  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.
