  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.

Quantum Physics