Schrödinger cat states provide a hardware-efficient platform for bosonic quantum error correction by encoding logical information in protected manifolds of harmonic oscillators. While previous work has demonstrated the dissipative stabilization of multi-mode Schrödinger cat states as robust quantum memories, a framework for universal quantum computation has remained unavailable. Here we work towards this by introducing a universal gate set for dissipatively stabilized multi-mode cat qubits as a necessary resource for computation. Using a chain of Kerr non-linear oscillators coupled through engineered non-local dissipation and an effective low-dimensional description, we show how single-qubit control can be achieved through arbitrary rotation around the
X-axis and
π/2-rotation around the
Z-axis. We further show how coupling two such stabilized arrays through just one oscillator on each respective array enables coherent entangling operations through implementation of the
XXπ/2 gate. Numerical simulations demonstrate high-fidelity gate dynamics and entanglement generation under realistic parameters. Finally, we analyze the effects of induced and intrinsic photon loss, disorder, and the validity regime of the effective low-dimensional theory. Our results establish dissipatively stabilized multi-mode Schrödinger cat states as a potential architecture for universal bosonic quantum computation.
The purpose of this Bachelor thesis is to study methods to engineer Schrödinger’s cat states in microwave resonators, as proposed in the paper Engineering quantum states of light by S. Puri et al. The thesis starts by introducing relevant notions and concepts. Thereafter, it provides several analytical as well as numerical derivations of the main equations and results in the paper by S. Puri et al. The Kerr non-linear resonator (KNR) is explored as a means to adiabatically generate cat states. The Hamiltonian of the KNR is modified by detuning and orthogonal drive modes to achieve faster initialisation. Some images are also replicated with Matlab and the Python toolbox QuTiP. Finally, we also construct a number of quantum gates using coherent states.
Explicit realization of quantum droplets, even and odd Schrödinger cat states is demonstrated in an atom-molecular Bose-Einstein condensate in the presence of interconversion and Kerr non-linear interactions. The crucial roles of both the
χ2-type nonlinearity and chemical potential in the formation of these macroscopic quantum states are shown, where the atomic condensate is in the cat state, with the corresponding molecular wave packet being a quantum droplet. The physical mechanism for their creation and common origin is established to be the non-linearity-induced self-trapping potentials, governed by photoassociation or Feshbach resonance, with the Kerr-type nonlinearities playing subdominant roles. The coexisting and controllable atom and molecular droplets are shown to realize the atom-molecular squeezed state with profiles ranging from Gaussian to flat-top super-Gaussian form. The Wigner functions are exhibited revealing the cat states' phase space interference and squeezing of droplets.