Quantum algorithm for data fitting.

MIT - Research Laboratory for Electronics and Department of Mechanical Engineering, Cambridge, MA 02139, USAWe provide a new quantum algorithm that efficiently determines the quality of a least-squaresfit over an exponentially large data set by building upon an algorithm for solving systems of linearequations efficiently (Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)). In many cases, ouralgorithm can also efficiently find a concise function that approximates the data to be fitted andbound the approximation error. In cases where the input data is a pure quantum state, the algorithmcan be used to provide an efficient parametric estimation of the quantum state and therefore can beapplied as an alternative to full quantum state tomography given a fault tolerant quantum computer.