Multi-spin couplers in superconducting quantum annealers – analysis based on perturbation theory

Multi-qubit interactions are important for many applications in quantum annealing, including the implementation of logical qubits for error correction and K^th order optimization problems with K > 2. One approach to the implementation of multi-qubit coupling is to use perturbative gadgets. We analyzed the properties of the couplers by the perturbative gadgets. We discuss the design of couplers optimized in the context of superconducting circuits, including gadgets based on ancilla qubits and other more general superconducting circuits. Critical problems in the design of perturbative gadgets with superconducting circuits are addressed.