Quantum circuit compilation with quantum computers

TL;DR

This paper introduces quantum algorithms for circuit compilation, demonstrating potential quantum advantage by outperforming classical methods in compiling large quantum circuits with higher fidelity.

Contribution

It presents a novel quantum approach to circuit compilation, achieving significant fidelity improvements and scalability over classical methods.

Findings

Successfully compiled a 64-qubit Hamiltonian simulation with 64 time-steps.

Compiled a 40-qubit Quantum Fourier Transform with 771 time-steps.

Quantum compilation outperforms classical approaches in fidelity for large circuits.

Abstract

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.