Quantum computing unveiling the Performance of the HHL algorithm Using quantum correlations

Abstract

Quantum computing is becoming progressively vital for solving complex problems with its newlinepotential to revolutionize computational efficiency that classical computers struggle with. newlineQuantum Harrow-Hassidim-Lloyd (HHL) algorithm stands out as a pivotal algorithm designed for newlinesolving systems of linear equations exponentially faster than classical methods. newlinePresent study delves deep into the literature of implementation of the HHL algorithm and newlineperformance improvement. Research study investigated for first time the role of quantum newlinecorrelations, particularly focusing on entanglement as a resource to enhance computational newlineperformance of the HHL algorithm. newlineQuantum correlations encompass various types of non-classical relationships between quantum newlinesystems, each playing a crucial role in the development of quantum technologies. Entanglement is newlinethe most well-known and powerful form, where the state of one particle is intrinsically linked to newlinethe state of another, regardless of the distance between them. This correlation is essential for newlinequantum algorithms, quantum teleportation, and cryptography. Another significant type is newlineQuantum Discord, which captures non-classical correlations even when entanglement is absent. It newlinehighlights that quantum correlations can exist in mixed states, offering potential in areas where newlineentanglement is not available. In this work, the convex combination of Bell states is used to newlinegenerate the Bell diagonal states (BDS) and explored the study of quantum correlations such as newlineentanglement, discord, and state of separability. The three dimensional visual approach is used to newlineenhance the deeper understanding of behaviour of each of these correlations in BDS, when passed newlinethrough the different channels. Moreover, the dynamical study of BDS, quantum channels and newlinequantum correlations explored accompanied by time using Dzyaloshinskii Moriya Hamiltonian newlineand identified the entanglement sudden death-birth zones. This research will definitely help to newlinereduce the noise, improve the performance of quantum algorithms