A SAT approach to the initial mapping problem in SWAP gate insertion for commuting gates

Most quantum circuits require SWAP gate insertion to run on hardware with limited qubit connectivity. A promising method for blocks of commuting two-qubit gates is a predetermined swap strategy which applies layers simultaneously executable the coupling map. good initial mapping reduces number required gates. However, even when circuit consists gates, e.g., as in Quantum Approximate Optimization Algorithm (QAOA) or trotterized simulations Ising Hamiltonians, finding hard problem. We present SAT-based approach find mappings transpiled strategies. Our achieves 65% reduction count random three-regular graphs 500 nodes. In addition, we heuristic that combines SAT formulation clustering algorithm reduce large problems manageable size. This by 25% compared both trivial and graph 1000 Good will therefore enable study algorithms, such QAOA Hamiltonian simulation applied sparse problems, noisy several hundreds qubits.