Towards Fault Tolerant Joint Stabilizer Measurements for Bosonic Qubits: Part 1

Encoding qubits in the larger Hilbert space of cavity modes has many potential advantages due to superior coherence times and Bosonic error correction. However, to gain this benefit we must also be fault tolerant to errors in the non-linear element used for quantum control. Progress has been made in engineering fault tolerant single qubit measurements[1] and gates[2] for bosonic qubits. Ultimately, all operations, including two-qubit entangling operations, must be made similarly fault tolerant. We extend the scheme demonstrated in [1] to fault tolerant, QND joint photon number parity measurements by combining chi-matching and beamsplitter couplings between two cavities. These types of joint parity measurements are useful for Bell state generation, logical ZZ measurements and stabilizing concatenated codes for a variety of Bosonic encodings. In part 1 we describe the scheme and its fault tolerance properties.

[1] Rosenblum Science (2019)

[2] Reinhold Nat. Phys. (2020)