A measurement-based surface code with flying-cat parity checks

Superpositions of coherent states (Schrödinger’s cat states) can be used to transmit quantum information between different nodes of a quantum computer, relaxing scalability requirements [1]. Such states have recently been realized in a number of platforms, including Rydberg atoms [2] and superconducting qubits coupled to microwave transmission lines [3-5]. In this talk, we present a fully deterministic approach to fault-tolerant, measurement-based quantum computing that leverages the ability of cat states to distribute entanglement between stationary qubits. In such a scheme, syndrome information is extracted through homodyne detection of propagating coherent states. We discuss error sources intrinsic to this encoding, as well as how to optimize the scheme in the presence of photon loss.

[1] Z. McIntyre and W. A. Coish, arXiv: 2306.13573 (2023).

[2] Hacker et al., Nature Photonics 13, 110-115 (2019).

[3] Kono et al., Nature Physics 14, 546-549 (2018).

[4] Besse et al., PRX 8, 021003 (2018).

[5] Besse et al., PRX 10, 011046 (2020).