Chiral cat code: enhanced error correction through higher-order nonlinearities

Cat states are noise-biased bosonic quantum codes that use coherent states with opposite phases to represent logical 0 and 1, efficiently suppressing bit-flip errors caused by photon-loss events [1]. Cat states are typically generated through two-photon pumping mechanisms and stabilized either by two-photon dissipation (dissipative cat) or by Kerr-type Hamiltonian nonlinearities (Kerr cat). Squeezing [2], detuning, and nonlinearity, in combination with hybrid confining mechanisms [3,4], can enhance the performance of cat-based logical qubits.

Here, we introduce the chiral cat code, which operates in regimes where higher-order nonlinearities are present. Normally, a cat state consists of only two coherent states, and dissipation introduces random jumps between them. In contrast, the chiral cat state supports the coexistence of two additional coherent states with different photon numbers. Crucially, when an error occurs, the state with a higher photon number mainly decays to the same corresponding state with a lower photon number, and vice versa. This structured decay leads to a chiral evolution in phase space, making it possible to detect and correct bit-flip errors. This code leverages the higher-order nonlinear processes that naturally emerge in nonlinear circuit-QED systems, which would normally be detrimental for Kerr cats.

[1] New J. Phys. 16, 045014 (2014).

[2] Phys. Rev. A 106, 022431 (2022).

[3] PRX Quantum 3, 020339 (2022).

[4] PRX Quantum 4, 020337 (2023).