.
