Fig. 1: Digital quantum simulations with reconfigurable atom arrays.

a, The honeycomb lattice used in this work with 104 total atomic qubits and periodic boundary conditions along the shorter direction, forming a cylinder (see also Extended Data Fig. 1a). The qubits are encoded in ⁸⁷Rb atoms and entangling gates are realized through excitation to interacting Rydberg states. To encode fermion statistics, we prepare a long-range entangled state characterized by hexagonal plaquette operators W_p = X₁Z₂Y₃X₄Z₅Y₆ that commute with the unitary evolution and are therefore conserved. The encoded Majorana fermions live on vertices, at the ends of operator strings, and conventional (complex) fermions are formed by combining two Majoranas along a chosen link orientation. b, The long-range entangled state is prepared using mid-circuit measurement of ancilla qubits, and plaquettes are deterministically flipped to be +1 using conditional single-qubit gates (red circle). c, The Floquet evolution cycle consists of atom reconfiguration interspersed with tunable entangling gates and global basis changes. d, Accumulated entangling phase upon repeated application of \(\exp ({\rm{i}}{\rm{\pi }}\theta [{\rm{Z}}\otimes {\rm{Z}}]/4)\) gates with a variable angle θ realized through fast, parameterized laser pulses (Extended Data Fig. 2). The values show extracted values of θ and error bars represent one standard deviation. AOD, acousto-optic deflector.