The engineered dissipation approach enables autonomous error correction, and Kerr-cat qubit supports bias-preserving gates which brings done the cost of fault-tolerant error correction by utilizing the noise structure. It seems bosonic qubits are really good in terms of error correction. I'm curious about what's the down-side of them? Are physical gate errors too high? Or is the coherence time too short? Or are they hard to manufacture?
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It's true what you are saying. Sadly they have a problem called loss. In a larger circuit the loss will be significant and we will not get the estimated output. If you want to know more about this I recomend you the Xanadu Quantum Photonics web: https://strawberryfields.ai/photonics/concepts/index.html
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I'm not an expert on this platform, but I believe one of the main problem with Kerr-cat qubits are practical problems from working with not perfectly coherent states. An ideal coherent state $$|\alpha\rangle = e^{-|\alpha|^2}\sum_{n=0}^{\infty} \frac{\alpha^n}{n!}|n\rangle$$ should be protected from annihilation losses. However, they also have an infinite number terms which include arbitrarily large $|n\rangle$. Even though such states have exponentially small coefficients, I believe the large (to infinite) energies associated with these higher terms causes such states to be incredibly difficult to generate and extremely lossy (with some kind of $n$-dependent loss process). For this reason, I think most demonstrations use a truncated Kerr-cat code which realizes many of the benefits, but only goes out to a fixed $n$ which means the qubit isn't fully protected from annihilation losses.
