Extended Data Fig. 8: Fermion exchange protocol.

a, Four complex-fermion sites involved in the fermion exchange experiments, and where they are embedded in the full lattice. b, Full gate sequence for the exchange protocol (partial pair creation, first hop, second hop, and readout of the exchange phase by repeating the partial pair creation). Four-body interaction terms for the hopping sections are realized by a sequence of two-qubit gate applications. c, Depiction of qubits undergoing the two-qubit gates at each time step, denoted by red lines. The black qubits are the atoms that are picked up by AOD traps to perform the gates, and the layout is designed such that gates can be applied in parallel at each time step, as illustrated in the diagrams. d, Demonstration of the hopping gate H₁ for the two-fermion basis state (created by applying R twice) and the fermionic vacuum state. e, Additional data for the exchange protocol, showing additional intermediate steps of the process. During the middle three steps, the state of the system is described by a superposition of zero fermions and two fermions at different positions in the lattice.