  It is imperative to compile quantum circuits for Noisy Intermediate-Scale
Quantum (NISQ) devices because of the limited connectivity of physical qubits
and the high error rates of gate operations. One of the most critical steps in
quantum circuit compilation is qubit routing, an NP-Hard problem that involves
placing and moving logical qubits to minimize compilation overhead. In this
study, we propose ISing mAchine Assisted Quantum compiler (ISAAQ) to perform
qubit routing with Ising machines, which can efficiently solve Quadratic
Unconstrained Binary Optimization (QUBO) problems. ISAAQ accurately estimates
the compilation costs by updating itself using previous compilation results,
and accelerates qubit routing by solving QUBO problems in parallel with
multiple Ising machines. In addition, ISAAQ exploits a cost-reduction method
that implements commutative logical Controlled-NOT (CNOT) gates with fewer
physical CNOT gates, which is particularly effective for planar devices when
implementing original gates. Experimental results on both IBM QX5 and IBM QX20
show that ISAAQ outperforms the heuristic methods available in Qiskit and tket,
as well as an existing QUBO method, requiring fewer physical CNOT gates for
most benchmark circuits. ISAAQ performs particularly well on large circuits,
demonstrating its strong scalability with respect to the number of logical CNOT
gates.
