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Azerbaijan Journal of High Performance Computing

A QUANTUM ALGORITHM BASED ON ENTANGLEMENT MEASURE FOR CLASSIFYING BOOLEAN MULTIVARIATE FUNCTION INTO NOVEL HIDDEN CLASSES REVISITED

Mohammed Zidan, Mahmoud Abdel‐Aty

Published Jun 30, 2021• 0 citations
Publisher

Abstract

The algorithm that solves a generalized form of the Deutsch- Jozsa problem was proposed. This algorithm uses the degree of entanglement computing model to classify an arbitrary Oracle Uf to one of the 2n classes. In this paper, we will analyze this algorithm based on the degree of entanglement.
DOI
10.32010/26166127.2021.4.1.48.52

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In this paper, we propose a novel algorithm that solves a generalized version of the Deutsch-Jozsa problem. The proposed algorithm has the potential to classify an oracle U F , that represents an unknown Boolean function on n Boolean variables, to one of 2 n different classes instead of only two classes which are constant and balanced classes in the case of Deutsch-Jozsa algorithm. The proposed algorithm is based on the use of entanglement measure to explore 2 n - 2 additional classes compared to the standard Deutsch-Jozsa algorithm. In addition, the comparison between the proposed quantum algorithm and the classical one is investigated in details. The comparison shows that the proposed algorithm is faster when the number of Boolean variables exceed 14 variables.
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Deutsch's algorithm for two qubits (one control qubit plus one auxiliary qubit) is extended to two ddd-dimensional quantum systems or qudits for the case in which ddd is equal to 2n2^n2n, n=1,2,...n=1,2,...n=1,2,... . This allows one to classify a certain oracle function by just one query, instead of the 2n−1+12^{n-1}+12n−1+1 queries required by classical means. The given algorithm for two qudits also solves efficiently the Bernstein-Vazirani problem. Entanglement does not occur at any step of the computation.
We present a generalized Deutsch-Jozsa (DJ) quantum algorithm that not only determines both the global type of an unknown Boolean function (constant or balanced) but also determines explicit output values of the function in a single oracle query. Unlike the original DJ algorithm, which identifies only whether a function is constant or balanced, our generalization retrieves actual function output values at the same time with using a Bell state as ancilla. This makes a richer function characterization with minimal queries to have practical quantum advantages, e.g. data classification, logistic regression, and quantum cryptography.