Systems and methods are provided for coupling two flux qubits. A quantum circuit assembly includes a first flux qubit, having at least two potential energy minima, and a second flux qubit, having at least two potential energy minima. A system formed by the first and second qubits has at least four potential energy minima prior to coupling, each of the four potential energy minima containing at least one eigenstate of a system comprising the first flux qubit and the second flux qubit. A coupler creates a first tunneling path between a first potential energy minimum of the system and a second potential energy minimum of the system, and a second tunneling path between a third potential energy minimum of the system and a fourth potential energy minimum of the system. The coupler creates the first and second tunneling paths between potential energy minima representing states of equal bit parity.