Preparation-Space Diagnostics and Logical Information Loss in a Driven Kerr-Cat Qubit Oscillator

A Kerr-cat qubit encodes a logical bit in the two wells of a parametrically driven nonlinear oscillator, and a logic gate is a transient change of the drive. In the phase plane, the gate deforms the double well and can split its separatrix into a turnstile that carries trajectories across the dividing surface between the wells; the same pulse, acting on the quantum oscillator, can corrupt the encoded bit. We study this process over a disk of coherent-state preparations, comparing classical phase-space transport diagnostics with the open-system quantum outcome on a common domain so that the two can be compared point by point. The central finding is that the corruption depends on the full temporal protocol, not on pulse strength alone: a sudden quench erases the bit, whereas a smooth ramp of the same peak amplitude largely preserves it. A finite-time sensitivity field locates the classical transport boundary, and a Loschmidt echo evaluated near the end of the gate predicts the much later quantum outcome. Sweeping the pulse amplitude, the pulse width, the cat size, and the rate of an engineered two-photon dissipation, we map where the classical transport picture predicts the quantum loss of the bit and where it does not.