Linear extrapolation for the graph of function of single variable based on walks

TL;DR

This paper introduces a novel model for the graph of a single-variable function based on quantum walk measures and proposes a linear extrapolation method derived from this model.

Contribution

It develops a new model for function graphs using quantum walk measures and introduces a linear extrapolation technique based on this model.

Findings

Proposes a quantum walk-based measure for function graph modeling

Introduces a linear extrapolation method for the graph of a function

Connects discrete quantum walk measures with continuous-time and space models

Abstract

The quantum walk was introduced as a quantum counterpart of the random walk and has been intensively studied since around 2000. Its applications include topological insulators, radioactive waste reduction, and quantum search. The first author in 2019 defined a time-series model based on the measure of the ``discrete-time" and ``discrete-space" quantum walk in one dimension. Inspired by his model, this paper proposes a new model for the graph of a function of a single variable determined by the measure which comes from the weak limit measure of a ``continuous-time or discrete-time" and ``discrete-space" walk. The measure corresponds to a ``continuous-time" and ``continuous-space" walk in one dimension. Moreover, we also presents a method of a linear extrapolation for the graph by our model.