Non-local photonic SWAP, CNOT, Toffoli, and Fredkin gates

The problem asks whether spatially separated photons can implement $\mathrm{SWAP}$, $\mathrm{CNOT}$, $\mathrm{Toffoli}$, and $\mathrm{Fredkin}$ without bringing them together, pre-sharing entanglement, or using Bell-state measurements. No proposer or earlier partial result is identified in the retrieved sources.

November 2025 preprint

Automated Discovery of Non-local Photonic Gates claims constructions for all four gates using path indistinguishability, without shared entangled pairs or Bell-state measurements. It reports higher-dimensional $\mathrm{SWAP}$ and $\mathrm{CNOT}$ schemes, four-ancilla $\mathrm{Toffoli}$ and $\mathrm{Fredkin}$ schemes, and attributes the discoveries to PyTheus. These are experimental proposals rather than an independently verified proof or implementation.

Current status (as of September 2026): A preprint claims all four gates under the stated restrictions; no retrieved source verifies the constructions, so the problem remains unresolved.