A method for performing a quantum gate operation on a logical qubit, comprising a plurality of physical qubits, that is resilient to noise on control signals, on the individual physical qubits, and on the coupling strengths between physical qubits, the method comprising: applying a set of control signals to provide a first Hamiltonian for a system comprising an array of physical qubits, the array of physical qubits including at least the plurality of physical qubits, and a plurality of coupling mechanisms, comprising a first set of coupling mechanisms, each of the first set of coupling mechanisms operatively coupling an associated pair of neighboring physical qubits within the array in a first direction of the array along a first axis of the Bloch sphere, such that, when a coupling strength of a given coupling mechanism is non-zero, it is energetically favorable for the states of the coupled qubits to align in a same direction along the first axis of the Bloch sphere, and a second set of coupling mechanisms, each of the second set of coupling mechanisms operatively coupling an associated pair of neighboring physical qubits within the array in a second direction of the array along a second axis of the Bloch sphere, such that, when a coupling strength of a given coupling mechanism is non-zero, it is energetically favorable for the states of the coupled qubits to align in a same direction along the second axis of the Bloch sphere, the first Hamiltonian representing, for each coupling mechanism, a coupling strength between zero and a maximum value; and applying a logical operator to the system as an adiabatic interpolation of the Hamiltonian of the system from the first Hamiltonian to a second Hamiltonian, the second Hamiltonian representing, for at least one of the plurality of coupling mechanisms, a coupling strength different from that of the first Hamiltonian, with each of the first Hamiltonian and the second Hamiltonian being selected such that the logical operator commutes with an arbitrary weighted sum of the first Hamiltonian and the second Hamiltonian. applying a set of control signals to provide a first Hamiltonian for a system comprising an array of physical qubits, the array of physical qubits including at least the plurality of physical qubits, and a plurality of coupling mechanisms, comprising a first set of coupling mechanisms, each of the first set of coupling mechanisms operatively coupling an associated pair of neighboring physical qubits within the array in a first direction of the array along a first axis of the Bloch sphere, such that, when a coupling strength of a given coupling mechanism is non-zero, it is energetically favorable for the states of the coupled qubits to align in a same direction along the first axis of the Bloch sphere, and a second set of coupling mechanisms, each of the second set of coupling mechanisms operatively coupling an associated pair of neighboring physical qubits within the array in a second direction of the array along a second axis of the Bloch sphere, such that, when a coupling strength of a given coupling mechanism is non-zero, it is energetically favorable for the states of the coupled qubits to align in a same direction along the second axis of the Bloch sphere, the first Hamiltonian representing, for each coupling mechanism, a coupling strength between zero and a maximum value; and applying a logical operator to the system as an adiabatic interpolation of the Hamiltonian of the system from the first Hamiltonian to a second Hamiltonian, the second Hamiltonian representing, for at least one of the plurality of coupling mechanisms, a coupling strength different from that of the first Hamiltonian, with each of the first Hamiltonian and the second Hamiltonian being selected such that the logical operator commutes with an arbitrary weighted sum of the first Hamiltonian and the second Hamiltonian.