Sample-size-reduction of quantum states for the noisy linear problem

TL;DR

This paper introduces an $ ext{ extit{ε}}$-random technique to reduce quantum sample sizes in noisy linear problems, significantly improving efficiency in quantum machine learning applications.

Contribution

It presents a novel randomization method that decreases quantum sample size to linearithmic order, enhancing the efficiency of solving noisy linear problems with quantum algorithms.

Findings

Quantum sample size reduced to linearithmic order.

Shorter run-time for noisy linear problem.

Improved efficiency in quantum machine learning.

Abstract

Quantum supremacy poses that a realistic quantum computer can perform a calculation that classical computers cannot in any reasonable amount of time. It has become a topic of significant research interest since the birth of the field, and it is intrinsically based on the efficient construction of quantum algorithms. It has been shown that there exists an expeditious way to solve the noisy linear (or learning with errors) problems in quantum machine learning theory via a well-posed quantum sampling over pure quantum states. In this paper, we propose an advanced method to reduce the sample size in the noisy linear structure, through a technique of randomizing quantum states, namely, $\varepsilon$-random technique. Particularly, we show that it is possible to reduce a quantum sample size in a quantum random access memory (QRAM) to the linearithmic order, in terms of the dimensions of the input-data. Thus, we achieve a shorter run-time for the noisy linear problem.