The key challenge of implementing is resolved with Rydberg atoms by combining the odd parity representation13 of equation (2) with enhanced Rydberg–Rydberg dressing19 schemes in a two-species mixture2021. In the odd parity representation, the sum of the four spins at each plaquette is either 2 or −2. We introduce a single ancilla qubit at each plaquette, which can compensate the two associated energies and make odd parity plaquette states degenerate ground states of the constraint Hamiltonian , with stabilizer operators , and energy gap . This allows to implement the four-body gauge constraints via appropriately designed two-body Ising interactions between physical and ancilla qubits.