scholarly journals Helping Students Learn Quantum Mechanics for Quantum Computing

2007 ◽  
Author(s):  
Chandralekha Singh
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing

QLB for Quantum Many-Body and Quantum Field Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Single Particle ◽  
Body Problem ◽  
Three Dimensions ◽  
Quantum Field ◽  
Many Body ◽  
Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

scholarly journals Using quantum computing to create efficient algorithms

2021 ◽  
Vol 2056 (1) ◽  
pp. 012059
Author(s):  
I N Balaba ◽  
G S Deryabina ◽  
I A Pinchuk ◽  
I V Sergeev ◽  
S B Zabelina
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Computational Model ◽  
Exponential Growth ◽  
Quantum Algorithms ◽  
Quantum Systems ◽  
Efficient Algorithms ◽  
Historical Overview ◽  
Computing Model ◽  
Computational Strategy

Abstract The article presents a historical overview of the development of the mathematical idea of a quantum computing model - a new computational strategy based on the postulates of quantum mechanics and having advantages over the traditional computational model based on the Turing machine; clarified the features of the operation of multi-qubit quantum systems, which ensure the creation of efficient algorithms; the principles of quantum computing are outlined and a number of efficient quantum algorithms are described that allow solving the problem of exponential growth of the complexity of certain problems.

Linear Algebra and the Dirac Notation

2006 ◽  
Author(s):  
Phillip Kaye ◽  
Raymond Laflamme ◽  
Michele Mosca
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Linear Algebra ◽  
Hilbert Spaces ◽  
Vector Spaces ◽  
Complex Vector ◽  
Dual Vector ◽  
Finite Dimensional ◽  
Basic Facts

We assume the reader has a strong background in elementary linear algebra. In this section we familiarize the reader with the algebraic notation used in quantum mechanics, remind the reader of some basic facts about complex vector spaces, and introduce some notions that might not have been covered in an elementary linear algebra course. The linear algebra notation used in quantum computing will likely be familiar to the student of physics, but may be alien to a student of mathematics or computer science. It is the Dirac notation, which was invented by Paul Dirac and which is used often in quantum mechanics. In mathematics and physics textbooks, vectors are often distinguished from scalars by writing an arrow over the identifying symbol: e.g a⃗. Sometimes boldface is used for this purpose: e.g. a. In the Dirac notation, the symbol identifying a vector is written inside a ‘ket’, and looks like |a⟩. We denote the dual vector for a (defined later) with a ‘bra’, written as ⟨a|. Then inner products will be written as ‘bra-kets’ (e.g. ⟨a|b⟩). We now carefully review the definitions of the main algebraic objects of interest, using the Dirac notation. The vector spaces we consider will be over the complex numbers, and are finite-dimensional, which significantly simplifies the mathematics we need. Such vector spaces are members of a class of vector spaces called Hilbert spaces. Nothing substantial is gained at this point by defining rigorously what a Hilbert space is, but virtually all the quantum computing literature refers to a finite-dimensional complex vector space by the name ‘Hilbert space’, and so we will follow this convention. We will use H to denote such a space. Since H is finite-dimensional, we can choose a basis and alternatively represent vectors (kets) in this basis as finite column vectors, and represent operators with finite matrices. As you see in Section 3, the Hilbert spaces of interest for quantum computing will typically have dimension 2n, for some positive integer n. This is because, as with classical information, we will construct larger state spaces by concatenating a string of smaller systems, usually of size two.

scholarly journals Qubit, Quantum Entanglement and all that: Quantum Computing Made Simple

2021 ◽  
Vol 7 (1) ◽  
pp. 1-9
Author(s):  
Zion Elani
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Popular Culture ◽  
Quantum Entanglement ◽  
High Tech ◽  
Quantum Computers ◽  
The World ◽  
Media Hype ◽  
The Impact ◽  
Fully Functioning

Quantum computing, a fancy word resting on equally fancy fundamentals in quantum mechanics, has become a media hype, a mainstream topic in popular culture and an eye candy for high-tech company researchers and investors alike. Quantum computing has the power to provide faster, more efficient, secure and accurate computing solutions for emerging future innovations. Governments the world over, in collaboration with high-tech companies, pour in billions of dollars for the advancement of computing solutions quantum-based and for the development of fully functioning quantum computers that may one day aid in or even replace classical computers. Despite much hype and publicity, most people do not understand what quantum computing is, nor do they comprehend the significance of the developments required in this field, and the impact it may have on the future. Through these lecture notes, we embark on a pedagogic journey of understanding quantum computing, gradually revealing the concepts that form its basis, later diving in a vast pool of future possibilities that lie ahead, concluding with understanding and acknowledging some major hindrance and speed breaking bumpers in their path.

scholarly journals Event-Based Quantum Mechanics: A Context for the Emergence of Classical Information

