New prospects for fault-tolerant quantum error correction with biased-noise cat-qubits

Exploiting the structure of noise or “noise-bias” in physical qubits could improve the threshold and overhead requirements for fault-tolerant quantum error correction. The challenge however is to be able to maintain the noise bias while performing elementary operations such as a CNOT gate. I will show how this challenge can be overcome by using the so called stabilized cat-qubits in a parametrically driven non-linear oscillators. In such a qubit, the bit-flip errors increase linearly with the size of the cat, while phase-flips are exponentially suppressed with the cat-size. The stabilized cat-qubit, therefore, exhibits a strongly biased-noise channel. In fact, the phase of the drive determines a continuous family of biased noise cat-states. I will discuss how a bias-preserving CNOT gate can be implemented with these cat-qubits by rotating them through the continuous family of the cat-states in the phase space. I will also present a set of other bias-preserving operations that can be performed with the stabilized cat-qubit. These results provide a new direction for designing error correction codes with high thresholds and reduced overheads.