Global Optimum Search in Quantum Deep Learning

TL;DR

This paper explores quantum circuit-based methods for global optimization in machine learning, proposing two approaches and analyzing their computational complexities to improve efficiency in finding global minima or maxima.

Contribution

Introduces two novel quantum circuit methods, the average approach and PSTC, for global optimization, with potential complexity improvements.

Findings

PSTC method has current cost $O(\sqrt{| heta|} N)$.

Potential to reduce PSTC cost to sublinear N.

Analysis suggests improved checking process can enhance efficiency.

Abstract

This paper aims to solve machine learning optimization problem by using quantum circuit. Two approaches, namely the average approach and the Partial Swap Test Cut-off method (PSTC) was proposed to search for the global minimum/maximum of two different objective functions. The current cost is $O(\sqrt{|\Theta|} N)$, but there is potential to improve PSTC further to $O(\sqrt{|\Theta|} \cdot sublinear \ N)$ by enhancing the checking process.