Chiral cat code: Enhanced error correction induced by higher-order nonlinearities

Abstract

We introduce a Schr\"odinger chiral cat qubit, a novel bosonic quantum code generalizing Kerr cat qubits that exploits higher-order nonlinearities. Compared to a standard Kerr cat, the chiral cat qubit allows additional correction of bit-flip errors within the Hilbert space of a single bosonic oscillator. Indeed, this code displays optical bistability, i.e., the simultaneous presence of multiple long-lived states. Two of them define the code space and two define an error space. Thanks to the chiral structure of the phase space of this system, the error space can be engineered to ``capture''bit flip events in the code space (a bit-flip trap), without affecting the quantum information stored in the system. Therefore, it is possible to perform detection and correction of errors. We demonstrate how this topological effect can be particularly efficient in the presence of large dephasing. We provide concrete examples of the performance of the code and show the possibility of applying quantum operations rapidly and efficiently. Beyond the interest in this single technological application, our work demonstrates how the topology of phase space can enhance the performance of bosonic codes.