# Quantum algorithm for total least squares data fitting

## TL;DR

This paper introduces a quantum algorithm for total least squares data fitting, transforming the problem into finding a Hamiltonian's ground state, and achieves polynomial speedup over classical methods.

## Contribution

It presents a novel quantum algorithm for TLS data fitting by mapping it to Hamiltonian ground state search, enabling faster solutions.

## Key findings

- Achieves polynomial speedup over classical algorithms
- Transforms TLS problem into Hamiltonian ground state search
- Uses quantum simulation of resonant transitions

## Abstract

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.