Construction of bias-preserving operations for pair-cat codes

Fault-tolerant quantum computation with depolarization error often requires demanding threshold and resource overhead. If the operations can maintain high noise bias---dominated by dephasing small bit-flip error---we achieve hardware-efficient fault-tolerant a more favorable threshold. Distinct from two-level physical systems, multilevel systems (such as harmonic oscillators) desirable set of bias-preserving while using continuous engineered dissipation or Hamiltonian protection to stabilize encoding subspace. For example, cat codes stabilized driven-dissipation Kerr nonlinearity possess gates continuously correcting bosonic error. However, are not compatible correction against excitation loss error, because it is challenging monitor parity correct photon errors. In this work, we generalize pair-cat codes, which be regarded multimode generalization both Our results open door towards robust information processing simultaneously