Conditional finite-size fusion-photon costs and an open-channel validation
Arjun Anand · Zenodo (CERN European Organization for Nuclear Research) · 2026
This working research manuscript studies a conditional finite size photon cost benchmark for four and eight photon fusion implementations in a periodic, Shor encoded six ring syndrome graph with unequal resource and ancillary photon loss parameters. The numerical study separates structural ambiguity from a uniform prior failure statistic and reports simultaneously certified finite size minima under an explicitly stated local check effective error model. Preparation cost sensitivity is used to identify when additional ancillary state overhead removes a conditional advantage from fusion boosting. A separate open boundary encoded-teleportation example tests transmission of an unknown logical qubit using an explicit unboosted fusion instrument. Exhaustive enumeration of 217 nonzero accessible measurement records agrees with the rank based prediction for entanglement fidelity and includes both recoverable and unrecoverable loss patterns. The six ring cost results are conditional benchmark results and are not claimed to be established physical logical channel costs. Deriving appropriate logical input/output boundaries and complete boosted measurement instruments remains open. The accompanying archive contains the LaTeX source, figures, validation programs, numerical results, frozen simulation archive and integrity hashes. This manuscript has not undergone peer review.