Fault-Tolerant Bell Measurements with the 4-Legged Schr?dinger-Cat Code

Previously, the 4-legged cat code has been used to realize a quantum memory surpassing the breakeven point [1] but we wish to perform a wider set of logical operations using this encoding. We propose a new scheme to perform destructive Bell measurements on pairs of 4-legged cat codes which requires only a beam-splitter coupling between two cavities and dispersively coupled transmon ancillae. Importantly, noise in these Bell measurements is at worst second order in the cavities’ single-photon loss and transmons’ relaxation and dephasing errors. With these Bell measurements, the cat-code can now be fused into a surface code cluster state. Since these are first-order fault tolerant measurements, we may achieve substantially lower logical error rates when concatenated with the surface code, than otherwise possible with unencoded physical qubits.

[1] Ofek et. al. Nature 536, 441–445 (2016)