Assembling a chain of 3 cat-qubits for phase-flip error detection (Part 1)

Bosonic codes provide a first level of error protection to limit the hardware overhead required for quantum error correction. However, to reach low enough error rates for practical quantum algorithms, these codes have to be concatenated with a discrete variable quantum error correction code, such as the surface code. Like other bosonic codes, autonomously stabilized cat-qubits have demonstrated this first layer of error correction, suppressing bit-flips exponentially with average photon number at a linear cost in phase-flips. However, the necessary concatenation with a repetition code to correct against phase-flip has yet to be demonstrated.

In this work, we show how to implement a phase-flip error detection scheme with 3 stabilized cat qubits by post-selecting on the negative/trivial error syndromes. This requires accurate error syndrome extraction which relies both on high fidelity CNOT gates and fast parity measurements. Performing error detection is an important milestone towards error correction. Further improving error syndrome extraction will enable full quantum error correction of a small scale repetition code in the near future.