Perfect fusion strategies for fusion-based quantum computation
Given a quantum error-correcting code encoding logical qubits, characterize the codes and fusion strategies for which the induced logical fusion succeeds for every pattern in which at most one of the physical fusions succeeds and all remaining physical fusions fail. In particular, determine this characterization for and determine which quantum parity-check codes admit such a perfect fusion strategy.
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Progress summary
A September 2026 preprint claims a major resolution for one encoded qubit and answers the parity-check-code question, but broader strategy optimization remains open.
The problem asks which quantum codes admit fusion strategies that remain perfect despite fusion failures. The new preprint claims a complete characterization when , including strategies surviving failure of all but one physical fusion.
September 2026 preprint
Optimal Fusion Strategies for Quantum Computation claims that quantum parity-check codes possess perfect fusion strategies and that suitable strategies generically exist for random graph codes. It also identifies codes tolerating failure of all but one physical fusion. The characterization is restricted to one encoded qubit, so the broader optimization problem remains open.
Current status (as of September 2026): A preprint claims the case and the quantum parity-check-code question are settled, while broader fusion-strategy optimization remains open.
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