Kerr-Cat Qubit: Biased-Noise Bit-Flip Protection

This simulator renders the phase-space potential a two-photon driven, dissipative resonator uses to stabilize a "cat qubit" — a logical qubit encoded in a superposition of two coherent states, |+α⟩ and |−α⟩, sitting in the wells of a double-well surface shaped by the stabilization drive. Drag the cat size α and you change the photon number n̄ = α² that separates the wells: the mean time between bit-flip errors grows exponentially with n̄ while the phase-flip rate only grows linearly, so a real cat-qubit resonator becomes an almost purely Z-biased noise source as it gets bigger — the trade-off that makes bias-preserving error correction with cat qubits practical. The marker wandering across the surface is a live stochastic simulation of that resonator state: watch how raising α nearly freezes the rare jumps between wells while the in-well jitter (dephasing) keeps ticking, exactly as the printed formulas predict.