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arXiv · 2609.02559

Optimal Fusion Strategies for Quantum Computation

Kenneth Goodenough·Andrew Landahl·Joon Lee·Antonio Russo·Kevin Thompson
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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.~\emph{perfect 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.

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Kenneth Goodenough, Andrew Landahl, Joon Lee, Antonio Russo, Kevin Thompson. 2026-09-02. Optimal Fusion Strategies for Quantum Computation. https://arxiv.org/abs/2609.02559

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