Quantum Gradient Algorithm for General Polynomials

• URL: http://arxiv.org/abs/2004.11086v1
• Date: Thu, 23 Apr 2020 11:28:45 GMT
• Title: Quantum Gradient Algorithm for General Polynomials
• Authors: Keren Li, Pan Gao, Shijie Wei, Jiancun Gao, Guilu Long
• Abstract summary: Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. We propose a quantum gradient algorithm for optimizing numericals with the dressed amplitude. For the potential values in high-dimension optimizations, this quantum algorithm is supposed to facilitate gradient-optimizations.
• Score: 5.008814514502094
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the gradient. The time required to calculating the gradient of $d$-dimensional problems is at a level of $\mathcal{O}(poly(d))$, which could be boosted by quantum techniques, benefiting the high-dimensional data processing, especially the modern machine-learning engineering with the number of optimized parameters being in billions. Here, we propose a quantum gradient algorithm for optimizing general polynomials with the dressed amplitude encoding, aiming at solving fast-convergence polynomials problems within both time and memory consumption in $\mathcal{O}(poly (\log{d}))$. Furthermore, numerical simulations are carried out to inspect the performance of this protocol by considering the noises or perturbations from initialization, operation and truncation. For the potential values in high-dimension optimizations, this quantum gradient algorithm is supposed to facilitate the polynomial-optimizations, being a subroutine for future practical quantum computer.

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