Learning Clifford-structured quantum unitaries and Hamiltonians

Researchers have made a breakthrough in learning algorithms for quantum unitaries and Hamiltonians with concise Clifford decompositions, even when they are dense in the Pauli basis. This development enables the learning of $n$-qubit quantum unitaries $U$ and Hamiltonians $H$ using query access to $U$ or the unitary evolution of $H$. The approach focuses on Clifford-structured quantum unitaries and Hamiltonians, which can be represented efficiently using Clifford gates. This is significant because many quantum algorithms rely on such unitaries and Hamiltonians, and learning them efficiently can lead to advancements in quantum computing and cryptography¹. The ability to learn these structures can also inform the development of new quantum algorithms and improve our understanding of quantum systems. So what matters to practitioners is that this breakthrough can potentially accelerate the development of quantum computing applications, ultimately rewriting assumptions about computation and cryptography.