Kenneth Goodenough, Andrew Landahl, Joon Lee, Antonio Russo, Kevin Thompson (Sep 03 2026).
Abstract: Logical fusions are important for a number of tasks in quantum information, such as quantum error correction and quantum repeaters. In the photonic setting one must contend with the fact that physical fusions are probabilistic (i.e.
the associated qubits are measured in product bases), which---depending on the failures and the associated bases---can lead to a failure on the logical level. The choice of failure basis of each qubit is known as a fusion strategy, and finding good fusion strategies is important for optimizing performance of fusion-based quantum computation. Here we provide a complete characterization when k=1 qubits are encoded, and in particular characterize those codes and fusion strategies such that all but one physical fusion can fail, i.e.\emphperfect fusion strategies. In doing so, we recover previously known perfect fusion strategies, and find perfect fusion strategies for quantum parity-check codes, answering an open question. We furthermore show that perfect fusion strategies are generic: random
[[n,1,d]] graph codes admit a perfect fusion strategy with probability exponentially close to
1. Additionally we motivate the study of a new graph parameter, namely the maximum degree of a graph at a given vertex taken over all LC-equivalent graphs, by giving a new operationally meaningful interpretation of it.
