2019/04/24 by Hefeng Wang, Hua Xiang
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Blind Source Separation Techniques #Computer science #Curve fitting #Hamiltonian (control theory) #Least-squares function approximation #Mathematical analysis #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Numerical Methods and Algorithms #Physics #Polynomial #Quantum #Quantum Computing Algorithms and Architecture #Quantum algorithm #Quantum error correction #Quantum mechanics #Quantum phase estimation algorithm #Speedup #Statistics #quant-ph
paper · pdf · doi:10.1016/j.physleta.2019.04.037
published as Physics Letters A, 383, 2235 (2019)
openalex publication_date 2019/04/24 · arxiv created 2019/06/04 · arxiv updated 2019/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the variables. In this work, the TLS problem is transformed to finding the ground state of a Hamiltonian matrix. We propose quantum algorithms for solving this problem based on quantum simulation of resonant transitions. Our algorithms can achieve at least polynomial speedup over the known classical algorithms.