The Quantum Version of Prediction for Binary Classification Problem by Ensemble Methods

In this work, we consider the performance of using a quantum algorithm to predict a result for a binary classification problem if a machine learning model is an ensemble from any simple classifiers. Such an approach is faster than classical prediction and uses quantum and classical computing, but it is based on a probabilistic algorithm. Let $N$ be a number of classifiers from an ensemble model and $O(T)$ be the running time of prediction on one classifier. In classical case, an ensemble model gets answers from each classifier and "averages" the result. The running time in classical case is $O\left( N \cdot T \right)$. We propose an algorithm which works in $O\left(\sqrt{N} \cdot T\right)$.

Quantum Algorithm for the Shortest Superstring Problem

In this paper, we consider the ``Shortest Superstring Problem''(SSP) or the ``Shortest Common Superstring Problem''(SCS). The problem is as follows. For a positive integer $n$, a sequence of n strings $S=(s^1,\dots,s^n)$ is given. We should construct the shortest string $t$ (we call it superstring) that contains each string from the given sequence as a substring. The problem is connected with the sequence assembly method for reconstructing a long DNA sequence from small fragments. We present a quantum algorithm with running time $O^*(1.728^n)$. Here $O^*$ notation does not consider polynomials of $n$ and the length of $t$.

The Quantum Version Of Classification Decision Tree Constructing Algorithm C5.0

In the paper, we focus on complexity of C5.0 algorithm for constructing decision tree classifier that is the models for the classification problem from machine learning. In classical case the decision tree is constructed in $O(hd(NM+N \log N))$ running time, where $M$ is a number of classes, $N$ is the size of a training data set, $d$ is a number of attributes of each element, $h$ is a tree height. Firstly, we improved the classical version, the running time of the new version is $O(h\cdot d\cdot N\log N)$. Secondly, we suggest a quantum version of this algorithm, which uses quantum subroutines like the amplitude amplification and the D{\"u}rr-H{\o}yer minimum search algorithms that are based on Grover's algorithm. The running time of the quantum algorithm is $O\big(h\cdot \sqrt{d}\log d \cdot N \log N\big)$ that is better than complexity of the classical algorithm.