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The total least squares~(TLS) method is widely used in data-fitting. Comparedwith the least squares fitting method, the TLS fitting takes into account notonly observation errors, but also errors from the measurement matrix of thevariables. In this work, the TLS problem is transformed to finding the groundstate of a Hamiltonian matrix. We propose quantum algorithms for solving thisproblem based on quantum simulation of resonant transitions. Our algorithms canachieve at least polynomial speedup over the known classical algorithms.

Quantum algorithm for total least squares data fitting