2024/07/31 by Murairi, Edison M., M. Sohaib Alam, Henry Lamm +6 · 3 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Molecular spectroscopy and chirality #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2408.00075
openalex publication_date 2024/07/31 · openalex created_date 2024/08/04 · openalex updated_date 2026/07/28
Quantum Fourier transformations are an essential component of many quantum algorithms, from prime factoring to quantum simulation. While the standard abelian QFT is well-studied, important variants corresponding to nonabelian groups of interest have seen less development. In particular, fast nonabelian Fourier transformations are important components for both quantum simulations of field theories as well as approaches to the nonabelian hidden subgroup problem. In this work, we present fast quantum Fourier transformations for a number of nonabelian groups of interest for high energy physics, \mathbbBT, \mathbbBO, Δ(27), Δ(54), and Σ(36×3). For each group, we derive explicit quantum circuits and estimate resource scaling for fault-tolerant implementations. Our work shows that the development of a fast Fourier transformation can substantively reduce simulation costs by up to three orders of magnitude for the finite groups that we have investigated.