Quantum Algorithm for Data Fitting
Abstract
We provide a new quantum algorithm that efficiently determines the quality of a leastsquares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)PRLTAO0031900710.1103/PhysRevLett.103.150502]. In many cases, our algorithm can also efficiently find a concise function that approximates the data to be fitted and bound the approximation error. In cases where the input data are pure quantum states, the algorithm can be used to provide an efficient parametric estimation of the quantum state and therefore can be applied as an alternative to full quantumstate tomography given a fault tolerant quantum computer.
 Publication:

Physical Review Letters
 Pub Date:
 August 2012
 DOI:
 10.1103/PhysRevLett.109.050505
 arXiv:
 arXiv:1204.5242
 Bibcode:
 2012PhRvL.109e0505W
 Keywords:

 03.67.Ac;
 02.60.Ed;
 42.50.Dv;
 Quantum algorithms protocols and simulations;
 Interpolation;
 curve fitting;
 Nonclassical states of the electromagnetic field including entangled photon states;
 quantum state engineering and measurements;
 Quantum Physics
 EPrint:
 6 pages, corrected version