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

Cat-Qubit Parameters

Cat size α 1.40

Single-photon loss κ₁ 0.15

Two-photon stabilization κ₂ 1.00

watching for errors…

Live Readouts

Photon number n̄ = α²

2.0

Phase-flip rate Γ_Z

0.04 /s

Mean bit-flip time T_X = e^(2α²)/κ₁

— s

Bit-flips seen

Phase-flips seen

Logical state: |0_L⟩ ≈ |+α⟩ well

How it works

A two-photon driven, dissipative microwave resonator stabilizes its field into one of two coherent states, |+α⟩ and |−α⟩, which encode a logical qubit: |0_L⟩ = 𝒩(|α⟩+|−α⟩), |1_L⟩ = 𝒩(|α⟩−|−α⟩). In phase space (Re β, Im β) this looks like a double-well potential with two minima at β = ±α separated by an energy barrier that grows with the photon number n̄ = |α|².

Stabilizing potential:  U(β) ∝ |β² − α²|²
Bit-flip (X) time:      T_X ∝ exp(2|α|²) / κ₁   — grows exponentially with n̄
Phase-flip (Z) rate:    Γ_Z ∝ κ₁ |α|²             — grows only linearly with n̄

Flipping the logical state means the resonator field must tunnel across the barrier from one well to the other — exponentially rare as α grows, because the barrier height scales with n̄. Ordinary single-photon loss (rate κ₁) instead nudges the phase of whichever coherent state the field is already in, which dephases the qubit (a Z error) at a rate that only grows linearly with n̄. The result is a strongly biased-noise qubit: essentially only Z errors occur, which lets an outer error-correction code spend almost all of its resources on one error type instead of two — the core idea behind Kerr-cat / dissipative-cat hardware roadmaps (AWS, Alice&Bob, Yale).

Cat size α — sets the separation of the two wells (n̄ = α²); larger α protects against bit-flips exponentially but dephases faster.
Single-photon loss κ₁ — the physical noise channel that drives both error types; it sets the overall timescale of both formulas above.
Two-photon stabilization κ₂ — how strongly the drive pins the field into the two wells; higher κ₂ tightens confinement around each well in this visualization.
The moving marker is the resonator's instantaneous phase-space point; a jump between wells is a simulated bit-flip, a visible kick within a well is a simulated phase-flip. Both are drawn as Poisson events at the rates printed above — watch how raising α all but freezes bit-flips while phase-flips keep ticking.

Resonator state (marker) Stabilized wells |±α⟩ Tunneling barrier

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