Two-particle scattering on general graphs

Quantum 10, 2038 (2026). https://doi.org/10.22331/q-2026-03-23-2038 Quantum walks in general graphs, or more specifically scattering on graphs, encompass enough complexity to perform universal quantum computation. Any given quantum circuit can be broken down into single- and two-qubit gates, which can then be translated into subgraphs – gadgets – that implement such unitaries on the logical qubits, simulated by particles traveling along a sparse graph. In this work, we start to develop a full theory of multi-particle scattering on graphs and give initial applications to build multi-particle gadgets with different properties.