Felix Burt

Scaling fault-tolerant quantum computers beyond a single processor is widely expected to require a network of matter-based quantum processing units (QPUs) connected by photonic links. Matter qubits inside each QPU experience predominantly Pauli noise, well handled by circuit-based quantum error correction (CBQC), while the inter-node channel is dominated by photon loss and probabilistic linear-optical operations. This mismatch makes distributed logical operations such as lattice-surgery merges the bottleneck of most modular architectures. Measurement- and fusion-based quantum computing (MBQC/FBQC) tolerate erasure far better than CBQC, but are typically treated as alternatives rather than as components that can be combined with it. We use a recent ZX-calculus translation between CBQC, MBQC and FBQC to construct hybrid protocols in which circuit-based surface-code patches are connected through a cluster state or fusion network, tailoring the error correction to the noise of each region. We give a generic recipe for converting sub-graphs of a stabiliser ZX diagram into equivalent cluster states and fusion networks while consistently translating the Pauli webs that define the checks and observables. Applying it to a lattice-surgery merge between two rotated surface-code patches yields a family of fusion-assisted lattice surgery protocols. We benchmark the fusion-assisted merge as a logical Bell pair generator under a joint Pauli-plus-erasure noise model using a minimum-weight parity-factor decoder, finding that the hybrid protocol tolerates around 25% photon erasure in the network, compared to a 5% depolarisation threshold for an equivalent protocol based on noisy matter-based Bell pairs. The construction extends naturally to multi-partite logical entanglement, suggesting a compiler framework that places fusion networks wherever the hardware is loss-dominated.