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 quasi-local compilation approach.
@article{arxiv.2408.00077,
title = {Quantum circuit compilation with quantum computers},
author = {Davide Rattacaso and Daniel Jaschke and Marco Ballarin and Ilaria Siloi and Simone Montangero},
journal= {arXiv preprint arXiv:2408.00077},
year = {2025}
}