A logical qubit, a quantum processor, and a method of performing an operation on the logical qubit are discussed. The logical qubit includes first and second tunable couplers and a plurality of fixed couplers, with at least one fixed coupler providing four physical qubit interaction. The first and second tunable couplers and the fixed couplers enforce even parity in any connected qubits. The logical qubit has a plurality of physical qubits with qubits connected to the first tunable coupler and a first fixed coupler, qubits connected to the second tunable coupler and a second fixed coupler, and qubits connected between the first fixed coupler and the second fixed coupler. Each fixed coupler is connected to at least two physical qubits and at least two paths connect the first tunable coupler and the second tunable coupler, with one path communicating with a microwave line.