Logical Gates on Grid Codes with Gaussian Operations, Part 2: Numerical Results for CZ and CNOT Gates

Grid codes not only offer strong protection against noise, but also offer potential for high-fidelity entangling gates, which are readily implementable via Gaussian operations [1]. Such gates are accessible via squeezing and beamsplitter operations, implementable via a coupler. However, in physical implementations of grid codes, distortion of the finite-energy normalization envelope limits gate fidelity, leading to coherent errors that can accumulate into logical errors if left uncorrected [2].

In this work, we demonstrate how modifying the small-Big-small (sBs) stabilization protocol after single-mode grid code gates can lead to significantly improved gate fidelities, without the need for post-selection. We demonstrate numerical results for an implementation of entangling CZ and CNOT gates between two grid code qubits, including analysis of imperfect input states, and report bounds on the achievable fidelities. We anticipate these techniques to hold more generally, including for other multimode codes, thus addressing one of the shortcomings of gates in grid codes.

References:

[1] B. Royer et al., PRX Quantum 3, 010335 (2022)

[2] I. Rojkov et al., Phys. Rev. Lett. 133,100601 (2024)