Quantum gradient descent and Newton’s method for constrained polynomial optimization
Name
Rebentrost_2019_New_J._Phys._21_073023.pdf
Description
Published version
Size
1.21 MB
Format
Adobe PDF
Checksum (MD5)
8e391a6098d3d7fb7d1a833940fe81c9
Author(s)
Rebentrost, Frank Patrick
Lloyd, Seth
Date Issued
July 2019
Journal
New journal of physics
Publisher
IOP Publishing
Citation
Rebentrost, Patrick et al. “Quantum gradient descent and Newton’s method for constrained polynomial optimization.” New journal of physics 21 (2019): 073023 © 2019 The Author(s)
Version
Final published version
Abstract
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into account curvature information and thereby often improves convergence. Here, we develop quantum versions of these iterative optimization algorithms and apply them to polynomial optimization with a unit norm constraint. In each step, multiple copies of the current candidate are used to improve the candidate using quantum phase estimation, an adapted quantum state exponentiation scheme, as well as quantum matrix multiplications and inversions. The required operations perform polylogarithmically in the dimension of the solution vector and exponentially in the number of iterations. Therefore, the quantum algorithm can be useful for high-dimensional problems where a small number of iterations is sufficient.
MIT Department
Massachusetts Institute of Technology. Research Laboratory of Electronics
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1088/1367-2630/AB2A9E
