ISAAQ: Ising Machine Assisted Quantum Compiler

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.