  In silicon quantum computers, a single electron is trapped in a
microstructure called a quantum dot, and its spin is used as a qubit. For
large-scale integration of qubits, we previously proposed an approach of
arranging the quantum dots in a two-dimensional array and sharing a control
gate in a row or column of the array. In our array, the shuttling of electrons
is a useful technique to operate the target qubit independently and avoid
crosstalk. However, since the shuttling is also conducted using shared control
gates, the movement of qubits is complexly constrained. We therefore propose a
formal model on the basis of state transition systems to describe those
constraints and operation procedures on the array. We also present an approach
to generate operation procedures under the constraints. Utilizing this
approach, we present a concrete method for our 16 $\times$ 8 quantum dot array.
By implementing the proposed method as a quantum compiler, we confirmed that it
is possible to generate operation procedures in a practical amount of time for
arbitrary quantum circuits. We also demonstrated that crosstalk can be avoided
by shuttling and that the fidelity in that case is higher than when crosstalk
is not avoided.
