Stabilization of cat-state manifolds using nonlinear reservoir engineering
Reservoir engineering has become valuable for preparing and stabilizing quantum systems. Notably, it has enabled the demonstration of dissipatively stabilized Schrödinger’s cat qubits through engineered two-photon loss which are interesting candidates for bosonic error-corrected quantum computation. Reservoir engineering is however limited to simple operators often derived from weak low-order expansions of some native system Hamiltonians. In this talk, I will introduce a novel reservoir engineering approach for stabilizing multi-component Schrödinger’s cat states. The fundamental principle of the method lies in the destructive interference at crossings of gain and loss Hamiltonian terms coupling an oscillator to a zero-temperature auxiliary system, which are nonlinear with respect to the oscillator’s energy. I will explain how the characteristics of these gain and loss terms influence the rotational symmetry, energy distributions, and degeneracy of the stabilized manifolds as well as their robustness against various errors when considered as bosonic codes. I will then give example implementations using the anharmonic laser-ion coupling of a trapped ion as well as using nonlinear superconducting circuits. Finally, I will show that our formalism can be extended to stabilize bosonic codes related to cat states through unitary transformations, such as quadrature-squeezed cats.