Extended Data Fig. 5: Fermion encoding description.

Details of the fermion-to-qubit mapping and its origins. a, An example Jordan-Wigner (JW) ordering spanning a honeycomb lattice on a cylinder. In our case the string is constructed as a product of link operators (see text). b, The operators which are fixed to +1 (stabilizers) on the topological state include the hexagonal plaquettes and the loops around the cylinder. c, A local fermion hopping term between two sites results in a macroscopic JW operator. The underlying long-range entanglement enables reducing this operator to a local one by multiplying the string with the relevant stabilizers. d, Construction of complex-fermion hopping in terms of spin operators. The length-4 Pauli string cancels the particle-creation terms resulting from the length-2 hopping operator. e, Table describing operator mapping between qubits and fermions. Sites i,k belong to the even sublattice and j belongs to the odd sublattice. Sites \({i}^{{\prime} }\),\({j}^{{\prime} }\) complement i,j along the ZZ links.