2019 ◽  
Author(s):  
Ignazio Licata ◽  
Leonardo Chiatti
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Time Scales ◽  
Quantum Jumps ◽  
Classical Information ◽  
Primary Element ◽  
Informational Constraint ◽  
Event Based ◽  
Physical Quantities

This paper explores an event-based version of quantum mechanics which differs from the commonly accepted one, even though the usual elements of quantum formalism, e.g., the Hilbert space, are maintained. This version introduces as primary element the occurrence of micro-events induced by usual physical (mechanical, electromagnetic and so on) interactions. These micro-events correspond to state reductions and are identified with quantum jumps, already introduced by Bohr in his atomic model and experimentally well established today. Macroscopic bodies are defined as clusters of jumps; the emergence of classicality thus becomes understandable and time honoured paradoxes can be solved. In particular, we discuss the cat paradox in this context. Quantum jumps are described as temporal localizations of physical quantities; if the information associated with these localizations has to be finite, two time scales spontaneously appear: an upper cosmological scale and a lower scale of elementary "particles''. This allows the interpretation of the Bekenstein limit like a particular informational constraint on the manifestation of a micro-event in the cosmos it belongs. The topic appears relevant in relation to recent discussions on possible spatiotemporal constraints on quantum computing.

scholarly journals Machine Learning: A Quantum Perspective

2021 ◽  
Author(s):  
Aishwarya Jhanwar ◽  
Manisha J. Nene
Keyword(s):  
Machine Learning ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Learning Algorithms ◽  
Machine Learning Algorithms ◽  
Quantum Computers ◽  
Learning Tasks ◽  
Current Scenario ◽  
Chip Fabrication ◽  
Classical Computing

Recently, increased availability of the data has led to advances in the field of machine learning. Despite of the growth in the domain of machine learning, the proximity to the physical limits of chip fabrication in classical computing is motivating researchers to explore the properties of quantum computing. Since quantum computers leverages the properties of quantum mechanics, it carries the ability to surpass classical computers in machine learning tasks. The study in this paper contributes in enabling researchers to understand how quantum computers can bring a paradigm shift in the field of machine learning. This paper addresses the concepts of quantum computing which influences machine learning in a quantum world. It also states the speedup observed in different machine learning algorithms when executed on quantum computers. The paper towards the end advocates the use of quantum application software and throw light on the existing challenges faced by quantum computers in the current scenario.

scholarly journals A Quantum Future: Preparing Canada for the Potential Impacts of Quantum Computing

2021 ◽  
Author(s):  
Sahar Shoja
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Computation ◽  
Barriers To Entry ◽  
Complex Tasks ◽  
Global Leader ◽  
Future Challenges ◽  
Potential Impact ◽  
The Way

Quantum computation has the potential to transform the way various Canadian industries do business. Unlike classical computers which use bits, computers built using principles of quantum mechanics use qubits, which allows them to perform several complex tasks simultaneously and at a exponentially faster speed. This research will analyze the potential impact of quantum computing on Canada's cybersecurity and workforce. It will also highlight barriers to entry for this burgeoning technology and provide recommendations that address current and future challenges. It is proposed that if Canada embraces this technology's opportunities and addresses its challenges, it can continue to be a global leader in the eld of quantum computing.

Quantum Lattice Boltzmann (QLB)

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Lattice Boltzmann ◽  
Quantum Physics ◽  
Newtonian Mechanics ◽  
Quantum Lattice ◽  
Recent Developments

The Lattice Boltzmann concepts and applications described so far refer to classical, i.e., non-quantum physics. However, the LB formalism is not restricted to classical Newtonian mechanics and indeed an LB formulation of quantum mechanics, going by the name of quantum LB (QLB) has been in existence for more than two decades. Even though it would far-fetched to say that QLB represents a mainstream, in the recent years it has captured some revived interest, mostly on account of recent developments in quantum-computing research. This chapter provides an account of the QLB formulation: stay tuned, LBE goes quantum!

Quantum

2017 ◽  
Author(s):  
Lance Fortnow
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Cryptography ◽  
Nobel Prize ◽  
Quantum Computers ◽  
Physical Systems ◽  
Medium Scale ◽  
Computer Scientists ◽  
Working Together ◽  
Richard Feynman

This chapter examines the power of quantum computing, as well as the related concepts of quantum cryptography and teleportation. In 1982, the Nobel prize-winning physicist Richard Feynman noticed there was no simple way of simulating quantum physical systems using digital computers. He turned this problem into an opportunity—perhaps a computational device based on quantum mechanics could solve problems more efficiently than more traditional computers. In the decades that followed, computer scientists and physicists, often working together, showed in theory that quantum computers can solve certain problems, such as factoring numbers, much faster. Whether one can actually build large or even medium-scale working quantum computers and determine exactly what these computers can or cannot do still remain significant challenges.

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