Meuli, GiuliaSoeken, MathiasDe Micheli, Giovanni2022-02-142022-02-142022-02-142022-01-2710.1038/s41534-021-00514-yhttps://infoscience.epfl.ch/handle/20.500.14299/185318WOS:000749181900004Quantum compilation is the task of translating a high-level description of a quantum algorithm into a sequence of low-level quantum operations. We propose and motivate the use of Xor-And-Inverter Graphs (XAG) to specify Boolean functions for quantum compilation. We present three different XAG-based compilation algorithms to synthesize quantum circuits in the Clifford + T library, hence targeting fault-tolerant quantum computing. The algorithms are designed to minimize relevant cost functions, such as the number of qubits, the T-count, and the T-depth, while allowing the flexibility of exploring different solutions. We present novel resource estimation results for relevant cryptographic and arithmetic benchmarks. The achieved results show a significant reduction in both T-count and T-depth when compared with the state-of-the-art.Quantum Science & TechnologyPhysics, AppliedPhysics, Atomic, Molecular & ChemicalPhysics, Condensed MatterPhysicsalgorithmtext::journal::journal article::research article