High-order and long-range connectivity for embedding problems in quantum annealing with superconducting flux qubits*

A high degree of connectivity between qubits is believed to be important in quantum annealing. An approach for implementing high connectivity in superconducting flux qubit annealers was proposed in which the qubits are connected via chains of rf-SQUID couplers. We report an application of this concept in building problem-specific annealing architectures with high-order connectivity. We analyzed the coupling strength between qubits and the coupler network induced qubit decoherence for application-oriented architectures, using both simplified spin models and full quantum circuit models. We designed devices with capacitively shunted flux qubits coupled by coupler trees. We discuss experimental prospects and the relevance for large scale annealing.