A Schrödinger-cat qubit encodes logical |0⟩/|1⟩ not in a single photon but in two well-separated coherent states of a microwave resonator, |α⟩ and |−α⟩. Two-photon dissipation continuously pins the oscillator onto the manifold spanned by the even/odd cat states:
|C_α^±⟩ = N(|α⟩ ± |−α⟩), n̄ = |α|² = mean photon number
The rendered surface is the state's Wigner quasi-probability function in phase space (x = position quadrature, p = momentum quadrature):
W(x,p) ∝ e^-[(x−α)²+p²] + e^-[(x+α)²+p²] + 2·e^-(x²+p²)·cos(2αp)
The two outer bumps are the classical-looking |α⟩ and |−α⟩ lobes; the ripples between them are pure interference — negative regions of W (rendered red) are a direct signature of quantumness with no classical analogue.
The whole point of the encoding is biased noise. Single-photon loss can only hop the state between the two lobes by an amount ∝ α, so a full logical bit-flip needs a rare large fluctuation — its rate is exponentially suppressed in n̄. Dephasing, in contrast, only needs to scramble the interference fringes, so it scales linearly:
Γ_X (bit-flip) = κ₁ · exp(−2n̄)
Γ_Z (phase-flip) = κ_φ · n̄
bias = T_X / T_Z = Γ_Z / Γ_X
Raise n̄ and watch T_X shoot up while T_Z barely moves — this exponential vs. linear split is exactly why cat qubits let error-correction codes spend almost all their overhead on the one error type (phase-flip) that remains, instead of two. Turn Stabilization off to see the unprotected case: both rates become flat and independent of n̄, and the bias collapses to 1.
Real-world relevance: this is the mechanism behind bosonic cat-qubit hardware from groups such as Alice&Bob, AWS and Yale, proposed as a shortcut to fault-tolerant quantum computing with far fewer physical qubits per logical qubit than a bare surface code.