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Journal of computing sciences in colleges

An algebraic approach for quantum computation

TranQuoc-Nam, DanielJennifer, AndreevValentin

Published Oct 1, 2006• 0 citations
Publisher

Abstract

Quantum computation is one of the very promising new fields of the new millennium for basic research in theoretical computer science and computational mathematics. Quantum computers have stimulated...
DOI
10.5555/1181811.1181837

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Quantum computation is one of the very promising new fields of the new millennium for basic research in theoretical computer science and computational mathematics. Quantum computers have stimulated great interests due to their promise of being able to solve problems considered infeasible on current computers. From a computer scientist's and mathematician's point of view, the growth in the capacities of the underlying hardware is vital since an inefficient algorithm can solve the problem with the faster new hardware. For decades, this attitude was irrelevant but the deadline to change it is near. That is why quantum computation has led to rapid developments in physics, mathematics and computer science.This tutorial paper summarizes our year long series of multidisciplinary seminars on the topics of using computational algebra in quantum computation for finding new theoretical models for the upcoming generation of computers together with finding the models' computational abilities.
Quantum computing represents one of the most profound technological and intellectual advances of the twenty-first century. Rooted in the principles of quantum mechanics and enriched by developments in computer science, mathematics, and engineering, quantum computing offers fundamentally new ways of processing information. By exploiting phenomena such as superposition, entanglement, and quantum interference, quantum computers promise to solve certain classes of problems that remain intractable for even the most powerful classical machines.
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction to some of the ideas in quantum computing. The paper begins by motivating the central ideas of quantum mechanics and quantum computation with simple toy models. From there we move on to a formal presentation of the small fraction of (finite dimensional) quantum mechanics that we will need for basic quantum computation. Central notions of quantum architecture (qubits and quantum gates) are described. The paper ends with a presentation of one of the simplest quantum algorithms: Deutsch's algorithm. Our presentation demands neither advanced mathematics nor advanced physics.
Modern technologies and innovations are making an impact on all areas of our lives. Among them, quantum computing stands out as one of the most advanced and promising fields. While traditional computers have certain limitations, quantum computing offers the ability to reach new heights. Quantum computers can solve complex problems quickly and efficiently. The ability to perform multiple calculations simultaneously using qubits is increasing the demand for quantum technologies. Today's students have the opportunity to become future specialists who will develop and manage these technologies. For students studying English, mathematics, computer science, and physics, learning quantum computing technologies will not be difficult and will further enhance and deepen their understanding of these subjects. This article discusses the basic concepts of quantum computing, the opportunities it offers students in education and research, and its impact on society.
Regarding the end of the 1900s, a small community of researchers in physics, computer science, mathematics and chemistry began to explore the fertile ground at the intersection of quantum mechanics with information theory, which led to a new and powerful paradigm of quantum computing.Quantum information processing promises to extend today's computing resources.Quantum computers, theoretically, could solve problems much more quickly than any classic computer.Intensive experimental efforts have been made to implement quantum computing since Shor and Grover developed their algorithms.In 1997, Nuclear Magnetic Resonance (NMR) emerged as one of the most promising experimental techniques for the implementation of quantum computing protocols.The isolation of nuclear spins and consequent long relaxation times, combined with the perfect dynamics implemented by radiofrequency pulses, led to important studies in the area.Therefore, nuclear spins are picked out as good candidates for quantum bits.In this scenario, quantum chemistry covers a vast field of quantum information science and can lead to advances in scientific research.