Quantum circuit compilation with quantum computers

Compilation optimizes quantum algorithms’ performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers, paving the way for a quantum advantage in compilation. We demonstrate the effectiveness of this approach via quantum and simulated annealing-based compilation: We successfully compile a Trotterized Hamiltonian simulation with up to 64 qubits and 64 time steps and a quantum Fourier transform with up to 40 qubits and 771 time steps. We show that, for a translationally invariant circuit, the compilation results in a fidelity gain that grows extensively in the size of the input circuit, outperforming any local or quasilocal compilation approach.