  All-to-all connections are required in general quantum annealing machines to
solve various combinatorial optimization problems. The Lechner, Hauke, and
Zoller (LHZ) method, which is used to realize the all-to-all connections,
requires many-body interactions in locally connected qubits. Because most of
the qubit interactions are two-body interactions, Lechner also proposed the
construction of each four-body interaction by six controlled-NOT (CNOT) gates
between two qubits. However, it is difficult to construct many CNOT gates.
Herein, we show more concrete sequences to produce four-body and three-body
interactions based on a two-dimensional solid-state qubit system. We show that
the number of operations needed to construct the many-body interactions can be
reduced using appropriate pulse sequences. These findings will help reduce
quantum computation costs for solving combinatorial problems.
