Fault-Tolerant Multiqubit Geometric Entangling Gates Using Photonic Cat-State Qubits

We propose a theoretical protocol to implement multiqubit geometric gates (i.e., the Molmer-Sorensen gate) using photonic cat-state qubits. These cat-state qubits stored in high -Q resonators are promising for hardware-efficient universal quantum computing. Specifically, in the limit of strong two-photon driv-ings, phase-flip errors of the cat-state qubits are effectively suppressed, leaving only a bit-flip error to be corrected. Because this dominant error commutes with the evolution operator, our protocol preserves the error bias, and, thus, can lower the code-capacity threshold for error correction. A geometric evolution guarantees the robustness of the protocol against stochastic noise along the evolution path. Moreover, by changing detunings of the cavity-cavity couplings at a proper time, the protocol can be robust against parameter imperfections (e.g., the total evolution time) without introducing extra noises into the system. As a result, the gate can produce multimode entangled cat states in a short time with high fidelities.