Towards a bias-preserving CNOT gate between stabilized cat qubits (Part 1)

Bosonic codes enable hardware-efficient quantum error correction by exploiting the infinite-dimensional Hilbert space of a quantum harmonic oscillator to implement some of the required redundancy for error correction. Autonomously stabilized cat qubits have demonstrated an exponential suppression of bit-flips errors with the average number of photons of the cat states, at the cost of a linear increase of phase-flips. This results in a strong noise-bias that reduces the hardware requirements for further error correction. However, leveraging this first error protection layer requires that all quantum gates preserve the error-bias. Concretely, applying a gate should produce bit-flip errors that are also exponentially suppressed with the cat state photon number. One gate of central importance is the CNOT gate that is used to measure the error syndrome of the repetition code considered to correct the remaining phase-flips errors.

In this work, we present our progress in realizing a bias-preserving CNOT gate between two stabilized cat qubits. This requires both improvement in the performance of the individual cat qubits along with a careful gate design. This work paves the way towards the demonstration of full quantum error correction based on repeated cat qubits.